Physics · JEE Main, NEET

Work Energy Power

183 practice questions with a worked solution for each. Tap an option to see instantly if you are right.

138MCQ45Numerical39With diagram
Start with question 1 See it move: Collisions, centre of mass and rocketsSee it move: Work, energy and power
  1. 1A body of mass mm moving with velocity vv makes a 1D elastic collision with a stationary body of mass MM. The body of mass mm rebounds with velocity −v/3-v/3. The mass MM is:JEE Main/MCQ/Medium
  2. 2A spring of force constant k=400 N/mk = 400\,\text{N/m} is compressed by 0.1 m0.1\,\text{m}. The elastic potential energy stored is:NEET/MCQ/Medium
  3. 3The rain drop of mass 11 g, starts with zero velocity from a height of 11 km. It hits the ground with a speed of 55 m/s. The work done by the unknown resistive force is _______ J. (take g=10g = 10 m/s2^2)JEE Main/MCQ/Medium/Work done
  4. 4A 11 kg block subjected to two simultaneous forces (2i^+3j^+4k^)(2\hat{i} + 3\hat{j} + 4\hat{k}) N and (3i^−j^−2k^)(3\hat{i} - \hat{j} - 2\hat{k}) N is moved a distance of 2525 m along (3i^−4j^)(3\hat{i} - 4\hat{j}) direction. The work done in this process is _____ J.JEE Main/Numerical/Medium/Work done
  5. 5A block of mass 25 kg is pulled along a horizontal surface by a force at an angle 45∘45^{\circ} with the horizontal. The friction coefficient between the block and the surface is 0.25. The displacement of 5 m of the block is:JEE Main/MCQ/Medium/Work done
  6. 6A force F=α+βx2\mathrm{F}=\alpha+\beta \mathrm{x}^2 acts on an object in the x -direction. The work done by the force is 5 J when the object is displaced by 1 m . If the constant α=1 N\alpha=1 \mathrm{~N} then β\beta will beJEE Main/MCQ/Medium/Work done
  7. 7A force f=x2yi^+y2j^\mathrm{f}=\mathrm{x}^2 \mathrm{y} \hat{\mathrm{i}}+\mathrm{y}^2 \hat{\mathrm{j}} acts on a particle in a plane x+y=10\mathrm{x}+\mathrm{y}=10. The work done by this force during a displacement from (0,0)(0,0) to (4 m,2 m)(4 \mathrm{~m}, 2 \mathrm{~m}) is \qquad Joule (round off to the nearest integer)JEE Main/Numerical/Medium/Work done
  8. 8A force F→=2i^+bj^+k^\overrightarrow{\mathrm{F}}=2 \hat{i}+\mathrm{b} \hat{j}+\hat{k} is applied on a particle and it undergoes a displacement i^−2j^−k^\hat{i}-2 \hat{j}-\hat{k}. What will be the value of bb, if work done on the particle is zero.JEE Main/MCQ/Medium/Work done
  9. 9A force (3x2+2x−5)N\left(3 x^2+2 x-5\right) \mathrm{N} displaces a body from x=2 mx=2 \mathrm{~m} to x=4 mx=4 \mathrm{~m}. Work done by this force is ________ JJ.JEE Main/Numerical/Medium/Work done
  10. 10A particle of mass mm moves on a straight line with its velocity increasing with distance according to the equation v=αxv=\alpha \sqrt{x}, where α\alpha is a constant. The total work done by all the forces applied on the particle during its displacement from x=0x=0 to x=dx=\mathrm{d}, will be :JEE Main/MCQ/Medium/Work done
  11. 11A block of mass 1kg1kg is pushed up a surface inclined to horizontal at an angle of 60∘60^{\circ} by a force of 10N10N parallel to the inclined surface as shown in figure. When the block is pushed up by 10m10m along inclined surface, the work done against frictional force is : [g=10ms−2]\left[g=10m{s}^{-2}\right]JEE Main/MCQ/Medium/Work done/With diagram
  12. 12A block of mass 100kg100kg slides over a distance of 10m10m on a horizontal surface. If the co-efficient of friction between the surfaces is 0.40.4 , then the work done against friction (in JJ) is:JEE Main/MCQ/Medium/Work done
  13. 13A block of mass 10kg10kg is moving along xx-axis under the action of force F=5xNF=5xN. The work done by the force in moving the block from x=2mx=2m to 4m4m will be _______ JJ.JEE Main/Numerical/Medium/Work done
  14. 14A force F⃗=(2+3x)i^\vec{F}=\left(2+3x\right)\hat{i} acts on a particle in the xx direction where FF is in Newton and xx is in meter. The work done by this force during a displacement from x=0x=0 to x=4mx=4m is _____ JJ.JEE Main/Numerical/Medium/Work done
  15. 15A force F=(5+3y2)F=(5+3{y}^{2}) acts on a particle in the yy-direction, where FF is newton and yy is in meter. The work done by the force during a displacement from y=2my=2m to y=5my=5m is ______ JJ.JEE Main/Numerical/Medium/Work done
  16. 16A small particle moves to position 5i^−2j^+k^5\hat{i}-2\hat{j}+\hat{k} from its initial position 2i^+3j^−4k^2\hat{i}+3\hat{j}-4\hat{k} under the action of force 5i^+2j^+7k^N5\hat{i}+2\hat{j}+7\hat{k}N. The value of work done will be ______ JJ.JEE Main/Numerical/Medium/Work done
  17. 17Identify the correct statements from the following:
    (A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative
    (B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative
    (C) Work done by friction on a body sliding down an inclined plane is positive
    (D) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero
    (E) Work done by the air resistance on an oscillating pendulum is negative
    Choose the correct answer from the options given below:    JEE Main/MCQ/Medium/Work done
  18. 18A body of mass 0.5kg0.5kg travels on straight line path with velocity v=(3x2+4)ms−1v=\left(3{x}^{2}+4\right)m{s}^{-1}. The net work done by the force during its displacement from x=0x=0 to x=2mx=2m isJEE Main/MCQ/Medium/Work done
  19. 19A particle of mass 500g500g is moving in a straight line with velocity v=bx52v=b{x}^{\dfrac{5}{2}}. The work done by the net force during its displacement from x=0x=0 to x=4mx=4m is (Take b=0.25m−32s−1b=0.25{m}^{\dfrac{-3}{2}}{s}^{-1}).JEE Main/MCQ/Medium/Work done
  20. 20Arrange the four graphs in descending order of total work done; where W1,W2,W3{W}_{1},{W}_{2},{W}_{3} and W4{W}_{4} are the work done corresponding to figure a,b,ca,b,c and dd respectively.
