Physics · JEE Main

Center of Mass, Momentum & Collision

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

102MCQ28Numerical37With diagram
Start with question 1 Revise Rotational Motion first
  1. 1The position of an object having mass 0.10.1 kg as a function of time tt is given as r⃗=(10t2i^+5t3j^)\vec{r} = \left(10t^2\hat{i} + 5t^3\hat{j}\right) m. At t=1t = 1 s, which of the following statements are correct?
    A. The linear momentum     p⃗=(2i^+1.5j^)\vec{p} = \left(2\hat{i} + 1.5\hat{j}\right) kg·m/s.
    B. The force acting on the object     F⃗=(2i^+3j^)\vec{F} = \left(2\hat{i} + 3\hat{j}\right) N.
    C. The angular momentum of the object about its origin     L⃗=15k^\vec{L} = 15\hat{k} J·s.
    D. The torque acting on the object about its origin     τ⃗=20k^\vec{\tau} = 20\hat{k} N·m.
    Choose the correct answer from the options given below :    JEE Main/MCQ/Medium/momentum
  2. 2A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2:2:32: 2: 3. The two pieces of equal masses fly off perpendicular to each other with a speed of 18 m/s18 \mathrm{~m} / \mathrm{s} each. The velocity of the heavier fragment is ____\_\_\_\_ m/s\mathrm{m} / \mathrm{s}.JEE Main/MCQ/Medium/momentum
  3. 3Given below are two statements :
    Statement I: For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles.
    Statement II: The total kinetic energy can be the sum of kinetic energy of the center of mass w.r.t to the origin and the kinetic energy of all the particles w.r.t. the center of mass as the reference.
    In the light of the above statements, choose the correct answer from the options given below :    JEE Main/MCQ/Medium/momentum
  4. 4
    Consider two blocks A and B of masses     m1=10 kgm_1=10 \mathrm{~kg} and m2=5 kgm_2=5 \mathrm{~kg} that are placed on a frictionless table. The block A moves with a constant speed v=3 m/sv=3 \mathrm{~m} / \mathrm{s} towards the block B kept at rest. A spring with spring constant k=3000 N/m\mathrm{k}=3000 \mathrm{~N} / \mathrm{m} is attached with the block B as shown in the figure. After the collision, suppose that the blocks A and B, along with the spring in constant compression state, move together, then the compression in the spring is, (Neglect the mass of the spring)    JEE Main/MCQ/Medium/momentum/With diagram
  5. 5Three bodies A, B and C have equal kinetic energies and their masses are 400 g400 \mathrm{~g}. 1.2 kg1.2 \mathrm{~kg} and 1.6 kg1.6 \mathrm{~kg} respectively. The ratio of their linear momenta is :JEE Main/MCQ/Medium/momentum
  6. 6When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be:JEE Main/MCQ/Medium/momentum
  7. 7Four particles A,B,C,DA, B, C, D of mass m2,m,2m,4m\frac{m}{2}, m, 2 m, 4 m, have same momentum, respectively. The particle with maximum kinetic energy is :JEE Main/MCQ/Medium/momentum
  8. 8A body of mass 1000kg1000kg is moving horizontally with a velocity 6ms−16m{s}^{-1}. If 200kg200kg extra mass is added, the final velocity (in ms−1m{s}^{-1}) is:JEE Main/MCQ/Medium/momentum
  9. 9Two bodies are having kinetic energies in the ratio 16:9.16:9. If they have same linear momentum, the ratio of their masses respectively is:JEE Main/MCQ/Medium/momentum
  10. 10A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is 1:21/31:{2}^{1/3}. Their respective speed have a ratio of n:1n:1. The value of nn is_________JEE Main/Numerical/Medium/momentum
  11. 11An average force of 125N125N is applied on a machine gun firing bullets each of mass 10g10g at the speed of 250ms−1250m{s}^{-1} to keep it in position. The number of bullets fired per second by the machine gun is :JEE Main/MCQ/Medium/momentum
  12. 12A machine gun of mass 10kg10kg fires 20g20g bullets at the rate of 180180 bullets per minute with a speed of 100ms–1100m{s}^{–1} each. The recoil velocity of the gun is :JEE Main/MCQ/Medium/momentum
