Physics · JEE Main, NEET, Olympiad (NSEP)

Rotational Motion

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195MCQ85Numerical100With diagram
Start with question 1 Revise Rotational Motion firstSee it move: Rotational dynamics and rolling
  1. 1A solid sphere and a thin uniform circular ring have identical mass MM and radius RR. The ratio of their moments of inertia about their respective central diameters is:JEE Main/MCQ/Medium
  2. 2The radius of gyration of a uniform solid sphere of radius RR about its central diameter is:NEET/MCQ/Medium
  3. 3A uniform solid cylinder of mass mm and radius RR rolls without slipping inside a concave parabolic track y=αx2y = \alpha x^2 about the vertex. The time period for small amplitude oscillations is:Olympiad (NSEP)/MCQ/Hard/With diagram
  4. 4A spinning symmetrical top of mass MM with moment of inertia IsI_s about its symmetry axis spins with high angular velocity Ω\Omega. The center of mass is at distance LL from pivot. Which of the following statements are CORRECT?Olympiad (NSEP)/Multi-correct/Hard
  5. 5A solid sphere (AA) of mass 5m5m and a spherical shell (BB) of mass mm, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of AA and BB, they start rolling without slipping with an acceleration of aAa_A and aBa_B, respectively. The ratio of aAa_A and aBa_B is __________.JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  6. 6A solid sphere of radius 44 cm and mass 55 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 12001200 rpm. It is brought to rest in 1010 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are _______ and _______ respectively.JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  7. 7An object of uniform density rolls up the curved path with the initial velocity v0v_0 as shown in the figure. If the maximum height attained by an object is 7v0210g\dfrac{7v_0^2}{10g} (gg = acceleration due to gravity), the object is a _______.
    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  8. 8A solid sphere of mass MM and radius RR is divided into two unequal parts. The smaller part having mass M/8M/8 is converted into a sphere of radius rr and the larger part is converted into a circular disc of thickness tt and radius 2R2R. If I1I_1 is moment of inertia of a sphere having radius rr about an axis through its centre and I2I_2 is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia I2/I1=I_2/I_1 = _____.JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  9. 9Moment of inertia about an axis ABAB for a rod of mass 4040 kg and length 33 m is same as that of a solid sphere of mass of 1010 kg and radius RR about an axis parallel to ABAB axis with separation of 33 m as shown in figure below. The value of RR is given as α2\sqrt{\dfrac{\alpha}{2}}. The value of α\alpha is _______.
    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies/With diagram
  10. 10A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is n cm\sqrt{n} \mathrm{~cm}. The value of nn isJEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  11. 11A uniform solid cylinder of length LL and radius RR has moment of inertia about its axis equal to I1I_{1}. A small co-centric cylinder of length L/2L / 2 and radius R/3R / 3 carved from this cylinder has moment of inertia about its axis equals to I2I_{2}. The ratio I1/I2I_{1} / I_{2} is ____\_\_\_\_.JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  12. 12Suppose there is a uniform circular disc of mass M kgM \mathrm{~kg} and radius r mr \mathrm{~m} shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis AA of the disc is given by x256Mr2\frac{x}{256} M r^{2}. The value of xx is ____\_\_\_\_.
    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies/With diagram
  13. 13The moment of inertia of a square loop made of four uniform solid cylinders, each having radius RR and length L(R<L)L(\mathrm{R}\lt \mathrm{L}) about an axis passing through the mid points of opposite sides, is (Take the mass of the entire loop as MM) :JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  14. 14Two masses mm and 2 m are connected by a light string going over a pulley (disc) of mass 30 m with radius r=0.1 mr=0.1 \mathrm{~m}. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2 m mass is released from rest and its speed when it has descended through a height of 3.6 m is ____\_\_\_\_ m/s\mathrm{m} / \mathrm{s}. (Assume string does not slip and g=10 m/s2\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2})JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  15. 15A circular disc has radius R1R_{1} and thickness T1T_{1}. Another circular disc made of the same material has radius R2R_{2} and thickness T2T_{2}. If the moment of inertia of both discs are same and R1R2=2\frac{R_{1}}{R_{2}}=2 then T1T2=1α\frac{T_{1}}{T_{2}}=\frac{1}{\alpha}. The value of α\alpha is ____\_\_\_\_.JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  16. 16A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is ____\_\_\_\_ kg.m2\mathrm{kg}. \mathrm{m}^{2}.JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  17. 17The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of MM. Two blocks of mass of MM and mm are attached to two ends of a light string passing over the pulley, which is hinged to rotate freely in vertical plane about its center. The magnitudes of the acceleration experienced by the blocks is ____\_\_\_\_ (assume no slipping of string on pulley).
    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  18. 18Two identical thin rods of mass M kgM \mathrm{~kg} and length L mL \mathrm{~m} are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point PP and perpendicular to the plane of the rods is x12ML2 kg m2\frac{x}{12} \mathrm{ML}^{2} \mathrm{~kg} \mathrm{~m}^{2}. The value of xx is ____\_\_\_\_.
    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies/With diagram
  19. 19A rod of linear mass density ' λ\lambda ' and length ' LL ' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is :JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  20. 20M and R be the mass and radius of a disc. A small disc of radius R/3R / 3 is removed from the bigger disc as shown in figure. The moment of inertia of remaining part of bigger disc about an axis AB passing through the centre O and perpendicular to the plane of disc is 4xMR2\frac{4}{x} M R^2. The value of xx is ________.
    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies/With diagram
  21. 21A,B\mathrm{A}, \mathrm{B} and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure.

    The moment of inertia of the given system about     PQP Q is X15I\frac{X}{15} I, where II is the moment of inertia of the disc about its diameter. The value of x is _______.    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies/With diagram
  22. 22The moment of inertia of a circular ring of mass MM and diameter r about a tangential axis lying in the plane of the ring is :JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  23. 23Moment of inertia of a rod of mass ' M ' and length 'L' about an axis passing through its center and normal to its length is ' α\alpha '. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is :JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  24. 24The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is nn times higher than the moment of inertia of the given ring. Here, n=\mathrm{n}=_________
    Consider all the bodies have equal masses.    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  25. 25Two iron solid discs of negligible thickness have radii R1R_1 and R2R_2 and moment of intertia I1I_1 and I2I_2, respectively. For R2=2R1R_2=2 R_1, the ratio of I1I_1 and I2I_2 would be 1/x1 / x, where x=\mathrm{x}= ________ -JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  26. 26A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be t1t_1 and t2t_2, respectively, thenJEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  27. 27A uniform circular disc of radius ' R ' and mass ' M ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R/2\mathrm{R} / 2 is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.

    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  28. 28Three balls of masses 2 kg,4 kg2 \mathrm{~kg}, 4 \mathrm{~kg} and 6 kg6 \mathrm{~kg} respectively are arranged at centre of the edges of an equilateral triangle of side 2 m2 \mathrm{~m}. The moment of intertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be _______ kgm2\mathrm{kg} \mathrm{m}^2.JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  29. 29Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB\mathrm{AB} as shown in figure is 8/x\sqrt{8 / x}. The value of xx is :
    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  30. 30Two identical spheres each of mass 2kg2kg and radius 50cm50cm are fixed at the ends of a light rod so that the separation between the centers is 150cm150cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is x20kgm2\dfrac{x}{20}kg{m}^{2}, where the value of xx isJEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  31. 31Four particles, each of mass 1kg1kg are placed at four corners of a square of side 2m2m. The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its vertex is ______kg{m}^{2}.JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  32. 32A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively (ksph:kcyl)\left({k}_{sph}:{k}_{cyl}\right) is 2:x2:\sqrt{x}. The value of xx is _______.JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  33. 33A solid sphere of mass 500g500g radius 5cm5cm is rotated about one of its diameter with angular speed of 10rads−110rad{s}^{-1}. If the moment of inertia of the sphere about its tangent is x×10−2x\times {10}^{-2} times its angular momentum about the diameter. Then the value of xx will beJEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  34. 34The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is1xMR2\dfrac{1}{x}{MR}^{2}, where RR is the radius and MM is the mass of the semicircular ring. The value of xx will be _______.JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  35. 35A ring and a solid sphere rotating about an axis passing through their centres have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is 2x\sqrt{\dfrac{2}{x}}. The value of xx is _____.JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  36. 36Two identical solid spheres each of mass 2kg2kg and radii 10cm10cmare fixed at the ends of a light rod. The separation between the centres of the spheres is 40cm.40cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is______\times {10}^{–3}kg{m}^{2}.JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  37. 37Moment of inertia of a disc of mass MM and radius 'RR' about any of its diameter is MR24\dfrac{M{R}^{2}}{4}. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, x2MR2\dfrac{x}{2}M{R}^{2}. The value of xx is ______.JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  38. 38Two discs of same mass and different radii are made of different materials such that their thicknesses are 1cm1cm and 0.5cm0.5cm respectively. The densities of materials are in the ratio 3:53:5. The moment of inertia of these discs respectively about their diameters will be in the ratio of x6\dfrac{x}{6}. The value of xx is ______.JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  39. 39If a solid sphere of mass 5kg5kg and a disc of mass 4kg4kg have the same radius, then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be x7\dfrac{x}{7}. The value of xx is ______.JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  40. 40ICM{I}_{CM} is moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. IAB{I}_{AB} is its moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance 23R\dfrac{2}{3}R from center, where R is the radius of the disc. The ratio of IAB{I}_{AB} and ICM{I}_{CM} is x:9x:9. The value of xx is ______.
    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies/With diagram
  41. 41A uniform solid cylinder with radius RR and length LL has moment of inertia I1{I}_{1}, about the axis of cylinder. A concentric solid cylinder of radius R′=R2{R}^{'}=\dfrac{R}{2} and length L′=L2{L}^{'}=\dfrac{L}{2} is carved out of the original cylinder. If I2{I}_{2} is the moment of inertia of the carved out portion of the cylinder then I1I2=\dfrac{{I}_{1}}{{I}_{2}}= __________.
    (Both     I1{I}_{1} and I2{I}_{2} are about the axis of the cylinder)    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  42. 42Solid sphere AA is rotating about an axis PQPQ. If the radius of the sphere is 5cm5cm, then its radius of gyration about PQPQ will be xcm\sqrt{x}cm. The value of xx is _____.
    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies/With diagram
  43. 43Four identical discs each of mass 'MM' and diameter 'aa' are arranged in a small plane as shown in figure. If the moment of inertia of the system about OO′O{O}^{'} is x4Ma2\dfrac{x}{4}M{a}^{2}. Then, the value of xx will be _____ .
    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies/With diagram
  44. 44The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be _____ m.m. Given, the length of the rod is 103m10\sqrt{3}m.JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  45. 45The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I1{I}_{1}. The same rod is bent into a ring and its moment of inertia about a diameter is I2{I}_{2}. If I1I2\dfrac{{I}_{1}}{{I}_{2}} is xπ23\dfrac{x{\pi }^{2}}{3}, then the value of xx will be ______.JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  46. 46Match List-I with List-II List-I List-II (A) Moment of inertia of solid sphere
    of radius     RR about any tangent. (I) 53MR2\dfrac{5}{3}{MR}^{2} (B) Moment of inertia of hollow sphere of radius
    (R)\left(R\right) about any tangent. (II) 75MR2\dfrac{7}{5}{MR}^{2} (C) Moment of inertia of circular ring of radius
    (R)\left(R\right) about its diameter. (III) 14MR2\dfrac{1}{4}{MR}^{2} (D) Moment of inertia of circular disc of radius
    (R)\left(R\right) about any diameter. (IV) 12MR2\dfrac{1}{2}{MR}^{2}    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  47. 47Moment of Inertia (M.I.) of four bodies having same mass MM and radius 2R2R are as follows
    I1={I}_{1}= M.I. of solid sphere about its diameter
    I2={I}_{2}= M.I. of solid cylinder about its axis
    I3={I}_{3}= M.I. of solid circular disc about its diameter
    I4={I}_{4}= M.I. of thin circular ring about its diameter
    If     2(I2+I3)+I4=xI12\left({I}_{2}+{I}_{3}\right)+{I}_{4}=x{I}_{1} then the value of xx will be _____ .    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  48. 48A system consists of two identical spheres each of mass 1.5kg1.5kg and radius 50cm50cm at the ends of a light rod. The distance between the centres of the two spheres is 5m.5m. What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint?JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  49. 49Moment of inertia of a square plate of side ll about the axis passing through one of the corner and perpendicular to the plane of square plate is given by:JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  50. 50The solid cylinder of length 80cm80cm and mass MM has a radius of 20cm.20cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis CDCD parallel to ABAB as shown in figure is 2.7kgm22.7kg{m}^{2}.
    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  51. 51Consider a badminton racket with length scales as shown in the figure.