    JEE Main/MCQ/Medium/Work done/With diagram
  21. 21Two persons AA and BB perform same amount of work in moving a body through a certain distance dd with application of forces acting at angles 45∘45^{\circ} and 60∘60^{\circ} with the direction of displacement respectively. The ratio of force applied by person AA to the force applied by person BB is 1x.\dfrac{1}{\sqrt{x}}. The value of xx is _________.JEE Main/Numerical/Medium/Work done
  22. 22A force of F=(5y+20)j^NF=(5y+20)\hat{j}N acts on a particle. The work done by this force when the particle is moved from y=0my=0m to y=10my=10m is ________JJ.JEE Main/Numerical/Medium/Work done
  23. 23A porter lifts a heavy suitcase of mass 80kg80kg and at the destination lowers it down by a distance of 80cm80cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase. (take g=9.8ms−2g=9.8{ms}^{-2} )JEE Main/MCQ/Medium/Work done
  24. 24A person pushes a box on a rough horizontal plateform surface. He applies a force of 200N200N over a distance of 15m15m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100N100N. The total distance through which the box has been moved is 30m30m. What is the work done by the person during the total movement of the box?JEE Main/MCQ/Medium/Work done
  25. 25Consider a force F⃗=−xi^+yj^\vec{F}=-x\hat{i}+y\hat{j} . The work done by this force in moving a particle from point A(1,0)A\left(1,0\right) to B(0,1)B\left(0,1\right) along the line segment is : (all quantities are in SI units)JEE Main/MCQ/Medium/Work done/With diagram
  26. 26A uniform cable of mass MM and length LL is placed on a horizontal surface such that its (1n)th{\left(\dfrac{1}{n}\right)}^{th} part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be:JEE Main/MCQ/Medium/Work done
  27. 27The velocity-time graph of a particle of mass 10kg10kg is shown in the figure. The net work done on the particle in the first two seconds of the motion is

    JEE Main/MCQ/Medium/Work done/With diagram
  28. 28When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude
    F = ax + bx2 where a and b are constants. The work done in stretching the unstretched rubber-band by L is :    JEE Main/MCQ/Medium/Work done
  29. 29A ball of mass 0.2 kg0.2 \mathrm{~kg} is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m0.2 \mathrm{~m} which applying the force and the ball goes upto 2 m2 \mathrm{~m} height further, find the magnitude of the force. Consider g=10 m/s2\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2JEE Main/MCQ/Medium/Work done
  30. 30A particle of mass 100 g100 \mathrm{~g} is thrown vertically upwards with a speed of 5 m/s5 \mathrm{~m} / \mathrm{s}. the work done by the force of gravity during the time the particle goes up isJEE Main/MCQ/Medium/Work done
  31. 31A wire fixed at the upper end stretches by length by applying a force F. The work done in stretching isJEE Main/MCQ/Medium/Work done
  32. 32A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows thatJEE Main/MCQ/Medium/Work done
  33. 33A force F⃗=(5i^+3j^+2k^)N\vec{F}=(5 \hat{i}+3 \hat{j}+2 \hat{k}) N is applied over a particle which displaces it from its origin to the point r⃗=(2i^−j^)m\vec{r}=(2 \hat{i}-\hat{j}) m. The work done on the particle in joules isJEE Main/MCQ/Medium/Work done
  34. 34A uniform chain of length 2 m2 \mathrm{~m} is kept on a table such that a length of 60 cm60 \mathrm{~cm} hangs freely from the edge of the table. The total mass of the chain is 4 kg4 \mathrm{~kg}. What is the work done in pulling the entire chain on the table?JEE Main/MCQ/Medium/Work done
  35. 35The velocity at which 66 kg mass (shown in figure) strikes the ground when it is released from a height of 66 m above the ground is __________ m/s. Assume pulley is massless and string is light and inextensible. (Take g =10= 10 m/s2^2)
    JEE Main/MCQ/Medium/Energy/With diagram
  36. 36A body of mass 11 kg moves along a straight line with a velocity v=2x2v = 2x^2. The work done by the body during displacement from x=0x = 0 to 55 m is __________ J.JEE Main/MCQ/Medium/Energy
  37. 37A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height hh as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height h=αRh = \alpha R. The value of α\alpha is _______.
    JEE Main/MCQ/Medium/Energy/With diagram
  38. 38A spherical ball of mass 22 kg falls from a height of 1010 m and is brought to rest after penetrating 1010 cm into sand. The average force exerted by sand on the ball is _______ N. (Take g=10g = 10 m/s2^2)JEE Main/MCQ/Medium/Energy
  39. 39A bead PP sliding on a frictionless semi-circular string (ACB)(A C B) and it is at point SS at t=0t =0 and at this instant the horizontal component of its velocity is vv. Another bead QQ of the same mass as PP is ejected from point AA at t=0t=0 along the horizontal string ABA B, with the speed vv, friction between the beads and the respective strings may be neglected in both cases. Let tPt_{P} and tQt_{Q} be the respective times taken by beads PP and QQ to reach the point BB, then the relation between tPt_{P} and tQt_{Q} is
    JEE Main/MCQ/Medium/Energy/With diagram
  40. 40A small bob AA of mass mm is attached to a massless rigid rod of length 1 m pivoted at point PP and kept at an angle of 60∘60^{\circ} with vertical as shown in figure. At distance of 1 m below point PP, an identical bob BB is kept at rest on a smooth horizontal surface that extends to a circular track of radius RR as shown in figure. If bob BB just manages to complete the circular path of radius RR upto a point QQ after being hit elastically by bob⁡A\operatorname{bob} A, then radius RR is ____\_\_\_\_ m.
    JEE Main/MCQ/Medium/Energy/With diagram
  41. 41Given below are two statements :
    Statement I: An object moves from position     r1r_{1} to position r2r_{2} under a conservative force field F⃗\vec{F}. The work done by the force is W=−∫r1r2F⃗⋅dr→W=-\int_{r_{1}}^{r_{2}} \vec{F} \cdot \overrightarrow{d r}.
    Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.
    In the light of the above statements, choose the correct answer from the options given below :    JEE Main/MCQ/Medium/Energy
  42. 42A body of mass 2 kg is moving along xx-direction such that its displacement as function of time is given by x(t)=αt2+βt+γmx(t)=\alpha t^{2}+\beta t+\gamma \mathrm{m}, where α=1 m/s2,β=1 m/s\alpha=1 \mathrm{~m} / \mathrm{s}^{2}, \beta=1 \mathrm{~m} / \mathrm{s} and γ=1 m\gamma=1 \mathrm{~m}. The work done on the body during the time interval t=2 st=2 \mathrm{~s} to t=3 st=3 \mathrm{~s}, is ____\_\_\_\_ J.JEE Main/MCQ/Medium/Energy
  43. 43Potential energy (VV) versus distance (xx) is given by the graph. Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low.