  13. 13A body of mass 8kg8kg and another of mass 2kg2kg are moving with equal kinetic energy. The ratio of their respective momenta will beJEE Main/MCQ/Medium/momentum
  14. 14A body of mass MM at rest explodes into three pieces, in the ratio of masses 1:1:21:1:2. Two smaller pieces fly off perpendicular to each other with velocities of 30ms−130{ms}^{-1} and 40ms−140{ms}^{-1} respectively. The velocity of the third piece will beJEE Main/MCQ/Medium/momentum
  15. 15A man of 60kg60kg is running on the road and suddenly jumps into a stationary trolly car of mass 120kg120kg. Then the trolly car starts moving with velocity 2ms−12{ms}^{-1}. The velocity of the running man was _____ ms−1m{s}^{-1}, when he jumps into the car.JEE Main/Numerical/Medium/momentum
  16. 16A bullet of 10g10g, moving with velocity vv, collides head-on with the stationary bob of a pendulum and recoils with velocity 100ms−1100m{s}^{-1}. The length of the pendulum is 0.5m0.5m and mass of the bob is 1kg1kg. The minimum value of vinms−1v\text{in}m{s}^{-1}, so that the pendulum describes a circle. (Assume the string to be inextensible and g=10ms−2g=10m{s}^{-2} )
    JEE Main/Numerical/Medium/momentum/With diagram
  17. 17A large block of wood of mass M=5.99kgM=5.99kg is hanging from two long massless cords. A bullet of mass m=10gm=10g is fired into the block and gets embedded in it. The (block ++ bullet) then swing upwards, their center of mass rising a vertical distance h=9.8cmh=9.8cm before the (block ++ bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before the collision is: (Take g=9.8ms−2g=9.8{ms}^{-2})
    JEE Main/MCQ/Medium/momentum/With diagram
  18. 18Particle AA of mass m1{m}_{1} moving with velocity (3i^+j^)ms−1\left(\sqrt{3}\hat{i}+\hat{j}\right){ms}^{-1} collides with another particle BB of mass m2{m}_{2} which is at rest initially. Let v⃗1{\vec{v}}_{1} and v⃗2{\vec{v}}_{2} be the velocities of particles AA and BB after collision respectively. If m1=2m2{m}_{1}=2{m}_{2} and after collision v⃗1−(i^+3j^)ms−1{\vec{v}}_{1}-\left(\hat{i}+\sqrt{3}\hat{j}\right){ms}^{-1}, the angle between v⃗1{\vec{v}}_{1} and v⃗2{\vec{v}}_{2} is :JEE Main/MCQ/Medium/momentum
  19. 19A thin rod of mass 0.9kg0.9kg and length 1m1m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0.1kg0.1kg moving in a straight line with velocity 80ms−180m{s}^{-1} hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rads−1rad{s}^{-1}) of the rod immediately after the collision will be …………
    JEE Main/Numerical/Medium/momentum/With diagram
  20. 20Consider a uniform rod of mass M=4mM=4m and length ll pivoted about its centre. A mass mm moving with velocity vv making angle θ=π4\theta =\dfrac{\pi }{4} to the rod’s long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is:JEE Main/MCQ/Medium/momentum
  21. 21A man (mass =50kg=50 kg ) and his son (mass =20kg=20 kg ) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70ms−10.70 m{s}^{-1} with respect to the man. The speed of the man with respect to the surface is:JEE Main/MCQ/Medium/momentum
  22. 22A particle of mass mm is moving with speed 2v2\text{v} and collides with a mass 2m2m moving with speed v\text{v} in the same direction. After the collision, the first mass is stopped completely while the second one splits into two particles each of mass m,m, which move at an angle 45o{45}^{o} with respect to the original direction. The speed of each of the moving particle will beJEE Main/MCQ/Medium/momentum
  23. 23An alpha- particle of mass mm suffers 1−1- dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing 6464% of its initial kinetic energy. The mass of the nucleus isJEE Main/MCQ/Medium/momentum