    If the mass of the linear and circular portions of the badminton racket are same (    MM) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, r2\dfrac{r}{2} distance from the end AA of the handle will be ______Mr2M{r}^{2}.    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies/With diagram
  52. 52In the given figure, two wheels PP and QQ are connected by a belt BB. The radius of PP is three times that of QQ. In the case of the same rotational kinetic energy, the ratio of rotational inertias (I1I2)\left(\dfrac{{I}_{1}}{{I}_{2}}\right) will be x:1.x:1. The value of xx will be ______.
    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies/With diagram
  53. 53The figure shows two solid discs with radius RR and rr respectively. If mass per unit area is the same for both, what is the ratio of MIMI of bigger disc around axis ABAB (Which is ⊥\perp to the plane of the disc and passing through its centre) of MIMI of smaller disc around one of its diameters lying on its plane? Given MM is the mass of the larger disc.
    (    MIMI stands for a moment of inertia)
    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  54. 54List-II List-IIII (a)(a) MIMI of the rod (length L,L, Mass M,M, about an axis ⊥\perp to the rod passing through the midpoint) (i)(i) 8ML23\dfrac{8M{L}^{2}}{3} (b)(b) MIMI of the rod (length L,L, Mass 2M,2M, about an axis ⊥\perp to the rod passing through one of its end) (ii)(ii) ML23\dfrac{M{L}^{2}}{3} (c)(c) MIMI of the rod (length 2L,2L, Mass M,M, about an axis ⊥\perp to the rod passing through its midpoint) (iii)(iii) ML212\dfrac{M{L}^{2}}{12} (d)(d) MIMI of the rod (Length 2L,2L, Mass 2M,2M, about an axis ⊥\perp to the rod passing through one of its end) (iv)(iv) 2ML23\dfrac{2M{L}^{2}}{3} Choose the correct answer from the options given below:JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  55. 55A solid disc of radius 20cm20cm and mass 10kg10kg is rotating with an angular velocity of 600rpm600rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10s10s is _________π×10−1Nm\pi \times {10}^{-1}NmJEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  56. 56Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
    Assertion A: Moment of inertia of a circular disc of mass     MM and radius RR about X,YX,Y axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be Ix,Iy{I}_{x},{I}_{y} and Iz{I}_{z}, respectively. The respective radii of gyration about all the three axes will be the same.
    Reason R: A rigid body making rotational motion has fixed mass and shape. In the light of the above statements, choose the most appropriate answer from the options given below:    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  57. 57Consider a uniform wire of mass MM and length LL. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is :JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  58. 58A thin circular ring of mass MM and radius rr is rotating about its axis with an angular speed ω.\omega . Two particles having mass mm each are now attached at diametrically opposite points. The angular speed of the ring will become:JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  59. 59Four equal masses, mm each are placed at the corners of a square of length (l)\left(l\right) as shown in the figure. The moment of inertia of the system about an axis passing through AA and parallel to DBDB would be :
    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  60. 60A cord is wound round the circumference of wheel of radius rr, The axis of the wheel is horizontal and the moment of inertia about it is II. A weight mgmg is attached to the cord at the end. The weight falls from rest. After falling through a distance h,h, the square of angular velocity of wheel will beJEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  61. 61Four identical solid spheres each of mass mm and radius aa are placed with their centres on the four corners of a square of side bb. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  62. 62A uniform thin bar of mass 6kg6kg and length 2.42.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is ___________ ×10−1kgm2.\times {10}^{-1}kg{m}^{2}.JEE Main/Numerical/Medium/Moment of inertia of rigid bodies
  63. 63Moment of inertia (M.I.)\left(M.I.\right) of four bodies, having same mass and radius, are reported as;
    I1=M.I.{I}_{1}=M.I. of thin circular ring about its diameter,
    I2=M.I.{I}_{2}=M.I. of circular disc about an axis perpendicular to disc and going through the centre,
    I3=M.I.{I}_{3}=M.I. of solid cylinder about its axis and
    I4=M.I.{I}_{4}=M.I. of solid sphere about its diameter.
    Then:    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  64. 64The linear mass density of a thin rod ABAB of length LL varies from AA to BB as λ(x)=λ0(1+xL)\lambda \left(x\right)={\lambda }_{0}\left(1+\dfrac{x}{L}\right), where xx is the distance from AA. If MM is the mass of the rod then its moment of inertia about an axis passing through AA and perpendicular to the rod :JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  65. 65Shown in the figure is a hollow ice-cream cone (it is open at top). If its mass is MM, radius of its top is RR and height, HH, then its moment of inertia about its axis is
    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  66. 66
    For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through     OO (the centre of mass) and OO' (corner point) is:    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  67. 67Consider two uniform discs of the same thickness and different radii R1=R{R}_{1}=R and R2=αR{R}_{2}=\alpha R made of the same material. If the ratio of their moments of inertia I1{I}_{1} and I2{I}_{2}, respectively, about their axes is I1:I2=1:16{I}_{1}:{I}_{2}=1:16 then the value of α\alpha is :JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  68. 68ABCABC is a plane lamina of the shape of an equilateral triangle. D,ED,E are mid-points of AB,ACAB,AC and GG is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through GG and perpendicular to the plane ABCABC is I0{I}_{0}. If part ADEADE is removed, the moment of inertia of the remaining part about the same axis is NI016\dfrac{N{I}_{0}}{16} where NN is an integer. Value of NN is:
    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies/With diagram
  69. 69An massless equilateral triangle EFG of side 'a' (As shown in figure) has three particles of mass mm situated at its vertices. The moment of inertia of the system about the line EX perpendicular to EG in the plane of EFG is N20ma2\dfrac{N}{20}{ma}^{2} where NN is an integer. The value of NN is ___________ .
    JEE Main/Numerical/Medium/Moment of inertia of rigid bodies/With diagram
  70. 70Moment of inertia of a cylinder of mass m,m, length LL and radius RR about an axis passing through its centre and perpendicular to the axis of the cylinder is I=M(R24+L212).I=M\left(\dfrac{{R}^{2}}{4}+\dfrac{{L}^{2}}{12}\right). If such a cylinder is to be made for a given mass of a material, the ratio LR\dfrac{L}{R} for it to have minimum possible II is:JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  71. 71