    JEE Main/MCQ/Medium/Energy/With diagram
  44. 44A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N/m200 \mathrm{~N} / \mathrm{m}. The block is pushed such that the length of the spring becomes 1 m and then released. At distance xm(x<2)\mathrm{x} \mathrm{m}(\mathrm{x} \lt 2) from the wall. the speed of the block will be :JEE Main/MCQ/Medium/Energy
  45. 45Which one of the following forces cannot be expressed in terms of potential energy?JEE Main/MCQ/Medium/Energy
  46. 46A block of mass 1 kg , moving along x with speed vi=10 m/s\mathrm{v}_{\mathrm{i}}=10 \mathrm{~m} / \mathrm{s} enters a rough region ranging from x=0.1 m\mathrm{x}=0.1 \mathrm{~m} to x=1.9 m\mathrm{x}=1.9 \mathrm{~m}. The retarding force acting on the block in this range is Fr=−kxN\mathrm{F}_{\mathrm{r}}=-\mathrm{kx} \mathrm{N}, with k=10 N/m\mathrm{k}=10 \mathrm{~N} / \mathrm{m}. Then the final speed of the block as it crosses rough region isJEE Main/MCQ/Medium/Energy
  47. 47A piston of mass MM is hung from a massless spring whose restoring force law goes as F=−kx3\mathrm{F}=-\mathrm{kx}^3, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' nn ' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height L0\mathrm{L}_0 to L1\mathrm{L}_1, the total energy delivered by the filament is (Assume spring to be in its natural length before heating)
    JEE Main/MCQ/Medium/Energy/With diagram
  48. 48A particle is released from height SS above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.JEE Main/MCQ/Medium/Energy
  49. 49A bead of mass ' mm ' slides without friction on the wall of a vertical circular hoop of radius ' RR ' as shown in figure. The bead moves under the combined action of gravity and a massless spring ( k ) attached to the bottom of the hoop. The equilibrium length of the spring is ' RR '. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' R ', would be (spring constant is ' k ', g is accleration due to gravity)
    JEE Main/MCQ/Medium/Energy/With diagram
  50. 50Given below are two statements: one is labelled as Assertion A\mathbf{A} and the other is labelled as Reason R\mathbf{R}
    Assertion A: In a central force field, the work done is independent of the path chosen.
    Reason R: Every force encountered in mechanics does not have an associated potential energy.
    In the light of the above statements, choose the most appropriate answer from the options given below    JEE Main/MCQ/Medium/Energy
  51. 51A ball having kinetic energy KE, is projected at an angle of 60∘60^{\circ} from the horizontal. What will be the kinetic energy of ball at the highest point of its flight ?JEE Main/MCQ/Medium/Energy
  52. 52A stationary particle breaks into two parts of masses mAm_A and mBm_B which move with velocities vAv_A and vBv_B respectively. The ratio of their kinetic energies (KB:KA)\left(K_B: K_A\right) is :JEE Main/MCQ/Medium/Energy
  53. 53A bullet of mass 50 g50 \mathrm{~g} is fired with a speed 100 m/s100 \mathrm{~m} / \mathrm{s} on a plywood and emerges with 40 m/s40 \mathrm{~m} / \mathrm{s}. The percentage loss of kinetic energy is :JEE Main/MCQ/Medium/Energy
  54. 54A body of mass 50 kg50 \mathrm{~kg} is lifted to a height of 20 m20 \mathrm{~m} from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be :
    JEE Main/MCQ/Medium/Energy/With diagram
  55. 55A body of m kgm \mathrm{~kg} slides from rest along the curve of vertical circle from point AA to BB in friction less path. The velocity of the body at BB is:

     (given, R=14 m,g=10 m/s2 and 2=1.4 ) \text { (given, } R=14 \mathrm{~m}, g=10 \mathrm{~m} / \mathrm{s}^2 \text { and } \sqrt{2}=1.4 \text { ) }    JEE Main/MCQ/Medium/Energy/With diagram
  56. 56If a rubber ball falls from a height hh and rebounds upto the height of h/2h / 2. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :JEE Main/MCQ/Medium/Energy
  57. 57A solid circular disc of mass 50kg50kg rolls along a horizontal floor so that its center of mass has a speed of 0.4ms−10.4m{s}^{-1}. The absolute value of work done on the disc to stop it is ______ JJ.JEE Main/Numerical/Medium/Energy
  58. 58An artillery piece of mass M1{M}_{1} fires a shell of mass M2{M}_{2} horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is :JEE Main/MCQ/Medium/Energy
  59. 59A particle is placed at the point AA of a frictionless track ABCABC as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point BB is: ((Take g=10ms−2)\left.g=10m{s}^{-2}\right).JEE Main/MCQ/Medium/Energy/With diagram
  60. 60A bob of mass mm is suspended by a light string of length LL. It is imparted a minimum horizontal velocity at the lowest point AA such that it just completes half circle reaching the top most position BB. The ratio of kinetic energies (K.E.)A(K.E.)B\dfrac{(K.E.{)}_{A}}{(K.E.{)}_{B}} is :JEE Main/MCQ/Medium/Energy/With diagram
  61. 61The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10m10m. If it dissipates 1010% of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use, g=10ms−2g=10m{s}^{-2} ]JEE Main/MCQ/Medium/Energy
  62. 62The potential energy function (in JJ ) of a particle in a region of space is given as U=(2x2+3y3+2z)U=\left(2{x}^{2}+3{y}^{3}+2z\right). Here x,yx,y and zz are in meter. The magnitude of xx - component of force (in NN ) acting on the particle at point P(1,2,3)mP(1,2,3)m is:JEE Main/MCQ/Medium/Energy
  63. 63Two bodies of mass 4g4g and 25g25g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :JEE Main/MCQ/Medium/Energy
  64. 64A body is released from a height equal to the radius (R)\left(R\right) of the earth. The velocity of the body when it strikes the surface of the earth will be: (Given g=g= acceleration due to gravity on the earth.)JEE Main/MCQ/Medium/Energy
  65. 65A car accelerates from rest of ums−1um{s}^{-1}. The energy spent in this process is EJEJ. The energy required to accelerate the car from ums−1um{s}^{-1} to 2ums−12um{s}^{-1} is nEJnEJ. The value of nn is _____.JEE Main/Numerical/Medium/Energy
  66. 66A body of mass (5±0.5)kg(5\pm 0.5)kg is moving with a velocity of (20±0.4)ms−1.(20\pm 0.4)m{s}^{-1}. Its kinetic energy will beJEE Main/MCQ/Medium/Energy
  67. 67A closed circular tube of average radius 15cm15cm, whose inner walls are rough, is kept in vertical plane. A block of mass 1kg1kg just fit inside the tube. The speed of block is 22ms−122m{s}^{-1}, when it is introduced at the top of tube. After completing five oscillations, the block stops at the bottom region of tube. The work done by the tube on the block is ________ JJ. (Given g=10ms−2g=10m{s}^{-2}).