  24. 24A body of mass 1 kg1 \mathrm{~kg} falls freely from a height of 100 m100 \mathrm{~m}, on a platform of mass 3 kg3 \mathrm{~kg} which is mounted on a spring having spring constant k=1.25×106 N/m\mathrm{k}=1.25 \times 10^{6} \mathrm{~N} / \mathrm{m}. The bodysticks to the platform and the spring's maximum compression is found to be xx. Given that g=10 ms−2,g=10 \mathrm{~ms}^{-2}, the value of x\mathrm{x} will be close to :JEE Main/MCQ/Medium/momentum
  25. 25A piece of wood of mass 0.03kg0.03kg is dropped from the top of a 100m100m height building. At the same time, a bullet of mass 0.02kg0.02kg is fired vertically upward, with a velocity 100ms−1,100m{s}^{-1}, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is: (g=10ms−2)\left(g=10m{s}^{-2}\right)JEE Main/MCQ/Medium/momentum
  26. 26In a collinear collision, a particle with an initial speed v0{v}_{0} strikes a stationary particle of the same mass. If the final total kinetic energy is 5050% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after the collision, isJEE Main/MCQ/Medium/momentum
  27. 27A projectile of mass MM is fired so that the horizontal range is 4 km4 \mathrm{~km}. At the highest point the projectile explodes in two parts of masses M/4M / 4 and 3M/43 M / 4 respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is :JEE Main/MCQ/Medium/momentum
  28. 28A boy of mass 20 kg20 \mathrm{~kg} is standing on a 80 kg80 \mathrm{~kg} free to move long cart. There is negligible friction between cart and ground. Initially, the boy is standing 25 m25 \mathrm{~m} from a wall. If he walks 10 m10 \mathrm{~m} on the cart towards the wall, then the final distance of the boy from the wall will beJEE Main/MCQ/Medium/momentum
  29. 29A spring is compressed between two blocks of masses m1m_1 and m2m_2 placed on a horizontal frictionless surface as shown in the figure. When the blocks are released, they have initial velocity of v1v_1 and v2v_2 as shown. The blocks travel distances x1x_1 and x2x_2 respectively before coming to rest. The ratio (x1x2)\left(\frac{x_1}{x_2}\right) is
    JEE Main/MCQ/Medium/momentum/With diagram
  30. 30A projectile moving vertically upwards with a velocity of 200 ms−1200 \mathrm{~ms}^{-1} breaks into two equal parts at a height of 490 m490 \mathrm{~m}. One part starts moving vertically upwards with a velocity of 400 ms−1400 \mathrm{~ms}^{-1}. How much time it will take, after the break up with the other part to hit the ground?JEE Main/MCQ/Medium/momentum
  31. 31A block of mass 0.50 kg0.50 \mathrm{~kg} is moving with a speed of 2.00 m/s2.00 \mathrm{~m} / \mathrm{s} on a smooth surface. It strikes another mass of 1.00 kg1.00 \mathrm{~kg} and then they move together as a single body. The energy loss during the collision isJEE Main/MCQ/Medium/momentum
  32. 32A body of mass m=3.513 kgm=3.513 \mathrm{~kg} is moving along the xx-axis with a speed of 5.00 ms−15.00 \mathrm{~ms}^{-1}. The magnitude of its momentum is recorded asJEE Main/MCQ/Medium/momentum
  33. 33A bomb of mass 16 kg16 \mathrm{~kg} at rest explodes into two pieces of masses of 4 kg4 \mathrm{~kg} and 12 kg12 \mathrm{~kg}. The velocity of the 12 kg12 \mathrm{~kg} mass is 4 ms−14 \mathrm{~ms}^{-1}. The kinetic energy of the other mass isJEE Main/MCQ/Medium/momentum
  34. 34The block of mass MM moving on the frictionless horizontal surface collides with a spring of spring constant K\mathrm{K} and compresses it by length L\mathrm{L}. The maximum momentum of the block after collision is
    JEE Main/MCQ/Medium/momentum/With diagram
  35. 35The position of center of mass of three masses 22 kg, 33 kg and 1515 kg placed with respect to mid point (pp) of normal bisector, as shown in the figure is _______.
    JEE Main/MCQ/Medium/Centre of mass of discrete particles/With diagram
  36. 36A rod of length 5 L is bent right angle keeping one side length as 2 L.