    Three solid spheres each of mass     mm and diameter dd are stuck together such that the lines connecting the centres form an equilateral triangle of side of length dd . The ratio I0IA\dfrac{{I}_{0}}{{I}_{A}} of moment of inertia I0{I}_{0} of the system about an axis passing the centroid and about center of any of the spheres IA{I}_{A} and perpendicular to the plane of the triangle is:    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  72. 72Mass per unit area of a circular disc of radius a depends on the distance rr from its centre as σ(r)=A+Br\sigma \left(r\right)=A+Br . The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is:JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  73. 73The radius of gyration of a uniform rod of length l,l, about an axis passing through a point l4\dfrac{l}{4} away from the centre of the rod, and perpendicular to it, is:JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  74. 74A circular disc of radius bb has a hole of radius aa at its centre(see figure). If the mass per unit area of the disc varies as (σ0r)\left(\dfrac{{\sigma }_{0}}{r}\right) then, the radius of gyration of the disc about its axis passing through the center is
    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  75. 75A solid sphere of mass MM and radius RR is divided into two unequal parts. The first part has a mass of 7M8\dfrac{7M}{8} and is converted into uniform disc of radius 2R2R . The second part is converted into a uniform solid sphere. Let I1{I}_{1} be the moment of inertia of the disc about its axis and I2{I}_{2} be the moment of inertia of the new sphere about its axis. The ratio I1/I2{I}_{1}/{I}_{2} is given by:JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  76. 76A thin disc of mass MM and radius RR has mass per unit area σ(r)=kr2\sigma \left(r\right)=k{r}^{2} where rr is the distance from its centre. Its moment inertia about an axis going through its centre of mass and perpendicular to its plane is:JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  77. 77A thin circular plate of mass MM and radius RR has its density varying as ρ(r)=ρ0r\text{ρ}(r){\text{=ρ}}_{\text{0}}\text{r} with ρ0{\rho }_{0} as constant and rr is the distance from its centre. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is I=aMR2I=aM{R}^{2}. The value of the coefficient aa is:JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  78. 78The moment of inertial of a solid sphere, about an axis parallel to its diameter and at a distance of xx from it, is ′I(x)′.'I{\left(x\right)}^{'}. Which one of the graphs represents the variation of I(x)I(x) with xx correctly?JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  79. 79Let the moment of inertia of a hollow cylinder of length 30cm30cm (inner radius 10cm10cm and outer radius 20cm20cm ), about its axis be I\text{I} . The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I,\text{I}, is:JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  80. 80A circular disc D1D_{1} of mass MM and radius RR has two identical discs⁡D2\operatorname{discs} D_{2} and D3D_{3} of the same mass MM and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO', passing through the centre of D1D_{1}, as shown in the figure, will be

    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  81. 81An equilateral triangle ABC\mathrm{ABC} is cut from a thin solid sheet of wood. (See figure) D,E\mathrm{D}, \mathrm{E} and F\mathrm{F} are the mid-points of its sides as shown and G\mathrm{G} is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G\mathrm{G} and perpendicular to the plane of the triangle is I0\mathrm{I}_{0}. If the smaller triangle DEF\mathrm{DEF} is removed from ABC\mathrm{ABC}, the moment of inertia of the remaining figure about the same axis is II. Then

    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  82. 82Two identical spherical balls of mass MM and radius RR each are stuck on two ends of a rod of length 2R2R and mass MM(see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is

    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  83. 83A thin circular disk is in the xyxy plane as shown in the figure. The ratio of its moment of inertia about zz and z′z' axes will be:
    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  84. 84From a uniform circular disc of radius R and mass 9 M, a small disc of radius R3\dfrac{R}{3} is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is:

    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  85. 85Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is:
    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  86. 86A circular hole of radius R4\dfrac{R}{4} is made in a thin uniform disc having mass and radius RR, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point OO and perpendicular to the plane of the disc is-
    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  87. 87Moment of inertia of an equilateral triangular lamina ABCABC, about the axis passing through its centre OO and perpendicular to its plane is I0{I}_{0} as shown in the figure. A cavity DEFDEF is cut out from the lamina, where D,E,FD,E,F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is:

    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  88. 88The moment of inertia of a uniform cylinder of length ll and radius RR about its perpendicular bisector is I.I. What is the ratio l/Rl/R such that the moment of inertia is minimum?JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  89. 89Consider a thin uniform square sheet made of a rigid material. If its side is aa, mass m and moment of inertia II about one of its diagonals, then:JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  90. 90From a solid sphere of mass MM and radius RR, a cube of the maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is:JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  91. 91A thin bar of length L\mathrm{L} has a mass per unit length λ\lambda, that increases linearly with distance from one end. If its total mass is MM and its mass per unit length at the lighter end is λO\lambda_{\mathrm{O}}, then the distance of the centre of mass from the lighter end is:JEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  92. 92A circular hole of diameter R\mathrm{R} is cut from a disc of mass MM and radius RR; the circumference of the cut passes through the centre of the disc. The moment of inertia of the remaining portion of the disc about an axis perpendicular to the disc and passing through its centre isJEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  93. 93Consider a uniform square plate of side ' aa ' and mass ' mm '. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners isJEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  94. 94For the given uniform square lamina ABCD\mathrm{A B C D}, whose centre is O\mathrm{O},
    JEE Main/MCQ/Medium/Moment of inertia of rigid bodies/With diagram
  95. 95Four point masses, each of value m\mathrm{m}, are placed at the corners of a square ABCDA B C D of side ℓ\ell. The moment of inertia through AA and parallel to BDB D isJEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  96. 96The moment of inertia of a uniform semicircular disc of mass MM and radius rr about a line perpendicular to the plane of the disc through the centre isJEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  97. 97One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively IA\mathrm{I}_{\mathrm{A}} and IB\mathrm{I}_{\mathrm{B}} such thatJEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  98. 98A circular disc XX of radius RR is made from an iron plate of thickness tt, and another disc YY of radius 4R4 \mathrm{R} is made from an iron plate of thickness t4\frac{\mathrm{t}}{4}. Then the relation between the moment of inertia IX\mathrm{I}_{\mathrm{X}} and IY\mathrm{I}_{\mathrm{Y}} isJEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  99. 99Moment of inertia of a circular wire of mass M and radius R about its diameter isJEE Main/MCQ/Medium/Moment of inertia of rigid bodies
  100. 100Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest the heavier mass is observed to fall 81 cm in 9 s. The rotational inertia of the pulley is ____\_\_\_\_ kg⋅m2\mathrm{kg} \cdot \mathrm{m}^{2}. (g=9.8 m/s2)\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)JEE Main/MCQ/Medium/Torque
  101. 101A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water.
    (Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is     1gm/cm31 \mathrm{gm} / \mathrm{cm}^3.) The unknown mass is ________ kg.    JEE Main/Numerical/Medium/Torque
  102. 102Which of the following are correct expression for torque acting on a body?
    B.     τ⃗=ddt(r→×p→)\vec{\tau}=\frac{\mathrm{d}}{\mathrm{dt}}(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{p}})
    C.     τ⃗=r→×dpdt\vec{\tau}=\overrightarrow{\mathrm{r}} \times \frac{\mathrm{d} \mathrm{p}}{\mathrm{dt}}
    D.     τ⃗=Iα⃗\vec{\tau}=\mathrm{I} \vec{\alpha}
    E.     τ⃗=r→×F→\vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}
    (     r→=\overrightarrow{\mathrm{r}}= position vector; p→=\overrightarrow{\mathrm{p}}= linear momentum;
    L→=\overrightarrow{\mathrm{L}}= angular momentum; α⃗=\vec{\alpha}= angular acceleration;
    I=I= moment of inertia; F⃗=\vec{F}= force; t=t= time)
    Choose the correct answer from the options given below :    JEE Main/MCQ/Medium/Torque
  103. 103A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg , kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is
    JEE Main/MCQ/Medium/Torque/With diagram
  104. 104
    A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of     2 rad/s22 \mathrm{~rad} / \mathrm{s}^2. Moment of inertia of the wheel is _____ kgm2\mathrm{kg} \mathrm{m}^2.
    (Acceleration due to gravity     =10 m/s2=10 \mathrm{~m} / \mathrm{s}^2)    JEE Main/Numerical/Medium/Torque/With diagram
  105. 105A square Lamina OABC of length 10 cm is pivoted at 'O'. Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is :
    JEE Main/MCQ/Medium/Torque/With diagram
  106. 106The coordinates of a particle with respect to origin in a given reference frame is \((1,1,1)\) meters. If a force of \(\overrightarrow{\mathrm{F}}=\hat{i}-\hat{j}+\hat{k}\) acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is ______.JEE Main/Numerical/Medium/Torque
  107. 107The torque due to the force (2i^+j^+2k^)(2 \hat{i}+\hat{j}+2 \hat{k}) about the origin, acting on a particle whose position vector is (i^+j^+k^)(\hat{i}+\hat{j}+\hat{k}), would beJEE Main/MCQ/Medium/Torque
  108. 108A heavy iron bar, of weight WW is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle θ\theta with the horizontal. The weight experienced by the person is :JEE Main/MCQ/Medium/Torque
  109. 109A heavy iron bar of weight 12kg12kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle 60∘60^{\circ} with the horizontal, the normal force applied by the man on bar is:JEE Main/MCQ/Medium/Torque
  110. 110A force of −Pk^-P\hat{k} acts on the origin of the coordinate system. The torque about the point (2,−3)(2,-3) is P(ai^+bj^)P(a\hat{i}+b\hat{j}), The ratio of ab\dfrac{a}{b} is x2\dfrac{x}{2}. The value of xx isJEE Main/Numerical/Medium/Torque
  111. 111An object of mass 8kg8kg is hanging from one end of a uniform rod CDCD of mass 2kg2kg and length 1m1m pivoted at its end CC on a vertical wall as shown in figure. It is supported by a cable ABAB such that the system is in equilibrium. The tension in the cable is:
    (Take     g=10ms−2g=10m{s}^{-2})
    JEE Main/MCQ/Medium/Torque/With diagram
  112. 112The torque of a force 5i^+3j^−7k^5\hat{i}+3\hat{j}-7\hat{k} about the origin is τ\tau. If the force acts on a particle whose position vector is 2i^+2j^+k^2\hat{i}+2\hat{j}+\hat{k}, then the value of τ\tau will beJEE Main/MCQ/Medium/Torque
  113. 113A uniform disc with mass M=4kgM=4kg and radius R=10cmR=10cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m=2kgm=2kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is _____ NN.
    (Take     g=10ms−2g=10{ms}^{-2})
    JEE Main/Numerical/Medium/Torque/With diagram
  114. 114A 34m\sqrt{34}m long ladder weighing 10kg10kg leans on a frictionless wall. Its feet rest on the floor 3m3m away from the wall as shown in the figure. If Ff{F}_{f} and Fw{F}_{w} are the reaction forces of the floor and the wall, then ratio of FwFf\dfrac{{F}_{w}}{{F}_{f}} will be :
    (Use     g=10ms−2g=10m{s}^{-2}.)
    JEE Main/MCQ/Medium/Torque/With diagram
  115. 115If force F⃗=3i^+4j^−2k^\vec{F}=3\hat{i}+4\hat{j}-2\hat{k} acts on a particle having position vector 2i^+j^+2k^2\hat{i}+\hat{j}+2\hat{k} then, the torque about the origin will be:JEE Main/MCQ/Medium/Torque
  116. 116A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10g10g are put one on the top of the other at the 10.0cm10.0cm mark the scale is found to be balanced at 40.0cm40.0cm mark. The mass of the metre scale is found to be x×10−2kgx\times {10}^{-2}kg. The value of xx is _____ .JEE Main/Numerical/Medium/Torque
  117. 117A solid cylinder of mass mm is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is:

    [The coefficient of static friction,     μs{\mu }_{s}, is 0.40.4 ]    JEE Main/MCQ/Medium/Torque/With diagram
  118. 118A triangular plate is shown. A force F⃗=4i^−3j^\vec{F}=4\hat{i}-3\hat{j} is applied at point P.P. The torque at point PP with respect to point OO and QQ are:
    JEE Main/MCQ/Medium/Torque/With diagram
  119. 119A force F⃗=4i^+3j^+4k^\vec{F}=4\hat{i}+3\hat{j}+4\hat{k} is applied on an intersection point of x=2x=2 plane and xx-axis. The magnitude of torque of this force about a point (2,3,4)\left(2,3,4\right) is ________.
    (Round off to the Nearest Integer)    JEE Main/Numerical/Medium/Torque
  120. 120A force F⃗=(i^+2j^+3k^)N\vec{F}=(\hat{i}+2\hat{j}+3\hat{k})N acts at a point (4i^+3j^−k^)m(4\hat{i}+3\hat{j}-\hat{k})m. Then the magnitude of torque about the point (i^+2j^+k^)m(\hat{i}+2\hat{j}+\hat{k})m will be xN−m.\sqrt{x}N-m.The value of xx is..........JEE Main/Numerical/Medium/Torque
  121. 121
    A uniform rod of length '     ℓ′{\ell }^{'} is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed ω\omega the rod makes an angle θ\thetawith it (see figure). To find θ\theta equate the rate of change of angular momentum (direction going into the paper) mℓ212ω2sin⁡θ\dfrac{m{\ell }^{2}}{12}{\omega }^{2}\sin \theta about the centre of mass (CM) to the torque provided by the horizontal and vertical forces FH{F}_{H}and Fv{F}_{v} about the CM. The value of θ\theta is then such that:    JEE Main/MCQ/Medium/Torque/With diagram
  122. 122Shown in the figure is rigid and uniform one meter long rod ABAB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is off mass ′m′'m' and has another weight of mass 2m2m hung at a distance of 75cm75cm from AA. The tension in the string at AA is:

    JEE Main/MCQ/Medium/Torque/With diagram
  123. 123A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of θ\theta, where θ\theta is the angle by which it has rotated, is given as kθ2k{\theta }^{2}. If its moment of inertia is II then the angular acceleration of the disc is:JEE Main/MCQ/Medium/Torque
  124. 124The magnitude of torque on a particle of mass 1 kg1 \mathrm{~kg} is 2.5 Nm about the origin. If the force acting on it is 1 N,1 \mathrm{~N}, and the distance of the particle from the origin is 5 m,5 \mathrm{~m}, the angle between the force and the position vector is (in radians):JEE Main/MCQ/Medium/Torque
  125. 125A slab is subjected to two forces F1→\overrightarrow{\mathrm{F}_{1}} and F2→\overrightarrow{\mathrm{F}_{2}} of same

    magnitude     FF as shown in the figure. Force F2→\overrightarrow{\mathrm{F}_{2}} is in XY-

    plane while force     F1\mathrm{F}_{1} acts along zz -axis at the point

    (2i⃗+3j⃗)(2 \vec{i}+3 \vec{j}). The moment of these forces about point O\mathrm{O} will be:

    JEE Main/MCQ/Medium/Torque/With diagram
  126. 126To mop-clean a floor, a cleaning machine presses a circular mop of radius RR vertically down with a total force FF and rotates it with a constant angular speed about its axis. If the force FF is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is μ,\mu , the torque, applied by the machine on the mop is:JEE Main/MCQ/Medium/Torque
  127. 127An LL -shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB=BC,AB=BC, and the angle made by ABAB with downward vertical is θ,\theta , then:
    JEE Main/MCQ/Medium/Torque/With diagram
  128. 128Two masses mm and m2\dfrac{m}{2} are connected at the two ends of a massless rigid rod of length l.l. The rod is suspended by a thin wire of torsional constant kk at the centre of mass of the rod-mass system (see figure). Because of torsional constant k,k, the restoring torque is τ=kθ\tau =k\theta for angular displacement θ.\theta . If the rod is rotated by θ0{\theta }_{0} and released, the tension in it when it passes through its mean position will be:

    JEE Main/MCQ/Medium/Torque/With diagram
  129. 129A force of 40N40N acts on a point BB at the end of an L-shaped object as shown in the figure. The angle θ\theta that will produce the maximum moment of the force about point AA is given by:
    JEE Main/MCQ/Medium/Torque/With diagram
  130. 130A uniform rod ABAB is suspended from a point XX, at a variable distance xx from AA, as shown. To make the rod horizontal, a mass mm is suspended from its end AA. A set of (m,x)(m,x) value is recorded. The appropriate variables that give a straight line, when plotted, are:

    JEE Main/MCQ/Medium/Torque/With diagram
  131. 131A force of 40 N40 \mathrm{~N} acts on a point B\mathrm{B} at the end of an L-shaped object, as shown in the figure. The angle θ\theta that will produce maximum moment of the force about point A\mathrm{A} is given by:
    JEE Main/MCQ/Medium/Torque/With diagram
  132. 132A uniform rod⁡AB\operatorname{rod} A B is suspended from a point XX, at a variable distance from xx from AA, as shown. To make the rod horizontal, a mass mm is suspended from its end AA. A set of (m,x)(m, x) values is recorded. The appropriate variable that give a straight line, when plotted, are:
    JEE Main/MCQ/Medium/Torque/With diagram
  133. 133In a physical balance working on the principle of moments, when 5mg5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?JEE Main/MCQ/Medium/Torque
  134. 134A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to:


    JEE Main/MCQ/Medium/Torque/With diagram
  135. 135A uniform sphere of weight WW and radius 5 cm5 \mathrm{~cm} is being held by a string as shown in the figure. The tension in the string will be :
    JEE Main/MCQ/Medium/Torque/With diagram
  136. 136A pulley of radius 2 m2 \mathrm{~m} is rotated about its axis by a force F=(20t−5t2)\mathrm{F}=\left(20 \mathrm{t}-5 \mathrm{t}^2\right) Newton (where t\mathrm{t} is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation made by the pulley before its direction of motion if reversed, is :JEE Main/MCQ/Medium/Torque
  137. 137A force of −Fk^-F \hat{k} acts on OO, the origin of the coordinate system. The torque about the point (1,−1)(1,-1)JEE Main/MCQ/Medium/Torque
  138. 138Let F⃗\vec{F} be the force acting on a particle having position vector r⃗\vec{r} and T⃗\vec{T} be the torque of this force about the origin. ThenJEE Main/MCQ/Medium/Torque
  139. 139A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s2\text{ s} it rotates through an angle θ1\theta_1 and in the next 2 s2\text{ s} it rotates through an angle θ2\theta_2. The ratio θ2θ1\dfrac{\theta_2}{\theta_1} is _______.JEE Main/MCQ/Medium/Rotational kinematics
  140. 140A particle is rotating in a circular path and at any instant its motion can be described as θ=5t440−t33\theta = \dfrac{5t^4}{40} - \dfrac{t^3}{3}. The angular acceleration of the particle after 1010 seconds is _______ rad/s2^2.JEE Main/MCQ/Medium/Rotational kinematics
  141. 141A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is ____\_\_\_\_ J.(g=10 m/s2)\mathrm{J}.\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)JEE Main/Numerical/Medium/Rotational kinematics
  142. 142Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure. If the mass of each disc is 600 gm and applied torque between two discs is 43×10543 \times 10^{5} dyne. cm, the angular acceleration of the discs about the given axis ABA B is ____\_\_\_\_ rad/s2\mathrm{rad} / \mathrm{s}^{2}.
    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  143. 143A uniform rod of mass mm and length ll suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is ____\_\_\_\_. (g(g acceleration due to gravity)
    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  144. 144A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of 25πNm25 \pi \mathrm{Nm} for 40 s, the speed increases to 2100 rpm. The diameter of the disk is ________ m.JEE Main/Numerical/Medium/Rotational kinematics
  145. 145A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m , would be :
    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  146. 146A uniform solid cylinder of mass ' mm ' and radius ' rr ' rolls along an inclined rough plane of inclination 45∘45^{\circ}. If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will beJEE Main/MCQ/Medium/Rotational kinematics
  147. 147A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that θ(t)=5t2−8t\theta(t)=5 t^2-8 t, where θ(t)\theta(t) is the angular position of the rotating disc as a function of time tt.
    How much power is delivered by the applied torque, when     t=2 st=2 \mathrm{~s} ?    JEE Main/MCQ/Medium/Rotational kinematics
  148. 148A circular disc reaches from top to bottom of an inclined plane of length ll. When it slips down the plane, if takes t st \mathrm{~s}. When it rolls down the plane then it takes (α2)1/2t s\left(\frac{\alpha}{2}\right)^{1 / 2} t \mathrm{~s}, where α\alpha is _________JEE Main/Numerical/Medium/Rotational kinematics
  149. 149A string is wrapped around the rim of a wheel of moment of inertia 0.40kgm20.40 \mathrm{kgm}^2 and radius 10 cm10 \mathrm{~cm}. The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of 40 N40 \mathrm{~N}. The angular velocity of the wheel after 10 s10 \mathrm{~s} is xrad/sx \mathrm{rad} / \mathrm{s}, where xx is _______JEE Main/Numerical/Medium/Rotational kinematics
  150. 150
    A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  151. 151A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is x5\frac{x}{5}. The value of xx is _____ .JEE Main/Numerical/Medium/Rotational kinematics
  152. 152A ball of mass 0.5kg0.5kg is attached to a string of length 50cm50cm. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400N400N. The maximum possible value of angular velocity of the ball in rads−1rad{s}^{-1} is,:JEE Main/MCQ/Medium/Rotational kinematics
  153. 153A light rope is wound around a hollow cylinder of mass 5kg5kg and radius 70cm70cm. The rope is pulled with a force of 52.5N52.5N. The angular acceleration of the cylinder will be _____ rads−2rad{s}^{-2}.JEE Main/Numerical/Medium/Rotational kinematics
  154. 154For rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is x5\dfrac{x}{5}. The value of xx is _____.JEE Main/Numerical/Medium/Rotational kinematics
  155. 155A circular plate is rotating in horizontal plane, about an axis passing through its centre and perpendicular to the plate, with an angular velocity ω\omega. A person sits at the centre having two dumbbells in his hands. When he stretched out his hands, the moment of inertia of the system becomes triple. If EE be the initial Kinetic energy of the system, then final Kinetic energy will be Ex\dfrac{E}{x}. The value of xx isJEE Main/Numerical/Medium/Rotational kinematics
  156. 156A thin uniform rod of length 2m2m, cross sectional area AA and density dd is rotated about an axis passing through the centre and perpendicular to its length with angular velocity ω\omega. If value of ω\omega in terms of its rotational kinetic energy EE is αEAd\sqrt{\dfrac{\alpha E}{Ad}}, then the value of α\alpha is ______.JEE Main/Numerical/Medium/Rotational kinematics
  157. 157A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of 4ms−14m{s}^{-1}, is _____cmcm.
    (take     g=10ms−2g=10m{s}^{-2})
    JEE Main/Numerical/Medium/Rotational kinematics/With diagram
  158. 158A pulley of radius 1.5m1.5m is rotated about its axis by a force F=(12t−3t2)NF=\left(12t-3{t}^{2}\right)N applied tangentially (while tt is measured in seconds). If moment of inertia of the pulley about its axis of rotation is 4.5kgm24.5kg{m}^{2}, the number of rotations made by the pulley before its direction of motion is reversed, will be Kπ\dfrac{K}{\pi }. The value of KK is _____ .JEE Main/Numerical/Medium/Rotational kinematics
  159. 159A disc of mass 1kg1kg and radius RR is free of rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, its angular speed will be 4x3Rrads−14\sqrt{\dfrac{x}{3R}}rad{s}^{-1} where x=x= _____ .JEE Main/Numerical/Medium/Rotational kinematics
  160. 160A fly wheel is accelerated uniformly from rest and rotates through 5rad5rad in the first second. The angle rotated by the fly wheel in the next second, will be :JEE Main/MCQ/Medium/Rotational kinematics
  161. 161A huge circular arc of length 4.4ly4.4ly subtends an angle 4s4s at the centre of the circle. How long it would take for a body to complete 44 revolution if its speed is 8AU8AU per second?
    Given :     1ly=9.46×1015m1ly=9.46\times {10}^{15}m
    1AU=1.5×1011m1AU=1.5\times {10}^{11}m    JEE Main/MCQ/Medium/Rotational kinematics
  162. 162The centre of a wheel rolling on a plane surface moves with a speed v0.{v}_{0}. A particle on the rim of the wheel at the same level as the centre will be moving at a speed xv0.\sqrt{x}{v}_{0}. Then the value of xx is ..JEE Main/Numerical/Medium/Rotational kinematics
  163. 163A body rotating with an angular speed of 600rpm600rpm is uniformly accelerated to 1800rpm1800rpm in 10sec⁡.10\sec . The number of rotations made in the process isJEE Main/Numerical/Medium/Rotational kinematics
  164. 164A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 5050% of its translational kinetic energy. The body is:JEE Main/MCQ/Medium/Rotational kinematics
  165. 165The angular speed of truck wheel is increased from 900rpm900rpm to 2460rpm2460rpm in 2626 seconds. The number of revolutions by the truck engine during this time is ______.
    (Assuming the acceleration to be uniform).    JEE Main/Numerical/Medium/Rotational kinematics
  166. 166Consider a 20kg20kg uniform circular disk of radius 0.2m0.2m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force F=20NF=20N through a massless string wrapped around its periphery as shown in the figure.

    Suppose the disk makes     nn number of revolutions to attain an angular speed of 50rads−150rad{s}^{-1}. The value of nn, to the nearest integer, is _______ .
    [Given : In one complete revolution, the disk rotates by     6.28rad6.28rad]    JEE Main/Numerical/Medium/Rotational kinematics/With diagram
  167. 167A person of 80kg80kg mass is standing on the rim of a circular platform of mass 200kg200kg rotating about its axis at 55 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpmrpm ) of the platform when the person reaches its centre....JEE Main/Numerical/Medium/Rotational kinematics
  168. 168Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1kg−m20.1kg-{m}^{2} and 10rads−110\text{rad}{s}^{-1} respectively while those for the second one are 0.2kg−m20.2kg-{m}^{2}and 5rads−15rad{s}^{-1} respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is :JEE Main/MCQ/Medium/Rotational kinematics
  169. 169A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5cm5cm and the angular speed of rotation is ωrads−1\omega rad{s}^{-1}. The difference in the height, h(incm)h\left(incm\right) of liquid at the Centre of vessel and at the sides of the vessel will be :
    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  170. 170A uniformly thick wheel with moment of inertia II and radius RR is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses m1{m}_{1} and m2(m1>m2){m}_{2}\left({m}_{1}\gt {m}_{2}\right) are attached to the ends of the string. The system Is released from rest. The angular speed of the wheel when m1{m}_{1} descends by a distance hh is:

    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  171. 171One end of a straight uniform 1m1m long bar is pivoted on horizontal table. It is released from rest when it makes an angle 30o{30}^{o} from the horizontal (see figure). Its angular speed when it hits the table is given as nrads−1\sqrt{n}rad{s}^{-1} , where nn is an integer. The value of nn is ____________

    JEE Main/Numerical/Medium/Rotational kinematics/With diagram
  172. 172A uniform sphere of mass 500g500g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00cms−15.00cm{s}^{-1}. Its kinetic energy is:JEE Main/MCQ/Medium/Rotational kinematics
  173. 173A smooth wire of length 2πr2\pi r is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed ω\omega about the vertical diameter AB,AB, as shown in figure, the bead is at rest with respect to the circular ring at position PP as shown. Then the value of ω2{\omega }^{2} is equal to:
    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  174. 174A uniform rod of length ll is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x)T(x) at a distance xx from the axis, then which of the following graphs depicts it most closely?JEE Main/MCQ/Medium/Rotational kinematics
  175. 175A metal coin of mass 5g5g and radius 1cm1cm is fixed to a thin stick ABAB of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about ABAB at 2525 rotations per second in 5s5s , is close to:
    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  176. 176Moment of inertia of a body about a given axis is 1.5kgm2.1.5kg{m}^{2}. Initially the body is at rest. In order to produce a rotational kinetic energy of 1200J,1200J, the angular acceleration of 20rad/s220rad/{s}^{2} must be applied about the axis for a duration of:JEE Main/MCQ/Medium/Rotational kinematics
  177. 177A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5cm5cm and its rotational speed is 22 rotations per second, then the difference in the heights between the center and the sides, in cm,cm, will be:JEE Main/MCQ/Medium/Rotational kinematics
  178. 178A rigid massless rod of length 3l3l has two masses attached at each end as shown in the figure. The rod is pivoted at point PP on the horizontal axis. When released from the initial horizontal position, its instantaneous angular acceleration will be

    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  179. 179A rod of length 50cm50cm is pivoted at one end. It is raised such that it makes an angle of 30o{30}^{o} from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rads−1rad{s}^{-1} ) will be (g=10ms−2)\left(g=10m{s}^{-2}\right)

    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  180. 180A thin rod MN\mathrm{MN}, free to rotate in the vertical plane about the fixed end N\mathrm{N}, is held horizontal. When the end M\mathrm{M} is released the speed of this end, when the rod makes an angle α\alpha with the horizontal, will be proportional to: (see figure)
    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  181. 181A uniform disc of radius RR and mass MM is free to rotate only about its axis. A string is wrapped over its rim and a body of mass mm is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is:

    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  182. 182A slender uniform rod of mass MM and length ll is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle θ\theta with the vertical is:

    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  183. 183A mass mm is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?
    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  184. 184A body of mass ' mm ' is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is 1 cm1 \mathrm{~cm}. If the angular velocity is doubled, the elongation in the spring is 5 cm5 \mathrm{~cm}. The original length of the spring is :JEE Main/MCQ/Medium/Rotational kinematics
  185. 185A tennis ball (treated as hollow spherical shell) starting from O\mathrm{O} rolls down a hill. At point A\mathrm{A} the ball becomes air borne leaving at an angle of 30∘30^{\circ} with the horizontal. The ball strikes the ground at B\mathrm{B}. What is the value of the distance AB\mathrm{AB} ?
    (Moment of inertia of a spherical shell of mass     mm and radius RR about its diameter =23mR2=\frac{2}{3} m R^2 )
    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  186. 186A solid sphere having mass mm and radius rr rolls down an inclined plane. Then its kinetic energy isJEE Main/MCQ/Medium/Rotational kinematics
  187. 187For a particle in uniform circular motion the acceleration a⃗\vec{a} at a point P(R,θ)P(R, \theta) on the circle of radius R\mathrm{R} is (here θ\theta is measured from the xx-axis)JEE Main/MCQ/Medium/Rotational kinematics
  188. 188A point P\mathrm{P} moves in counter-clockwise direction on a circular path as shown in the figure. The movement of ' P\mathrm{P} ' is such that it sweeps out a length s=t3+5s=t^3+5, where ss is in metres and tt is in seconds. The radius of the path is 20 m20 \mathrm{~m}. The acceleration of ' P\mathrm{P} ' when t=2 st=2 \mathrm{~s} is nearly
    JEE Main/MCQ/Medium/Rotational kinematics/With diagram
  189. 189A thin uniform rod of length ℓ\ell and mass mm is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ω\omega. Its centre of mass rises to a maximum height ofJEE Main/MCQ/Medium/Rotational kinematics
  190. 190A solid sphere, a hallow sphere and a ring are released from top of an inclined plane (frictionless)
    so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)    JEE Main/MCQ/Medium/Rotational kinematics
  191. 191When the position vector r⃗=xi^+yj^+zk^\vec{r}=x \hat{i}+y \hat{j}+z \hat{k} changes sign as −r⃗-\vec{r}, which one of the following vector will not flip under sign change ?JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  192. 192A thin uniform rod (X)(X) of mass MM and length LL is pivoted at a height (L3)\left(\frac{L}{3}\right) as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top, is ____\_\_\_\_. (g=\mathrm{g}= gravitational acceleration)
    JEE Main/MCQ/Medium/Angular momentum and Angular impulse/With diagram
  193. 193Two small balls with masses mm and 2 m are attached to both ends of a rigid rod of length dd and negligible mass. If angular momentum of this system is LL about an axis (AA) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about AA is :JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  194. 194Two cars AA and BB each of mass 103 kg10^{3} \mathrm{~kg} are moving on parallel tracks separated by a distance of 10 m, in same direction with speeds 72 km/h72 \mathrm{~km} / \mathrm{h} and 36 km/h36 \mathrm{~km} / \mathrm{h}. The magnitude of angular momentum of car⁡A\operatorname{car} A with respect to car⁡B\operatorname{car} B is ____\_\_\_\_ J.s.JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  195. 195A solid sphere with uniform density and radius R is rotating initially with constant angular velocity (ω1)\left(\omega_1\right) about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become R/2R / 2 is xω1x \omega_1. The value of xx is ________JEE Main/Numerical/Medium/Angular momentum and Angular impulse
  196. 196If L→\overrightarrow{\mathrm{L}} and P→\overrightarrow{\mathrm{P}} represent the angular momentum and linear momentum respectively of a particle of mass ' m ' having position vector r→=a(i^cos⁡ωt+j^sin⁡ωt)\overrightarrow{\mathrm{r}}=\mathrm{a}(\hat{\mathrm{i}} \cos \omega \mathrm{t}+\hat{\mathrm{j}} \sin \omega \mathrm{t}). The direction of force isJEE Main/MCQ/Medium/Angular momentum and Angular impulse
  197. 197

    Three equal masses     mm are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At t=0t=0, they are given an initial velocity V⃗A=V0AC→,V⃗B=V0BA→\vec{V}_A=V_0 \overrightarrow{A C}, \vec{V}_B=V_0 \overrightarrow{B A} and V⃗C=V0CB→\vec{V}_C=V_0 \overrightarrow{C B}. Here, AC→,CB→\overrightarrow{A C}, \overrightarrow{C B} and BA→\overrightarrow{B A} are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :    JEE Main/MCQ/Medium/Angular momentum and Angular impulse/With diagram
  198. 198An object of mass ' m ' is projected from origin in a vertical xyx y plane at an angle 45∘45^{\circ} with the x axis with an initial velocity v0\mathrm{v}_0. The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [ g is acceleration due to gravity]JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  199. 199The position vectors of two 1 kg particles, (A) and (B), are given by
    r→A=(α1t2i^+α2tj^+α3tk^)m\overrightarrow{\mathrm{r}}_{\mathrm{A}}=\left(\alpha_1 \mathrm{t}^2 \hat{i}+\alpha_2 \mathrm{t} \hat{j}+\alpha_3 \mathrm{t} \hat{k}\right) \mathrm{m} and r→B=(β1ti^+β2t2j^+β3tk^)m\overrightarrow{\mathrm{r}}_{\mathrm{B}}=\left(\beta_1 \mathrm{t} \hat{i}+\beta_2 \mathrm{t}^2 \hat{j}+\beta_3 \mathrm{t} \hat{k}\right) \mathrm{m}, respectively; (α1=1 m/s2,α2=3nm/s,α3=2 m/s,β1=2 m/s,β2=−1 m/s2,β3=4pm/s)\left(\alpha_1=1 \mathrm{~m} / \mathrm{s}^2, \alpha_2=3 \mathrm{n} \mathrm{m} / \mathrm{s}, \alpha_3=2 \mathrm{~m} / \mathrm{s}, \beta_1=2 \mathrm{~m} / \mathrm{s}, \beta_2=-1 \mathrm{~m} / \mathrm{s}^2, \beta_3=4 \mathrm{pm} / \mathrm{s}\right), where t is time, n and p are constants. At t=1 s,∣VA→∣=∣V⃗B∣t=1 \mathrm{~s},\left|\overrightarrow{V_A}\right|=\left|\vec{V}_B\right| and velocities V⃗A\vec{V}_A and V⃗B\vec{V}_B of the particles are orthogonal to each other. At t=1 st=1 \mathrm{~s}, the magnitude of angular momentum of particle (A) with respect to the position of particle (B) is Lkgm2 s−1\sqrt{\mathrm{L}} \mathrm{kgm}^2 \mathrm{~s}^{-1}. The value of L is _______ .    JEE Main/Numerical/Medium/Angular momentum and Angular impulse
  200. 200A thin circular disc of mass MM and radius RR is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity ω\omega. If another disc of same dimensions but of mass M/2\mathrm{M} / 2 is placed gently on the first disc co-axially, then the new angular velocity of the system is :JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  201. 201If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be ______ hours 30 minutes.JEE Main/Numerical/Medium/Angular momentum and Angular impulse
  202. 202A body of mass mm is projected with a speed uu making an angle of 45o{45}^{o} with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as 2mu3Xg\dfrac{\sqrt{2}m{u}^{3}}{Xg}. The value of XX is_______.JEE Main/Numerical/Medium/Angular momentum and Angular impulse
  203. 203Consider a disc of mass 5kg5kg, radius 2m2m, rotating with angular velocity of 10rads−110rad{s}^{-1} about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is _________JJ.JEE Main/Numerical/Medium/Angular momentum and Angular impulse/With diagram
  204. 204A body of mass 5kg5kg moving with a uniform speed 32ms−13\sqrt{2}m{s}^{-1} in X−YX-Y plane along the line y=x+4y=x+4. The angular momentum of the particle about the origin will be _______kgm2s−1kg{m}^{2}{s}^{-1}.JEE Main/Numerical/Medium/Angular momentum and Angular impulse
  205. 205A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is π:22\pi :22 then, the value of its angular speed will be_________rad{s}^{-1}.JEE Main/Numerical/Medium/Angular momentum and Angular impulse
  206. 206A spherical shell of 1kg1kg mass and radius RR is rolling with angular speed ω\omega on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin OO is a3R2ω\dfrac{a}{3}{R}^{2}\omega. The value of aa will be
    JEE Main/MCQ/Medium/Angular momentum and Angular impulse/With diagram
  207. 207The position vector of 1kg1kg object is r⃗=(3i^−j^)m\vec{r}=\left(3\hat{i}-\hat{j}\right)m and its velocity v⃗=(3j^+k^)ms−1\vec{v}=\left(3\hat{j}+\hat{k}\right)m{s}^{-1}. The magnitude of its angular momentum is xNms\sqrt{x}Nms, where xx isJEE Main/Numerical/Medium/Angular momentum and Angular impulse
  208. 208A thin circular ring of mass MM and radius RR is rotating with a constant angular velocity 2rads−12rad{s}^{-1} in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass mm be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rads−1rad{s}^{-1}).JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  209. 209Angular momentum of a single particle moving with constant speed along circular path :JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  210. 210Two discs have moments of intertia I1{I}_{1} and I2{I}_{2} about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, ω1{\omega }_{1} and ω2{\omega }_{2} respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by:JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  211. 211A particle of mass mm is moving in time tt on a trajectory given by,
    r⃗=10αt2i^+5β(t−5)j^\vec{r}=10\alpha {t}^{2}\hat{i}+5\beta \left(t-5\right)\hat{j}
    where     α\alpha and β\beta are dimensional constants.
    The angular momentum of the particle becomes the same as it was for     t=0t=0 at time t=t=_____ seconds.    JEE Main/Numerical/Medium/Angular momentum and Angular impulse
  212. 212A mass MM hangs on a massless rod of length ll which rotates at a constant angular frequency. The mass MM moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity ω.\omega . The angular momentum of MM about point AA is LA{L}_{A} which lies in the positive zz direction and the angular momentum of MM about BB is LB.{L}_{B}. The correct statement for this system is:
    JEE Main/MCQ/Medium/Angular momentum and Angular impulse/With diagram
  213. 213A ball of mass 10kg10kg moving with a velocity 103ms−110\sqrt{3}{ms}^{-1} along XX-axis, hits another ball of mass 20kg20kg which is at rest. After the collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along YY-axis at a speed of 10ms−110m{s}^{-1}. The second piece starts moving at a speed of 20ms−120m{s}^{-1} at an angle θ\theta (degree) with respect to the XX-axis. The configuration of pieces after the collision is shown in the figure. The value of θ\theta to the nearest integer is _________.
    JEE Main/Numerical/Medium/Angular momentum and Angular impulse/With diagram
  214. 214The maximum and minimum distances of a comet from the Sun are 1.6×1012m1.6\times {10}^{12}m and 8.0×1010m8.0\times {10}^{10}m respectively. If the speed of the comet at the nearest point is 6×104ms−16\times {10}^{4}{ms}^{-1}, the speed at the farthest point isJEE Main/MCQ/Medium/Angular momentum and Angular impulse
  215. 215A sphere of radius aa and mass mm rolls along a horizontal plane with constant speed v0{v}_{0}. It encounters an inclined plane at angle θ\theta and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?
    JEE Main/MCQ/Medium/Angular momentum and Angular impulse/With diagram
  216. 216Four point masses, each of mass mm, are fixed at the corners of a square of side I. The square is rotating with angular frequency ω,\omega , about an axis passing through one of the corners of the square and parallel to tis diagonal, as shown in the figure. The angular momentum of the square about the axis is
    JEE Main/MCQ/Medium/Angular momentum and Angular impulse/With diagram
  217. 217A wheel is rotating freely with an angular speed ω\omega on a shaft. The moment of inertia of the wheel is II and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  218. 218A circular disc of mass M\text{M} and radius R\text{R} is rotating about its axis with angular speed ω1{\omega }_{1}. If another stationary disc having radius R2\dfrac{\text{R}}{2} and same mass M\text{M} is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed ω2{\omega }_{2}. The energy lost in the process is \text{p%} of the initial energy. Value of pp is ______JEE Main/Numerical/Medium/Angular momentum and Angular impulse
  219. 219A block of mass m=1kgm=1kg slides with velocity v=6ms−1v=6m{s}^{-1} on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about OO and swings as a result of the collision making angle θ\theta before momentarily coming to rest. if the rod has mass M=2kg,M=2kg, and length ℓ=1m,\ell =1m, the value of θ\theta is approximately(takeg=10ms−2)\left.(takeg=10m{s}^{-2}\right)
    JEE Main/MCQ/Medium/Angular momentum and Angular impulse/With diagram
  220. 220A person of mass MM is sitting on a swing of length LL and swinging with and an angular amplitude θ0.{\theta }_{0}. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance l(l<<L),l\left(l\lt \lt L\right), is close to:JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  221. 221The time dependence of the position of a particle of mass m=2m=2 is given by r⃗(t)=2ti^−3t2j^\vec{r}\left(t\right)=2t\hat{i}-3{t}^{2}\hat{j} . Its angular momentum, with respect to the origin, at time t=2t=2 is:JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  222. 222Two coaxial discs, having moments of inertia I1{I}_{1} and I12\dfrac{{I}_{1}}{2} , are rotating with respective angular velocities ω1{\omega }_{1} and ω12\dfrac{{\omega }_{1}}{2} , about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If Ef{E}_{f} and Ei{E}_{i} are the final and initial total energies, then (Ef−Ei)\left({E}_{f}-{E}_{i}\right) is:JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  223. 223A thin smooth rod of length LL and mass MM is rotating freely with angular speed ω0{\omega }_{0} about an axis perpendicular to the rod and passing through center. Two beads of mass mm and negligible size are at the center of the rod initially. The beads of mass mm and negligible size are at the center of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod, will be:JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  224. 224A rectangular solid box of length 0.3m0.3m is held horizontally, with one of its sides on the edge of a platform of height 5m5m . When released, it slips off the table in a very short time τ=0.01s\tau =0.01s , remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to:
    JEE Main/MCQ/Medium/Angular momentum and Angular impulse/With diagram
  225. 225A thin uniform bar of length L\mathrm{L} and mass 8 m8 \mathrm{~m} lies on a smooth horizontal table. Two point masses m\mathrm{m} and 2 m2 \mathrm{~m} moving in the same horizontal plane from opposite sides of the bar with speeds 2v2 \mathrm{v} and vv respectively. The masses stick to the bar after collision at a distance L3\frac{\mathrm{L}}{3} and L6\frac{\mathrm{L}}{6} respectively from the centre of the bar. If the bar starts rotating about its center of mass as a result of collision, the angular speed of the bar will be:
    JEE Main/MCQ/Medium/Angular momentum and Angular impulse/With diagram
  226. 226A cubical block of side 30cm30cm is moving with velocity 2ms−12m{s}^{-1} on a smooth horizontal surface. The surface has a bump at a point OO as shown in the figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :
    JEE Main/MCQ/Medium/Angular momentum and Angular impulse/With diagram
  227. 227A particle of mass m is moving along the side of a square of side 'a', with a uniform speed υυ in the x-y plane as shown in the figure:


    Which of the following statements is false for the angular momentum     L⃗\vec{L} about the origin?    JEE Main/MCQ/Medium/Angular momentum and Angular impulse/With diagram
  228. 228A particle of mass 2kg2kg is on a smooth horizontal table and moves in a circular path of radius 0.6m0.6m. The height of the table from the ground is 0.8m0.8m. If the angular speed of the particle is 12rads−112rad{s}^{-1} , the magnitude of its angular momentum about a point on the ground right under the center of the circle is:JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  229. 229A ball of mass 160g160g is thrown up at an angle of 60∘60^{\circ} to the horizontal at a speed of 10ms−110m{s}^{-1}. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly (g=10ms−2)\left(g=10m{s}^{-2}\right)JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  230. 230A particle is moving in a circular path of radius a, with a constant velocity v\mathrm{v} as shown in the figure. The centre of circle is marked by ' C\mathrm{C} '. The angular momentum from the origin O\mathrm{O} can be written as:
    JEE Main/MCQ/Medium/Angular momentum and Angular impulse/With diagram
  231. 231A bob of mass m attached to an inextensible string of length l⁡l⁡ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed ω\omega rad/s about the vertical. About the point of suspension :JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  232. 232A particle of mass 2 kg2 \mathrm{~kg} is moving such that at time tt, its position, in meter, is given by r⃗(t)=5i^−2t2j^\vec{r}(t)=5 \hat{i}-2 t^2 \hat{j}. The angular momentum of the particle at t=2st=2 s about the origin in kgm−2 s−1\mathrm{kg} \mathrm{m}^{-2} \mathrm{~s}^{-1} is :JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  233. 233A hoop of radius r\text{r} and mass m\text{m} rotating with an angular velocity ω0{\omega }_{0} is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  234. 234A stone of mass mm, tied to the end of a string, is whirled around in a circle on a horizontal frictionless table. The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by T=ArnT=A r^n, where AA is a constant, rr is the instantaneous radius of the circle. The value of nn is equal toJEE Main/MCQ/Medium/Angular momentum and Angular impulse
  235. 235This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
    Statement 1: When moment of inertia     II of a body rotating about an axis with angular speed ω\omega increases, its angular momentum LL is unchanged but the kinetic energy KK increases if there is no torque applied on it.
    Statement 2:     L=IωL=I \omega, kinetic energy of rotation =12Iω2=\frac{1}{2} I \omega^2    JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  236. 236A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc:JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  237. 237Angular momentum of the particle rotating with a central force is constant due toJEE Main/MCQ/Medium/Angular momentum and Angular impulse
  238. 238A thin circular ring of mass m\mathrm{m} and radius R\mathrm{R} is rotating about its axis with a constant angular velocity ω\omega. Two objects each of mass MM are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ω′=\omega^{\prime}=JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  239. 239A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  240. 240A particle performing uniform circular motion has angular frequency is doubled \& its kinetic energy halved, then the new angular momentum isJEE Main/MCQ/Medium/Angular momentum and Angular impulse
  241. 241A particle of mass mm moves along line PCP C with velocity vv as shown. What is the angular momentum of the particle about P?\mathrm{P} ?
    JEE Main/MCQ/Medium/Angular momentum and Angular impulse/With diagram
  242. 242Initial angular velocity of a circular disc of mass MM is ω1\omega_1. Then two small spheres of mass mm are attached gently to diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?JEE Main/MCQ/Medium/Angular momentum and Angular impulse
  243. 243A solid cylinder having radius RR and length LL is slipping on a rough horizontal plane. At time t=0t=0 the cylinder has a translational velocity v0=49v_0=49 m/s, perpendicular to its axis and a rotational velocity v0/4Rv_0/4R about the centre. The time taken by the cylinder to start rolling is ________ seconds. (coefficient of kinetic friction μK=0.25\mu_K=0.25 and g=9.8g=9.8 m/s2^2)JEE Main/MCQ/Medium/Rolling without Slipping
  244. 244A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is x5\sqrt{\frac{x}{5}} where x=\mathrm{x}= _____JEE Main/Numerical/Medium/Rolling without Slipping
  245. 245A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is :JEE Main/MCQ/Medium/Rolling without Slipping
  246. 246A solid sphere of mass ' mm ' and radius ' rr ' is allowed to roll without slipping from the highest point of an inclined plane of length ' LL ' and makes an angle 30∘30^{\circ} with the horizontal. The speed of the particle at the bottom of the plane is v1v_1. If the angle of inclination is increased to 45∘45^{\circ} while keeping LL constant. Then the new speed of the sphere at the bottom of the plane is v2v_2. The ratio v12:v22v_1^2: v_2^2 isJEE Main/MCQ/Medium/Rolling without Slipping
  247. 247A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed vv. The sphere and the cylinder reaches upto maximum heights h1h_1 and h2h_2, respectively, above the initial level. The ratio h1:h2h_1: h_2 is n10\frac{n}{10}. The value of nn is______.JEE Main/Numerical/Medium/Rolling without Slipping
  248. 248A disc of radius RR and mass MM is rolling horizontally without slipping with speed vv. It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is:JEE Main/MCQ/Medium/Rolling without Slipping/With diagram
  249. 249A cylinder is rolling down on an inclined plane of inclination 60∘60^{\circ}. Its acceleration during rolling down will be x3ms−2\dfrac{x}{\sqrt{3}}m{s}^{-2}, where x=x= _______(use g=10ms−2g=10m{s}^{-2}).JEE Main/Numerical/Medium/Rolling without Slipping
  250. 250A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is 7x\dfrac{7}{x}, where xx is ______.JEE Main/Numerical/Medium/Rolling without Slipping
  251. 251A solid cylinder is released from rest from the top of an inclined plane of inclination 30∘30^{\circ} and length 60cm60cm. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ______ ms−1m{s}^{-1}. (Given g=10ms−2g=10m{s}^{-2})
    JEE Main/Numerical/Medium/Rolling without Slipping/With diagram
  252. 252A solid sphere of mass 1kg1kg rolls without slipping on a plane surface. Its kinetic energy is 7×10−3J7\times {10}^{-3}J. The speed of the centre of mass of the sphere is ______ cms−1cm{s}^{-1}.JEE Main/Numerical/Medium/Rolling without Slipping
  253. 253A uniform disc of mass 0.5kg0.5kg and radius rr is projected with velocity 18ms−118m{s}^{-1} at t=0st=0s on a rough horizontal surface. It starts off with a purely sliding motion at t=0st=0s. After 2s2s it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after 2s2s will be ______ JJ.
    (given, coefficient of friction is     0.30.3 and g=10ms−2g=10m{s}^{-2}).
    JEE Main/Numerical/Medium/Rolling without Slipping/With diagram
  254. 254A solid cylinder and a solid sphere, having same mass MM and radius RR, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will beJEE Main/MCQ/Medium/Rolling without Slipping
  255. 255Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation isJEE Main/MCQ/Medium/Rolling without Slipping
  256. 256Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is x2.\dfrac{\sqrt{x}}{2}. Then, the value of xx isJEE Main/Numerical/Medium/Rolling without Slipping
  257. 257A circular disc reaches from top to bottom of an inclined plane of length L.L. When it slips down the plane, it takes time t1{t}_{1}. When it rolls down the plane, it takes time t2{t}_{2}. The value of t2t1\dfrac{{t}_{2}}{{t}_{1}} is 3x\sqrt{\dfrac{3}{x}}. The value of xx will beJEE Main/Numerical/Medium/Rolling without Slipping
  258. 258A sphere of mass 2kg2kg and radius 0.5m0.5m is rolling with an initial speed of 1ms−11{ms}^{-1} goes up an inclined plane which makes an angle of 30∘30^{\circ} with the horizontal plane, without slipping. How low will the sphere take to return to the starting point AA?
    JEE Main/MCQ/Medium/Rolling without Slipping/With diagram
  259. 259The following bodies,
    (1)\left(1\right) a ring
    (2)\left(2\right) a disc
    (3)\left(3\right) a solid cylinder
    (4)\left(4\right) a solid sphere,
    of same mass     mm and radius RR are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is
    [Mark the body as per their respective numbering given in the question]
    JEE Main/Numerical/Medium/Rolling without Slipping/With diagram
  260. 260A solid disc of radius aa and mass mm rolls down without slipping on an inclined plane making an angle θ\theta with the horizontal. The acceleration of the disc will be 2bgsin⁡θ\dfrac{2}{b}g\sin \theta, where bb is _______. (Round off to the Nearest Integer)
    (    g=g= acceleration due to gravity)
    (    θ=\theta = angle as shown in figure)
    JEE Main/Numerical/Medium/Rolling without Slipping/With diagram
  261. 261