    JEE Main/Numerical/Medium/Energy/With diagram
  68. 68A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3ms−13m{s}^{-1} (as shown in figure). Maximum height with respect to the initial position covered by it will be _____ cmcm
    (take,     g=10ms−2g=10m{s}^{-2})    JEE Main/Numerical/Medium/Energy/With diagram
  69. 69A body of mass 5kg5kg is moving with a momentum of 10kgms−110kgm{s}^{-1}. Now a force of 2N2N acts on the body in the direction of its motion for 5s5s. The increase in the Kinetic energy of the body is _____ JJ.JEE Main/Numerical/Medium/Energy
  70. 70A bullet of mass 0.1kg0.1kg moving horizontally with speed 400ms−1400m{s}^{-1} hits a wooden block of mass 3.9kg3.9kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20m20m before coming to rest. The coefficient of friction between the block and the surface is _______.JEE Main/MCQ/Medium/Energy
  71. 71The momentum of a body is increased by 5050%. The percentage increase in the kinetic energy of the body is________%.JEE Main/Numerical/Medium/Energy
  72. 72A body is dropped on ground from a height h1{h}_{1} and after hitting the ground, it rebounds to a height h2{h}_{2}. If the ratio of velocities of the body just before and after hitting ground is 44, then percentage loss in kinetic energy of the body is x4\dfrac{x}{4}. The value of xx is _____.JEE Main/Numerical/Medium/Energy
  73. 73A small particle of mass mm moves in such a way that its potential energy U=12mω2r2U=\dfrac{1}{2}m{\omega }^{2}{r}^{2} where ω\omega is constant and rr is the distance of the particle from origin. Assuming Bohr’s quantization of momentum and circular orbit, the radius of nth{n}^{th} orbit will be proportional toJEE Main/MCQ/Medium/Energy
  74. 74A block is fastened to a horizontal spring. The block is pulled to a distance x=10cmx=10cm from its equilibrium position (at x=0x=0) on a frictionless surface from rest. The energy of the block at x=5cmx=5cm is 0.25J0.25J. The spring constant of the spring is ______ Nm−1N{m}^{-1}.JEE Main/Numerical/Medium/Energy
  75. 75A lift of mass M=500kgM=500kg is descending with speed of 2ms−12m{s}^{-1}. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of 2ms−22m{s}^{-2}. The kinetic energy of the lift at the end of fall through to a distance of 6m6m will be ______ kJkJ.JEE Main/Numerical/Medium/Energy
  76. 76A 0.4kg0.4kg mass takes 8s8s to reach ground when dropped from a certain height PP above surface of earth. The loss of potential energy in the last second of fall is ______ JJ. [Take g=10ms−2g=10m{s}^{-2}]JEE Main/Numerical/Medium/Energy
  77. 77An object of mass mm initially at rest on a smooth horizontal plane starts moving under the action of force F=2NF=2N. In the process of its linear motion, the angle θ\theta (as shown in figure) between the direction of force and horizontal varies as θ=kx\theta =kx, where kk is a constant and xx is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be E=nksin⁡θE=\dfrac{n}{k}\sin \theta. The value of nn is ______.
    JEE Main/Numerical/Medium/Energy/With diagram
  78. 78A spherical body of mass 2kg2kg starting from rest acquires a kinetic energy of 10000J10000J at the end of 5th{5}^{\text{th}} second. The force acted on the body is _____ NN.JEE Main/Numerical/Medium/Energy
  79. 79If momentum of a body is increased by 2020%, then its kinetic energy increases by :JEE Main/MCQ/Medium/Energy
  80. 80A bullet of mass 200g200g having initial kinetic energy 90J90J is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to 40J40J within 1s1s, the minimum length of the pool, the bullet has to travel so that it completely comes to rest is
    JEE Main/MCQ/Medium/Energy/With diagram
  81. 81A block of mass 'mm' (as shown in figure) moving with kinetic energy EE compresses a spring through a distance 25cm25cm when, its speed is halved. The value of spring constant of used spring will be nENm−1nEN{m}^{-1} for n=n=_____.
    JEE Main/Numerical/Medium/Energy/With diagram
  82. 82Two inclined planes are placed as shown in figure.
    A block is projected from the Point     AA of inclined plane ABAB along its surface with a velocity just sufficient to carry it to the top Point BB at a height 10m10m. After reaching the Point BB the block slides down on inclined plane BCBC. Time it takes to reach to the point CC from point AA is t(2+1)st\left(\sqrt{2}+1\right)s. The value of t is _____ (use g=10ms−2g=10m{s}^{-2})
    JEE Main/Numerical/Medium/Energy/With diagram
  83. 83As per the given figure, two blocks each of mass 250g250g are connected to a spring of spring constant 2Nm−12N{m}^{-1}. If both are given velocity vv in opposite directions, then maximum elongation of the spring is
    JEE Main/MCQ/Medium/Energy/With diagram
  84. 84A bag of sand of mass 9.8kg9.8kg is suspended by a rope. AA bullet of 200g200g travelling with speed 10ms−110{ms}^{-1} gets embedded in it, then loss of kinetic energy will beJEE Main/MCQ/Medium/Energy
  85. 85In the given figure, the block of mass mm is dropped from the point ′A′'A'. The expression for kinetic energy of block when it reaches point ′B′'B' is
    JEE Main/MCQ/Medium/Energy/With diagram
  86. 86Water falls from a 40m40m high dam at the rate of 9×104kg9\times {10}^{4}kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy number of 100W100W lamps, that can be lit, is
    (Take     g=10ms−2g=10{ms}^{-2})    JEE Main/MCQ/Medium/Energy
  87. 87A pendulum is suspended by a string of length 250cm250cm. The mass of the bob of the pendulum is 200g200g. The bob is pulled aside until the string is at 60∘60^{\circ} with vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be _____ ms−1m{s}^{-1}. (if g=10ms−2g=10m{s}^{-2})
    JEE Main/Numerical/Medium/Energy/With diagram
  88. 88A rolling wheel of 12kg12kg is on an inclined plane at position PP and connected to a mass of 3kg3kg through a string of fixed length and pulley as shown in figure.
    Consider     PRPR as friction free surface.
    The velocity of centre of mass of the wheel when it reaches at the bottom     QQ of the inclined plane PQPQ will be 12xghms−1\dfrac{1}{2}\sqrt{xgh}m{s}^{-1}. The value of xx (rounded off to the nearest integer) is _____.