    The position of the centre of mass of the system: (Consider     L=10 cm\mathrm{L}=10 \mathrm{~cm})    JEE Main/MCQ/Medium/Centre of mass of discrete particles/With diagram
  37. 37The center of mass of a thin rectangular plate (fig - x ) with sides of length aa and bb, whose mass per unit area (σ)(\sigma) varies as σ=σ0xab\sigma=\frac{\sigma_0 x}{a b} (where σ0\sigma_0 is a constant), would be \qquad
    JEE Main/MCQ/Medium/Centre of mass of discrete particles/With diagram
  38. 38In a system two particles of masses m1=3 kgm_1=3 \mathrm{~kg} and m2=2 kgm_2=2 \mathrm{~kg} are placed at certain distance from each other. The particle of mass m1m_1 is moved towards the center of mass of the system through a distance 2 cm2 \mathrm{~cm}. In order to keep the center of mass of the system at the original position, the particle of mass m2m_2 should move towards the center of mass by the distance _____ cm\mathrm{cm}.JEE Main/Numerical/Medium/Centre of mass of discrete particles
  39. 39The identical spheres each of mass 2M2M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 4m4m each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is 42x\dfrac{4\sqrt{2}}{x}, where the value of xx is ________.JEE Main/Numerical/Medium/Centre of mass of discrete particles
  40. 40A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3:23:2. The ratio of their nuclear sizes will be (x3)13{\left(\dfrac{x}{3}\right)}^{\dfrac{1}{3}}. The value of ‘xx’ is:JEE Main/Numerical/Medium/Centre of mass of discrete particles
  41. 41Two bodies of mass 1kg1kg and 3kg3kg have position vectors i^+2j^+k^\hat{i}+2\hat{j}+\hat{k} and −3i^−2j^+k^-3\hat{i}-2\hat{j}+\hat{k} respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :JEE Main/MCQ/Medium/Centre of mass of discrete particles
  42. 42Three identical spheres each of mass MM are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3m3m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be xm\sqrt{x}m. The value of xx isJEE Main/Numerical/Medium/Centre of mass of discrete particles
  43. 43Two blocks of masses 10kg10kg and 30kg30kg are placed on the same straight line with coordinates (0,0)cm\left(0,0\right)cm and (x,0)cm\left(x,0\right)cm respectively. The block of 10kg10kg is moved on the same line through a distance of 6cm6cm towards the other block. The distance through which the block of 30kg30kg must be moved to keep the position of centre of mass of the system unchanged isJEE Main/MCQ/Medium/Centre of mass of discrete particles
  44. 44Three point particles of masses 1.0kg,1.5kg1.0kg,1.5kg and 2.5kg2.5kg are placed at three corners of a right angle triangle of sides 4.0cm,3.0cm4.0cm,3.0cm and 5.0cm5.0cm as shown in the figure. The centre of mass of the system is at a point:
    JEE Main/MCQ/Medium/Centre of mass of discrete particles/With diagram
  45. 45Three particles of masses 50g50g, 100g100g and 150g150g are placed at the vertices of an equilateral triangle of side 1m1m (as shown in the figure). The (x,y)\left(x, y\right) coordinates of the centre of mass will be:

    JEE Main/MCQ/Medium/Centre of mass of discrete particles/With diagram
  46. 46Consider a two particle system with particles having masses m1m_1 and m2m_2. If the first particle is pushed towards the centre of mass through a distance dd, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?JEE Main/MCQ/Medium/Centre of mass of discrete particles
  47. 47A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, isJEE Main/MCQ/Medium/Centre of mass of continuous mass distribution
  48. 48Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will beJEE Main/MCQ/Medium/Centre of mass of continuous mass distribution
  49. 49A uniform thin metal plate of mass 10 kg10 \mathrm{~kg} with dimensions is shown. The ratio of x\mathrm{x} and y\mathrm{y} coordinates of center of mass of plate in n9\frac{n}{9}. The value of nn is ________