    As shown in the figure, a bob of mass     mm is tied to a massless string whose other end portion is wound on a fly wheel (disc) of radius rr and mass m.m. When released from rest the bob starts falling vertically. When it has covered a distance of h,h, the angular speed of the wheel will be:    JEE Main/MCQ/Medium/Rolling without Slipping/With diagram
  262. 262The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane: (i) a ring of radius R,R, (ii) a solid cylinder of radius R2\dfrac{R}{2} and (iii) a solid sphere of radius R4.\dfrac{R}{4}. If, in each case, the speed of the center of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is:JEE Main/MCQ/Medium/Rolling without Slipping
  263. 263A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights hsph{h}_{sph} and hcyl{h}_{cyl} on the inline. The ratio hsphhcyl\dfrac{{h}_{sph}}{{h}_{cyl}} is given by:
    JEE Main/MCQ/Medium/Rolling without Slipping/With diagram
  264. 264a string is wound around a hollow cylinder of mass 5 kg5 \mathrm{~kg} and radius 0.5 m0.5 \mathrm{~m}. If the string is now pulled with a horizontal force of 40 N40 \mathrm{~N}, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string)

    JEE Main/MCQ/Medium/Rolling without Slipping/With diagram
  265. 265A homogeneous solid cylindrical roller of radius RR and mass MM is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is:JEE Main/MCQ/Medium/Rolling without Slipping
  266. 266A uniform solid cylindrical roller of mass mm is being pulled on a horizontal surface with force FF parallel to the surface and applied at its centre. If the acceleration of the cylinder is aa and it is rolling without slipping then the value of FF is:JEE Main/MCQ/Medium/Rolling without Slipping
  267. 267Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration 'a' perpendicular to the axis of the cylinder. What is Ffriction at point P ? It is assumed that the cylinder does not slip.
    JEE Main/MCQ/Medium/Rolling without Slipping/With diagram
  268. 268A cylinder of mass Mc and sphere of mass Ms are placed at points A and B of two inclines, respectively. (See figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio sinθcsinθs\dfrac{sin{\theta }_{\text{c}}}{sin{\theta }_{\text{s}}} is :
    JEE Main/MCQ/Medium/Rolling without Slipping/With diagram
  269. 269A thick-walled hollow sphere has outside radius R0R_0. It rolls down an incline without slipping and its speed at the bottom is v0v_0. Now the incline is waxed, so that it is practically frictionless and the sphere is observed to slide down (without any rolling). Its speed at the bottom is observed to be 5v0/45 v_0 / 4. The radius of gyration of the hollow sphere about an axis through its centre isJEE Main/MCQ/Medium/Rolling without Slipping
  270. 270A mass m\mathrm{m} hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m\mathrm{m} and radius R\mathrm{R}. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass mm, if the string does not slip on the pulley, isJEE Main/MCQ/Medium/Rolling without Slipping
  271. 271A round uniform body of radius R\mathrm{R}, mass M\mathrm{M} and moment of inertia 'I\mathrm{I}', rolls down (without slipping) an inclined plane making an angle θ\theta with the horizontal. Then its acceleration isJEE Main/MCQ/Medium/Rolling without Slipping
  272. 272A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is 8 m/s8 \mathrm{~m} / \mathrm{s}. The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be :JEE Main/MCQ/Medium/Combination of translation and rotation
  273. 273A solid sphere of mass 2kg2kg is making pure rolling on a horizontal surface with kinetic energy 2240J2240J. The velocity of centre of mass of the sphere will be ______ ms−1m{s}^{-1}.JEE Main/Numerical/Medium/Combination of translation and rotation
  274. 274A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy isJEE Main/MCQ/Medium/Combination of translation and rotation
  275. 275Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by E=20cos⁡(2×1010t−200x)Vm−1.E=20\cos \left(2\times {10}^{10}t-200x\right)V{m}^{-1}. The dielectric constant of the medium is equal to:
    (Take     μr=1){\mu }_{r}=1)    JEE Main/MCQ/Medium/Combination of translation and rotation
  276. 276A solid sphere is rolling on a surface as shown in figure, with a translational velocity v m s−1v \mathrm{~m} \mathrm{~s}^{-1}. If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is
    JEE Main/MCQ/Medium/Combination of translation and rotation/With diagram
  277. 277A 'T' shaped object with dimensions shown in the figure, is lying on a smooth floor. A force FF is applied at the point PP parallel to ABA B, such that the object has only the translational motion without rotation. Find the location of PP with respect to CC
    JEE Main/MCQ/Medium/Combination of translation and rotation/With diagram
  278. 278A uniform bar of length 12 cm and mass 20m20 m lies on a smooth horizontal table. Two point masses mm and 2m2 m are moving in opposite directions with same speed of vv and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency ω\omega. The ratio of vv and ω\omega is :
    JEE Main/MCQ/Medium/Collisions in rotation/With diagram
  279. 279Two discs of moment of inertia I1=4kgm2{I}_{1}=4kg{m}^{2} and I2=2kgm2{I}_{2}=2kg{m}^{2} about their central axes & normal to their planes, rotating with angular speeds 10rad{s}^{-1}&4rad{s}^{-1} respectively are brought into contact face to face with their axe of rotation coincident. The loss in kinetic energy of the system in the process is _________JJ.JEE Main/Numerical/Medium/Collisions in rotation
  280. 280A ring of mass MM and radius RR is rotating about its axis with angular velocity ω\omega. Two identical bodies each of mass mm are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be :JEE Main/MCQ/Medium/Collisions in rotation

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