    JEE Main/Numerical/Medium/Energy/With diagram
  89. 89A 0.5kg0.5kg block moving at a speed of 12ms−112{ms}^{-1} compresses a spring through a distance 30cm30cm when its speed is halved. The spring constant of the spring will be _____ Nm−1{Nm}^{-1}JEE Main/Numerical/Medium/Energy
  90. 90Potential energy as a function of rr is given by U=Ar10−Br5U=\dfrac{A}{{r}^{10}}-\dfrac{B}{{r}^{5}}, where rr is the interatomic distance, AA and BB are positive constants. The equilibrium distance between the two atoms will be :JEE Main/MCQ/Medium/Energy
  91. 91A ball of mass 100g100g is dropped from a height h=10cmh=10cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance h2\dfrac{h}{2}. The spring constant is _____ Nm−1N{m}^{-1}
    (Use     g=10ms−2g=10{ms}^{-2})
    JEE Main/Numerical/Medium/Energy/With diagram
  92. 92A particle experiences a variable force F⃗=(4xi^+3y2j^)\vec{F}=\left(4x\hat{i}+3{y}^{2}\hat{j}\right) in a horizontal x−yx-y plane. Assume distance in meters and force is newton. If the particle moves from point (1,2)\left(1,2\right) to point (2,3)\left(2,3\right) in the x−yx-y plane, then Kinetic Energy changes by :JEE Main/MCQ/Medium/Energy
  93. 93An engine is attached to a wagon through a shock absorber of length 1.5m.1.5m. The system with a total mass of 40,000kg40,000kg is moving with a speed of 72kmh−172km{h}^{-1} when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by 1.0m1.0m. If 9090% of energy of the wagon is lost due to friction, the spring constant is _________\times {10}^{5}N{m}^{-1}.JEE Main/Numerical/Medium/Energy
  94. 94A body of mass mm dropped from a height hh reaches the ground with a speed of 0.8gh.0.8\sqrt{gh}. The value of work done by the air-friction is:JEE Main/MCQ/Medium/Energy
  95. 95A block moving horizontally on a smooth surface with a speed of 40ms−140m{s}^{-1} splits into two parts with masses in the ratio of 1:2.1:2. If the smaller part moves at 60ms−160m{s}^{-1} in the same direction, then the fractional change in kinetic energy is :JEE Main/MCQ/Medium/Energy
  96. 96A block moving horizontally on a smooth surface with a speed of 40ms−140{ms}^{-1} splits into two equal parts. If one of the parts moves at 60ms−160{ms}^{-1} in the same direction, then the fractional change in the kinetic energy will be x:4x:4 where x=x= ________.JEE Main/Numerical/Medium/Energy
  97. 97The height of victoria's falls is 63m63m. What is the difference in the temperature of water at the top and at the bottom of the fall? [Given 1cal=4.2J1cal=4.2J and specific heat of water =1calg−1C∘−1]\left.=1cal{g}^{-1}{C^{\circ}}^{-1}\right]JEE Main/MCQ/Medium/Energy
  98. 98A uniform chain of length 3m3m and mass 3kg3kg overhangs a smooth table with 2m2m laying on the table. If KK is the kinetic energy of the chain in JJ as it completely slips off the table, then the value of KK is
    (Takeg=10ms−2)\left(\text{Take}g=10m{s}^{-2}\right)    JEE Main/Numerical/Medium/Energy
  99. 99Given below is the plot of a potential energy function U(x)U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x)F(x) acts on it. Suppose that Emech=8J{E}_{\text{mech}}=8J, the incorrect statement for this system is :
    JEE Main/MCQ/Medium/Energy/With diagram
  100. 100If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be:JEE Main/MCQ/Medium/Energy
  101. 101A ball of mass 4kg4kg, moving with a velocity of 10ms−110{ms}^{-1}, collides with a spring of length 8m8m and force constant 100Nm−1100N{m}^{-1}. The length of the compressed spring is xmxm. The value of xx, to the nearest integer, is ___ .JEE Main/Numerical/Medium/Energy
  102. 102A particle of mass mm moves in a circular orbit under the central potential field, U(r)=−CrU\left(r\right)=\dfrac{-C}{r}, where CC is a positive constant. The correct radius - velocity graph of the particle's motion is :JEE Main/MCQ/Medium/Energy
  103. 103As shown in the figure, a particle of mass 10kg10kg is placed at a point A.A. When the particle is slightly displaced to its right, it starts moving and reaches the point B.B. The speed of the particle at BB is xms−1xm{s}^{-1}. (Take g=10ms−2)\left.g=10m{s}^{-2}\right) The value of xx to the nearest integer is
    JEE Main/Numerical/Medium/Energy/With diagram
  104. 104A boy is rolling a 0.5kg0.5kg ball on the frictionless floor with the speed of 20ms−1.20{ms}^{-1}. The ball gets deflected by an obstacle on the way. After deflection it moves with 55% of its initial kinetic energy. What is the speed of the ball now?JEE Main/MCQ/Medium/Energy
  105. 105Two particles having masses 4g4g and 16g16g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n:2n:2. The value of nn will be ___.JEE Main/Numerical/Medium/Energy
  106. 106The potential energy (U)\left(U\right) of a diatomic molecule is a function dependent on rr (interatomic distance) as U=αr10−βr5−3U=\dfrac{\alpha }{{r}^{10}}-\dfrac{\beta }{{r}^{5}}-3 where, α\alpha and β\beta are positive constants. The equilibrium distance between two atoms will be (2αβ)ab,{\left(\dfrac{2\alpha }{\beta }\right)}^{\dfrac{a}{b}}, where a=a=______ .JEE Main/Numerical/Medium/Energy
  107. 107Two solids AA and BB of mass 1kg1kg and 2kg2kg respectively are moving with equal linear momentum. The ratio of their kinetic energies (K.E.)A:(K.E.)B{\left(K.E.\right)}_{A}:{\left(K.E.\right)}_{B} will be A1,\dfrac{A}{1}, so the value of AA will be _________.JEE Main/Numerical/Medium/Energy
  108. 108If the potential energy between two molecules is given by U=Ar6+Br12,U=\dfrac{A}{{r}^{6}}+\dfrac{B}{{r}^{12}}, then at equilibrium, separation between molecules, and the potential energy are:JEE Main/MCQ/Medium/Energy
  109. 109Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to:JEE Main/MCQ/Medium/Energy
  110. 110A cricket ball of mass 0.15kg0.15kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20m20m after leaving the machine. If the part pushing the ball applies a constant force FF on the ball applies a constant force FF on the ball and moves horizontally a distance of 0.2m0.2m while launching the ball, the value of F(inN)F(inN) is (g=10ms−2)\left(g=10m{s}^{-2}\right)JEE Main/Numerical/Medium/Energy
  111. 111A particle (m=1kg)\left(m=1kg\right) slides down a frictionless track (AOC)\left(AOC\right) starting from rest at a point AA (height 2m2m ). After reaching C,C, the particle continues to move freely in air as a projectile. When it reaching its highest point PP (height 1m1m ), the kinetic energy of the particle (in JJ ) is: (Figure drawn is schematic and not to scale; take g=10ms−2g=10m{s}^{-2} ) ______________.