    JEE Main/Numerical/Medium/Centre of mass of continuous mass distribution/With diagram
  50. 50The distance of centre of mass from end AA of a one dimensional rod (AB)\left(AB\right) having mass density ρ=ρ0(1−x2L2)kgm−1\rho ={\rho }_{0}\left(1-\dfrac{{x}^{2}}{{L}^{2}}\right)kg{m}^{-1} and length LL (in meter) is 3Lαm\dfrac{3L}{\alpha }m. The value of α\alpha is _____ (where xx is the distance form end AA)JEE Main/Numerical/Medium/Centre of mass of continuous mass distribution
  51. 51The position of the centre of mass of a uniform semi-circular wire of radius RR placed in x−yx-y plane with its centre at the origin and the line joining its ends as x−x-axis is given by, (0,xRπ).\left(0,\dfrac{xR}{\pi }\right). Then, the value of ∣x∣|x| is ..JEE Main/Numerical/Medium/Centre of mass of continuous mass distribution
  52. 52The disc of mass MM with uniform surface mass density σ\sigma is shown in the figure. The center of mass of the quarter disc (the shaded area) is at the position (xa3π,xa3π)\left(\dfrac{xa}{3\pi },\dfrac{xa}{3\pi }\right) where xx is _______ . (Round off to the Nearest Integer) [aa is an area as shown in the figure]
    JEE Main/Numerical/Medium/Centre of mass of continuous mass distribution/With diagram
  53. 53A circular hole of radius (a2)\left(\dfrac{a}{2}\right) is cut out of a circular disc of radius aa as shown in figure. The centroid of the remaining circular portion with respect to point OO will be:
    JEE Main/MCQ/Medium/Centre of mass of continuous mass distribution/With diagram
  54. 54The centre of mass of a solid hemisphere of radius 8cm8cm is xcmxcm from the centre of the flat surface. Then value of xx isJEE Main/Numerical/Medium/Centre of mass of continuous mass distribution
  55. 55A square shaped hole of sidel=a2l=\dfrac{a}{2} is carved out at a distance d=a2d=\dfrac{a}{2} from the centre 'OO' of a uniform circular disk of radius a. If the distance of the centre of mass of the remaining portion from OO is −ax-\dfrac{a}{x}, value of XX (to the nearest integer) is :
    JEE Main/Numerical/Medium/Centre of mass of continuous mass distribution/With diagram
  56. 56A rod of length ll has non-uniform linear mass density given by ρ(x)=a+b(xl)2,\rho \left(x\right)=a+b{\left(\dfrac{x}{l}\right)}^{2}, where aa and bb are constants and 0≤x≤l0\leq x\leq l The value of xx for the centre of mass of the rod is at:JEE Main/MCQ/Medium/Centre of mass of continuous mass distribution
  57. 57As shown in figure. When a spherical cavity (centred at OO ) of radius 11 is cut out of a uniform sphere of radius RR (centred at CC ), the centre of mass of remaining (shaded part of sphere is at G,G, i.e., on the surface of the cavity. RR can be determined by the equation:
    JEE Main/MCQ/Medium/Centre of mass of continuous mass distribution/With diagram
  58. 58The coordinates of the centre of mass of a uniform flag-shaped lamina (thin flat plate) of mass 4kg4kg. (The coordinates of the same are shown in the figure) are:

    JEE Main/MCQ/Medium/Centre of mass of continuous mass distribution/With diagram
  59. 59A uniform rectangular thin sheet ABCDABCD of mass MM has length aa and breadth bb, as shown in the figure. If the shaded portion HBGOHBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be:

    JEE Main/MCQ/Medium/Centre of mass of continuous mass distribution/With diagram
  60. 60The position vector of the center of mass r⃗cm{\vec{r}}_{cm} of an asymmetric uniform bar of negligible area of cross-section as shown in figure is:

    JEE Main/MCQ/Medium/Centre of mass of continuous mass distribution/With diagram
  61. 61In the figure shown ABCABC is a uniform wire. If the center of mass of the wire lies vertically below point AA, then BCAB\dfrac{BC}{AB} is close to

    JEE Main/MCQ/Medium/Centre of mass of continuous mass distribution/With diagram
  62. 62A uniform thin rod AB of length LL has linear mass density μ(x)=a+bxL\mu \left(x\right)=a+\dfrac{bx}{L}, where xx is measured from A. If the CM of the rod lies at a distance of (712L)\left(\dfrac{7}{12}L\right) from A, then aa and bb are related as:JEE Main/MCQ/Medium/Centre of mass of continuous mass distribution
  63. 63Distance of the centre of mass of a solid uniform cone from its vertex is z0{z}_{0}. If the radius of its base is RR and its height is hh then z0{z}_{0} is equal to:JEE Main/MCQ/Medium/Centre of mass of continuous mass distribution
  64. 64A thin rod of length ' LL ' is lying along the xx-axis with its ends at x=0x=0 and x=Lx=L. Its linear density (mass/length) varies with xx ask (xL)n\left(\frac{x}{L}\right)^n, where nn can be zero or any positive number. If the position xCMx_{\mathrm{CM}} of the centre of mass of the rod is plotted against ' nn ', which of the following graphs best approximates the dependence of xCMx_{\mathrm{CM}} on nn ?JEE Main/MCQ/Medium/Centre of mass of continuous mass distribution
  65. 65A circular disc of radius R\mathrm{R} is removed from a bigger circular disc of radius 2R\mathrm{2R} such that the circumferences of the discs coincide. The centre of mass of the new disc is α/R\mathrm{\alpha / R} from the centre of the bigger disc. The value of α\mathrm{\alpha} isJEE Main/MCQ/Medium/Centre of mass of continuous mass distribution
  66. 66Two identical bodies AA and BB of equal masses have initial velocities v1⃗=4i^\vec{v_1} = 4\hat{i} m/s and v2⃗=4j^\vec{v_2} = 4\hat{j} m/s respectively. The body AA has acceleration a1⃗=6i^+6j^\vec{a_1} = 6\hat{i} + 6\hat{j} m/s2^2 while the acceleration of the other body BB is zero. The centre of mass of the two bodies moves in __________ path.JEE Main/MCQ/Medium/Motion of centre of mass
  67. 67Two blocks of masses 22 kg and 11 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in 22 s is _______ m. (Take g=10g = 10 m/s2^2)
    JEE Main/MCQ/Medium/Motion of centre of mass/With diagram
  68. 68Four particles A,B,CA,B,C and DD with masses mA=m,mB=2m,mC=3m{m}_{A}=m,{m}_{B}=2m,{m}_{C}=3m  and mD=4m{m}_{D}=4m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is:
    JEE Main/MCQ/Medium/Motion of centre of mass/With diagram
  69. 69A body AA of mass MM while falling vertically downwards under gravity breaks into two parts; a body B of mass 1/3M1 / 3 \mathrm{M} and a body C\mathrm{C} of mass 2/3M2 / 3 \mathrm{M}. The centre of mass of bodies B\mathrm{B} and C\mathrm{C} taken together shifts compared to that of body A\mathrm{A} towardsJEE Main/MCQ/Medium/Motion of centre of mass
  70. 70Two identical particles move towards each other with velocity 2v2 v and vv respectively. The velocity of centre of mass isJEE Main/MCQ/Medium/Motion of centre of mass
  71. 71A player caught a cricket ball of mass 150 g150 \mathrm{~g} moving at a speed of 20 m/s20 \mathrm{~m} / \mathrm{s}. If the catching process is completed in 0.1 s0.1 \mathrm{~s}, the magnitude of force exerted by the ball on the hand of the player is:JEE Main/MCQ/Medium/Impulse
  72. 72A uniform rod ABAB of mass 2kg2kg and Length 30cm30cm at rest on a smooth horizontal surface. An impulse of force 0.2Ns0.2Ns is applied to end B. The time taken by the rod to turn through at right angles will be πxs,\dfrac{\pi }{x}s, where x=x= ____.JEE Main/Numerical/Medium/Impulse
  73. 73A spherical body of mass 100g100g is dropped from a height of 10m10m from the ground. After hitting the ground, the body rebounds to a height of 5m5m. The impulse of force imparted by the ground to the body is given by: (given g=9.8ms−2g=9.8m{s}^{-2})JEE Main/MCQ/Medium/Impulse
  74. 74A bullet of 10g10g leaves the barrel of gun with a velocity of 600ms−1600m{s}^{-1}. If the barrel of gun is 50cm50cm long and mass of gun is 3kg,3kg, then value of impulse supplied to the gun will be:JEE Main/MCQ/Medium/Impulse
  75. 75Figures (a), (b), (c) and (d) show variation of force with time.