    JEE Main/Numerical/Medium/Energy/With diagram
  112. 112A wedge of mass M=4mM=4m lies on a frictionless plane. A particle of mass mm approaches the wedge with speed v.v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by:JEE Main/MCQ/Medium/Energy
  113. 113A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled 3m3m is:
    JEE Main/MCQ/Medium/Energy/With diagram
  114. 114A particle of mass 20g20g is released with an initial velocity 5ms−15m{s}^{-1} along the curve from the point A,A, as shown in the figure. The point AA is at height hh from point B.B. The particle slides along the frictionless surface. When the particle reaches point B,B, its angular momentum about OO will be: (Take g=10ms−2g=10m{s}^{-2})

    JEE Main/MCQ/Medium/Energy/With diagram
  115. 115A particle which is experiencing a force, given by F⃗=3i^−12j^\vec{F}=3\hat{i}-12\hat{j}, undergoes a displacement of d⃗=4i^\vec{d}=4\hat{i}. If the particle had a kinetic energy of 3J3J at the beginning of the displacement, what is its kinetic energy at the end of the displacement?JEE Main/MCQ/Medium/Energy
  116. 116A force acts on a 2kg2kg object so that its position is given as a function of time as x=3t2+5.x=3{t}^{2}+5. What is the work done by this force in first 55 seconds?JEE Main/MCQ/Medium/Energy
  117. 117A block of mass m,m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k.k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force F,F, the maximum speed of the block is:

    JEE Main/MCQ/Medium/Energy/With diagram
  118. 118Two particles of the same mass mm are moving in circular orbits because of force, given by F(r)=−16r−r3F\left(r\right)=-\dfrac{16}{r}-{r}^{3}. The first particle is at a distance r=1r=1, and the second, at r=4r=4. The best estimate for the ratio of kinetic energies of the first and the second particle is closest toJEE Main/MCQ/Medium/Energy
  119. 119A body of mass mm starts moving from rest along x−x-axis so that its velocity varies as v=asv=a\sqrt{s} where aa is a constant and ss is the distance covered by the body. The total work done by all the forces acting on the body in the first tt second after the start of the motion isJEE Main/MCQ/Medium/Energy
  120. 120A particle is moving in a circular path of radius a under the action of an attractive potential U=−k2r2.U=-\dfrac{k}{2{r}^{2}}. Its total energy is:JEE Main/MCQ/Medium/Energy
  121. 121An object is dropped from a height hh from the ground. Every time it hits the ground it loses 5050% of its kinetic energy. The total distance covered as t→∞t\rightarrow \infty is:JEE Main/MCQ/Medium/Energy
  122. 122A body of mass m=10−2kgm={10}^{-2}kg is moving in a medium and experiences a frictional force F=−kv2.F=-k{v}^{2}. Its initial speed is v0=10ms−1.{v}_{0}=10m{s}^{-1}. After 10s10s its kinetic energy is 18mv02,\dfrac{1}{8}m{v}_{0}^{2}, then value of kk will be:-JEE Main/MCQ/Medium/Energy
  123. 123A time dependent force F=6tF=6t acts on a particle of mass 1kg1kg. If the particle starts from the rest, the work done by the force during the first 1sec⁡1\sec will be:JEE Main/MCQ/Medium/Energy
  124. 124A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies 3.8×1073.8\times {10}^{7} J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g=9.8ms−2g=9.8m{s}^{-2} :JEE Main/MCQ/Medium/Energy
  125. 125A particle is moving in a circle of radius rr under the action of a force F=αr2F=\alpha {r}^{2} which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy=0=0 for r=0r=0):JEE Main/MCQ/Medium/Energy
  126. 126A block of mass m=0.1kgm=0.1kg is connected to a spring of unknown spring constant k. It is compressed to a distance xx from its equilibrium position and released from rest. After approaching half the distance (x2)\left(\dfrac{x}{2}\right) from the equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with velocity 3ms−13m{s}^{-1}. The total initial energy of the spring is:JEE Main/MCQ/Medium/Energy
  127. 127A block of mass m=10kgm=10kg rests on a horizontal table. The coefficient of friction between the block and the table is 0.050.05. When hit by a bullet of mass 50g50g moving with speed vv, that gets embedded in it, the block moves and comes to stop after moving a distance of 2m2m on the table. If a freely falling object were to acquire speed v10\dfrac{v}{10} after being dropped from height HH, then neglecting energy losses and taking g=10ms−2g=10m{s}^{-2}, the value of HH is close toJEE Main/MCQ/Medium/Energy
  128. 128A spring of unstretched length 1 has a mass mm with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity vv is:JEE Main/MCQ/Medium/Energy
  129. 129A small ball of mass m\mathrm{m} starts at a point A\mathrm{A} with speed vo\mathrm{v}_{\mathrm{o}} and moves along a frictionless track AB\mathrm{AB} as shown. The track BC\mathrm{BC} has coefficient of friction μ\mu. The ball comes to stop at C\mathrm{C} after travelling a distance LL which is:
    JEE Main/MCQ/Medium/Energy/With diagram
  130. 130Two springs of force constants 300 N/m300 \mathrm{~N} / \mathrm{m} (Spring A) and 400 N/m400 \mathrm{~N} / \mathrm{m} (Spring B) are joined together in series. The combination is compressed by 8.75 cm8.75 \mathrm{~cm}. The ratio of energy stored in A\mathrm{A} and B\mathrm{B} is EAEB\frac{E_A}{E_B}. Then EAEB\frac{E_A}{E_B} is equal to:JEE Main/MCQ/Medium/Energy
  131. 131The force F⃗=Fi^\vec{F}=F \hat{i} on a particle of mass 2 kg2 \mathrm{~kg}, moving along the xx-axis is given in the figure as a function of its position xx. The particle is moving with a velocity of 5 m/s5 \mathrm{~m} / \mathrm{s} along the xx-axis at x=0x=0. What is the kinetic energy of the particle at x=8 m?x=8 \mathrm{~m} ?
    JEE Main/MCQ/Medium/Energy/With diagram
  132. 132A particle gets displaced by Δrˉ=(2i^+3j^+4k^)m\Delta \bar{r}=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \mathrm{m} under the action of a force F⃗=(7i^+4j^+3k^)\vec{F}=(7 \hat{i}+4 \hat{j}+3 \hat{k}). The change in its kinetic energy isJEE Main/MCQ/Medium/Energy
  133. 133The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x)=ax12−bx6U(x)=\frac{a}{x^{12}}-\frac{b}{x^6}, where a and bb are constants and xx is the distance between the atoms. If the dissociation energy of the molecule is D=[U(x=∞)−Uat equilbrium ],DD=\left[U(x=\infty)-U_{\text {at equilbrium }}\right], D isJEE Main/MCQ/Medium/Energy
  134. 134An athlete in the olympic games covers a distance of 100 m100 \mathrm{~m} in 10 s10 \mathrm{~s}. His kinetic energy can be estimated to be in the rangeJEE Main/MCQ/Medium/Energy
  135. 135The potential energy of a 1 kg1 \mathrm{~kg} particle free move along the x\mathrm{x}-axis is given by
    V(x)=(x44−x22)JV(x)=\left(\frac{x^4}{4}-\frac{x^2}{2}\right) J
    The total mechanical energy of the particle     2 J2 \mathrm{~J}. Then, the maximum speed (in m/s\mathrm{m} / \mathrm{s} ) is    JEE Main/MCQ/Medium/Energy
  136. 136A spherical ball of mass 20 kg20 \mathrm{~kg} is stationary at the top of a hill of height 100 m100 \mathrm{~m}. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m30 \mathrm{~m} and finally rolls down to a horizontal base at a height of 20 m20 \mathrm{~m} above the ground. The velocity attained by the ball isJEE Main/MCQ/Medium/Energy
  137. 137A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm3 \mathrm{~cm}. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?JEE Main/MCQ/Medium/Energy
  138. 138A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x\mathrm{x} is proportional toJEE Main/MCQ/Medium/Energy
  139. 139A spring of spring constant 5×103 N/m5 \times 10^3 \mathrm{~N} / \mathrm{m} is stretched initially by 5 cm5 \mathrm{~cm} from the unstretched position. Then the work required to stretch it further by another 5 cm5 \mathrm{~cm} isJEE Main/MCQ/Medium/Energy
  140. 140Consider the following two statements:
    (A) Linear momentum of a system of particles is zero
    (B) Kinetic energy of a system of particles is zero
    Then    JEE Main/MCQ/Medium/Energy
  141. 141A ball whose kinetic energy is E, is projected at an angle of 45∘45^{\circ} to the horizontal. The kinetic energy of the ball at the highest point of its flight will beJEE Main/MCQ/Medium/Energy
  142. 142A spring of force constant 800 N/m800 \mathrm{~N} / \mathrm{m} has an extension of 5 cm5 \mathrm{~cm}. The work done is extending it from 5 cm5 \mathrm{~cm} to 15 cm15 \mathrm{~cm} isJEE Main/MCQ/Medium/Energy
  143. 143A body of mass 22 kg begins to move under the influence of time dependent force F⃗=(2ti^+6t2j^)\vec{F} = (2t\hat{i} + 6t^2\hat{j}) N, where i^\hat{i} and j^\hat{j} are unit vectors along xx and yy-axis respectively. The power produced by the force at t=2t = 2 s is _____ W.JEE Main/Numerical/Medium/Power
  144. 144An object of mass 1000 g experiences a time dependent force F⃗=(2ti^+3t2j^)N\vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right) N. The power generated by the force at time tt is :JEE Main/MCQ/Medium/Power
  145. 145A sand dropper drops sand of mass m(t)m(t) on a conveyer belt at a rate proportional to the square root of speed (v)(v) of the belt, i.e. dmdt∝v\frac{\mathrm{dm}}{\mathrm{dt}} \propto \sqrt{v}. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?JEE Main/MCQ/Medium/Power
  146. 146A body of mass 4 kg is placed on a plane at a point P having coordinate (3,4)m(3,4) \mathrm{m}. Under the action of force F→=(2i^+3j^)N\overrightarrow{\mathrm{F}}=(2 \hat{i}+3 \hat{j}) \mathrm{N}, it moves to a new point Q having coordinates (6,10)m(6,10) \mathrm{m} in 4 sec . The average power and instanteous power at the end of 4 sec are in the ratio of :JEE Main/MCQ/Medium/Power
  147. 147A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t\mathrm{t} is proportional to :JEE Main/MCQ/Medium/Power
  148. 148A body of mass 2kg2kg begins to move under the action of a time dependent force given by F⃗=(6ti^+6t2j^)N\vec{F}=\left(6t\hat{i}+6{t}^{2}\hat{j}\right)N. The power developed by the force at the time tt is given by:JEE Main/MCQ/Medium/Power
  149. 149The ratio of powers of two motors is 3xx+1,\dfrac{3\sqrt{x}}{\sqrt{x+1}}, that are capable of raising 300kg300kg water in 55 minutes and 50kg50kg water in 22 minutes respectively from a well of 100m100m deep. The value of xx will beJEE Main/MCQ/Medium/Power
  150. 150To maintain a speed of 80kmh−180km{h}^{-1} by a bus of mass 500kg500kg on a plane rough road for 4km4km distance, the work done by the engine of the bus will be _____ kJkJ. [The coefficient of friction between tyre of bus and road is 0.040.04]JEE Main/Numerical/Medium/Power
  151. 151A block of mass 5kg5kg starting from rest pulled up on a smooth incline plane making an angle of 30∘30^{\circ} with horizontal with an effective acceleration of 1ms−21m{s}^{-2}. The power delivered by the puling force at t=10st=10s from the start is _____ WW.