    The impulse is highest in figure.    JEE Main/MCQ/Medium/Impulse/With diagram
  76. 76In two different experiments, an object of mass 5kg5kg moving with a speed of 25ms−125{ms}^{-1} hits two different walls and comes to rest within
    (i)     33 second, (ii) 55 seconds, respectively.
    Choose the correct option out of the following :    JEE Main/MCQ/Medium/Impulse
  77. 77A ball of mass 0.15kg0.15kg hits the wall with its initial speed of 12ms−112m{s}^{-1} and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100N100N. calculate the time duration of the contact of ball with the wall.JEE Main/MCQ/Medium/Impulse
  78. 78Two billiard balls of mass 0.05kg0.05kg each moving in opposite directions with 10ms−110{ms}^{-1} collide and rebound with the same speed. If the time duration of contact is t=0.005st=0.005s, then what is the force exerted on the ball due to each other?JEE Main/MCQ/Medium/Impulse
  79. 79A batsman hits back a ball of mass 0.4kg0.4kg straight in the direction of the bowler without changing its initial speed of 15ms−115{ms}^{-1}. The impulse imparted to the ball is _____ NsNs.JEE Main/Numerical/Medium/Impulse
  80. 80If 1022{10}^{22} gas molecules each of mass 10−26{10}^{-26} kg collides with a surface (perpendicular to it) elastically per second over an area 1m21{m}^{2} with a speed 104m/s,{10}^{4}m/s, the pressure exerted by the gas molecules will be of the order of:JEE Main/MCQ/Medium/Impulse
  81. 81The figure shows the position - time (x−t)(x-t) graph of one-dimensional motion of a body of mass 0.4 kg0.4 \mathrm{~kg}. The magnitude of each impulse is
    JEE Main/MCQ/Medium/Impulse/With diagram
  82. 82In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of 10 m/s10 \mathrm{~m} / \mathrm{s} and 30 m/s30 \mathrm{~m} / \mathrm{s}, respectively, strike each other and stick together. The rise in temperature (in ∘C{ }^{\circ} \mathrm{C}), if all the heat produced during the collision is retained by these spheres, is : (specific heat of sphere material 31cal/kg.∘C31 \mathrm{cal} / \mathrm{kg}.{ }^{\circ} \mathrm{C} and 1cal=4.2 J1 \mathrm{cal}=4.2 \mathrm{~J})JEE Main/MCQ/Medium/Collisions
  83. 83Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

    Assertion (A) :

    Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities     vA=5 m/s,vB=2 m/s,vC=4 m/sv_{\mathrm{A}}=5 \mathrm{~m} / \mathrm{s}, v_{\mathrm{B}}=2 \mathrm{~m} / \mathrm{s}, v_{\mathrm{C}}=4 \mathrm{~m} / \mathrm{s}. If we wait sufficiently long for elastic collision to happen, then vA=4 m/s,vB=2 m/sv_{\mathrm{A}}=4 \mathrm{~m} / \mathrm{s}, v_{\mathrm{B}}=2 \mathrm{~m} / \mathrm{s}, vC=5 m/sv_{\mathrm{C}}=5 \mathrm{~m} / \mathrm{s} will be the final velocities.

    Reason (R): In an elastic collision between identical masses, two objects exchange their velocities.
    In the light of the above statements, choose the correct answer from the options given below :    JEE Main/MCQ/Medium/Collisions/With diagram
  84. 84As shown below, bob \(A\) of a pendulum having massless string of length ' \(R\) ' is released from \(60^{\circ}\) to the vertical. It hits another bob \(B\) of half the mass that is at rest on a friction less table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity.)