    [Use     g=10ms−2g=10m{s}^{-2}]
    (Calculate the nearest integer value)    JEE Main/Numerical/Medium/Power
  152. 152If the maximum load carried by an elevator is 1400kg1400kg (600kg-Passengers+800kg-elevator)(600kg\text{-Passengers}+800kg\text{-elevator}) , which is moving up with a uniform speed of 3ms−13m{s}^{-1} and the frictional force acting on it is 2000N2000N, then the maximum power used by the motor is _____________kW.(g=10ms−2)kW.\left(g=10m{s}^{-2}\right)JEE Main/Numerical/Medium/Power
  153. 153A body of mass 2kg2kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power PP. Its displacement in 4s4s is 13α2Pm\dfrac{1}{3}{\alpha }^{2}\sqrt{P}m. The value of α\alpha will be ______.JEE Main/Numerical/Medium/Power
  154. 154A body of mass 1kg1kg begins to move under the action of a time dependent force F⃗=(ti^+3t2j^)N\vec{F}=\left(t\hat{i}+3{t}^{2}\hat{j}\right)N, where i^\hat{i} and j^\hat{j} are the unit vectors along xx and yy axis. The power developed by above force, at the time t=2st=2s, will be _______WW.JEE Main/Numerical/Medium/Power
  155. 155Sand is being dropped from a stationary dropper at a rate of 0.5kgs−10.5kg{s}^{-1} on a conveyor belt moving with a velocity of 5ms−15m{s}^{-1}. The power needed to keep belt moving with the same velocity will beJEE Main/MCQ/Medium/Power
  156. 156A particle of mass mm is moving in a circular path of constant radius rr such that its centripetal acceleration ac{a}_{c} is varying with time tt as ac=k2rt2{a}_{c}={k}^{2}r{t}^{2} , where kk is a constant. The power delivered to the particle by the force acting on it is -JEE Main/MCQ/Medium/Power
  157. 157An automobile of mass mm accelerates starting from the origin and initially at rest, while the engine supplies constant power PP. The position is given as a function of time by:JEE Main/MCQ/Medium/Power
  158. 158A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time tt is proportional to :-JEE Main/MCQ/Medium/Power
  159. 159A body of mass 2kg2kg is driven by an engine delivering a constant power of 1Js−11J{s}^{-1}. the body starts from rest and moves in a straight line. After 9s9s, the body has moved a distance (in mm)….JEE Main/Numerical/Medium/Power
  160. 160In a reactor, 2kg2kg of U23592U23592 fuel is fully used up in 3030 days. The energy released fission is 200MeV200MeV. Given that the Avogadro number, N=6.023×1026N=6.023\times {10}^{26} per kilo mole and 1eV=1.6×10−19J1eV=1.6\times {10}^{-19}J. The power output of the reactor is close to:JEE Main/MCQ/Medium/Power
  161. 161A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n2Rt2{n}^{2}R{t}^{2}, where nn is a constant. The power delivered to the particle by the force acting on it, is :JEE Main/MCQ/Medium/Power
  162. 162A car of weight W is on an inclined road that rises by 100 m over a distance of 1km and applies a constant frictional force W20\dfrac{W}{20} on the car. While moving uphill on the road at a speed of 10ms−110m{s}^{-1} , the car needs power P. If it needs power P2\dfrac{P}{2} while moving downhill at speed υυ then value of υυ is:JEE Main/MCQ/Medium/Power
  163. 163A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed vv, the electrical power output will be most likely proportional toJEE Main/MCQ/Medium/Power
  164. 164A 70 kg70 \mathrm{~kg} man leaps vertically into the air from a crouching position. To take the leap the man pushes the ground with a constant force FF to raise himself. The center of gravity rises by 0.5 m0.5 \mathrm{~m} before he leaps. After the leap the c.g. rises by another 1 m1 \mathrm{~m}. The maximum power delivered by the muscles is : (Take g=10 ms−2\mathrm{g}=10 \mathrm{~ms}^{-2} )JEE Main/MCQ/Medium/Power
  165. 165A body of mass mm is accelerated uniformly from rest to a speed vv in a time TT. The instantaneous power delivered to the body as a function time is given byJEE Main/MCQ/Medium/Power
  166. 166A body of mass mm, accelerates uniformly from rest to v1v_1 in time t1t_1. The instantaneous power delivered to the body as a function of time tt isJEE Main/MCQ/Medium/Power
  167. 167A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time ' tt ' is proportional toJEE Main/MCQ/Medium/Power
  168. 168In case of vertical circular motion of a particle by a thread of length rr if the tension in the thread is zero at an angle 30∘30^{\circ} shown in figure, the velocity at the bottom point (A)(A) of the circular path is (g=g= gravitational acceleration)
    JEE Main/MCQ/Medium/Circular motion/With diagram
  169. 169A body of mass ' \(m\) ' connected to a massless and unstretchable string goes in verticle circle of radius ' \(R\) 'under gravity \(g\). The other end of the string is fixed at the center of circle. If velocity at top of circular path is \(n \sqrt{g R}\), where, \(n \geqslant 1\), then ratio of kinetic energy of the body at bottom to that at top of the circle isJEE Main/MCQ/Medium/Circular motion
  170. 170A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point AA is 10 m/s10 \mathrm{~m} / \mathrm{s}. The ratio of its kinetic energies at point BB and CC is :



    (Take acceleration due to gravity as     10 m/s210 \mathrm{~m} / \mathrm{s}^2 )    JEE Main/MCQ/Medium/Circular motion/With diagram
  171. 171A bob of mass mm is suspended at a point OO by a light string of length ll and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity v0v_0 at the point ' A ', the string becomes slack when, the bob reaches at the point ' D '. The ratio of the kinetic energy of the bob at the points BB and CC is ______ -.

    JEE Main/MCQ/Medium/Circular motion/With diagram
  172. 172A circular table is rotating with an angular velocity of ωrad/s\omega \mathrm{rad} / \mathrm{s} about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of 1 m1 \mathrm{~m} on the groove. All the surfaces are smooth. If the radius of the table is 3 m3 \mathrm{~m}, the radial velocity of the ball w.r.t. the table at the time ball leaves the table is x2ωm/sx \sqrt{2} \omega \mathrm{m} / \mathrm{s}, where the value of xx is _____.
    JEE Main/Numerical/Medium/Circular motion/With diagram
  173. 173A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle (θ)(\theta ) of thread deflection in the extreme position will be :JEE Main/MCQ/Medium/Circular motion
  174. 174A stone tide to a string of length LL is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed uu. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is x(u2−gL)\sqrt{x\left({u}^{2}-gL\right)}. The value of xx isJEE Main/MCQ/Medium/Circular motion
  175. 175For a particle in uniform circular motion, the acceleration a⃗\vec{a} at any point P(R,θ)P\left(R,\theta \right) on the circular path of radius RR is (when θ\theta is measured from the positive xx-axis and vv is uniform speed):JEE Main/MCQ/Medium/Circular motion
  176. 176A stone of mass mm, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string isJEE Main/MCQ/Medium/Circular motion
  177. 177Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to :

    (Take the radius of the drum to be 1.25 m and its axle to be horizontal) :    JEE Main/MCQ/Medium/Circular motion
  178. 178If a body moving in a circular path maintains constant speed of 10ms−110m{s}^{-1} , then which of the following correctly describes the relation between acceleration and radius?JEE Main/MCQ/Medium/Circular motion
  179. 179
    A particle is released on a vertical smooth semicircular track from point     XX so that, OXOX makes angle θ\theta from the vertical (see figure). The normal reaction of the track on the particle vanishes at the point YY where OYOY makes an angle ϕ\phi with the horizontal. Then    JEE Main/MCQ/Medium/Circular motion/With diagram
  180. 180A bullet of mass 10 g10 \mathrm{~g} and speed 500 m/s500 \mathrm{~m} / \mathrm{s} is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m1.0 \mathrm{~m} wide and weighs 12 kg12 \mathrm{~kg}. It is hinged at one end and rotates about a vertical axis practically without friction. The angular speed of the door just after the bullet embeds into it will be :JEE Main/MCQ/Medium/Circular motion
  181. 181Two cars of masses m1m_1 and m2m_2 are moving in circles of radii r1r_1 and r2r_2, respectively. Their speeds are such that they make complete circles in the same time tt. The ratio of their centripetal acceleration isJEE Main/MCQ/Medium/Circular motion
  182. 182An annular ring with inner and outer radii R1R_1 and R2R_2 is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, F1/F2F_1 / F_2 isJEE Main/MCQ/Medium/Circular motion
  183. 183Which of the following statements is false for a particle moving in a circle with a constant angular speed?JEE Main/MCQ/Medium/Circular motion

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