    JEE Main/MCQ/Medium/Collisions/With diagram
  85. 85A simple pendulum of length 1m1m has a wooden bob of mass 1kg1kg. It is struck by a bullet of mass 10−2kg{10}^{-2}kg moving with a speed of 2×102ms−12\times {10}^{2}m{s}^{-1}. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use g=10ms−2g=10m{s}^{-2})JEE Main/MCQ/Medium/Collisions
  86. 86A particle of mass mm moving with velocity vv collides with a stationary particle of mass 2m2m. After collision, they stick together and continue to move together with velocityJEE Main/MCQ/Medium/Collisions
  87. 87A ball is dropped from a height of 20m20m. If the coefficient of restitution for the collision between ball and floor is 0.50.5, after hitting the floor, the ball rebounds to a height of ______ mm.JEE Main/Numerical/Medium/Collisions
  88. 88100100 balls each of mass mm moving with speed vv simultaneously strike a wall normally and reflected back with same speed, in time tsts. The total force exerted by the balls on the wall isJEE Main/MCQ/Medium/Collisions
  89. 89A ball of mass 200g200g rests on a vertical post of height 20m20m. A bullet of mass 10g10g, travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance 30m30m and the bullet at a distance of 120m120m from the foot of the post. The value of initial velocity of the bullet will be (if g=10ms−2g=10m{s}^{-2}) :JEE Main/MCQ/Medium/Collisions
  90. 90As per the given figure, a small ball PP slides down the quadrant of a circle and hits the other ball QQ of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball QQ after collision will be : (g=10ms−2)(g=10m{s}^{-2})
    JEE Main/MCQ/Medium/Collisions/With diagram
  91. 91A body of mass 1kg1kg collides head on elastically with a stationary body of mass 3kg3kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2ms−12m{s}^{-1}. The initial speed of the smaller body before collision is ______ ms−1m{s}^{-1}.JEE Main/Numerical/Medium/Collisions
  92. 92A pendulum of length 2m2m consists of a wooden bob of mass 50g50g. A bullet of mass 75g75g is fired towards the stationary bob with a speed vv. The bullet emerges out of the bob with a speed v3\dfrac{v}{3} and the bob just completes the vertical circle. The value of vv is _____ ms−1m{s}^{-1}
    (if     g=10ms−2g=10m{s}^{-2}).    JEE Main/Numerical/Medium/Collisions
  93. 93What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 55 times its mass?
    (Assume the collision to be head-on elastic collision)    JEE Main/MCQ/Medium/Collisions
  94. 94A body of mass MM moving at speed V0{V}_{0} collides elastically with a mass mm at rest. After the collision, the two masses move at angles θ1{\theta }_{1} and θ2{\theta }_{2} with respect to the initial direction of motion of the body of mass M.M.. The largest possible value of the ratio Mm,\dfrac{M}{m}, for which the angles θ1{\theta }_{1} and θ2{\theta }_{2} will be equal, is :JEE Main/MCQ/Medium/Collisions
  95. 95Three objects A,BA,B and CC are kept in a straight line on a frictionless horizontal surface. The masses of A,BA,B and CC are m,2mm,2m and 2m2m respectively. AA moves towards BB with a speed of 9ms−19m{s}^{-1} and makes an elastic collision with it. Thereafter BB makes a completely inelastic collision with C.C. All motions occur along the same straight line. The final speed of CC is :
    JEE Main/MCQ/Medium/Collisions/With diagram
  96. 96A body of mass 2kg2kg moving with a speed of 4ms−14m{s}^{-1} makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is x/10x/10. Find the value of x.JEE Main/Numerical/Medium/Collisions
  97. 97A rod of mass MM and length LL is lying on a horizontal frictionless surface. A particle of mass mm travelling along the surface hits at one end of the rod with a velocity uu in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses (mM)\left(\dfrac{m}{M}\right) is 1x.\dfrac{1}{x}. The value of xx will beJEE Main/Numerical/Medium/Collisions
  98. 98A body having specific charge 8μCg−18\mu C{g}^{-1} is resting on a frictionless plane at a distance 10cm10cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100Vm−1100V{m}^{-1} is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ____s.
    JEE Main/Numerical/Medium/Collisions/With diagram
  99. 99An object of mass m1{m}_{1} collides with another object of mass m2{m}_{2}, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses m2:m1{m}_{2}:{m}_{1} is :JEE Main/MCQ/Medium/Collisions
  100. 100A ball of mass 10kg10kg moving with a velocity 103ms−110\sqrt{3}m{s}^{-1} along the xx -axis, hits another ball of mass 20kg20kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along yy -axis with a speed of 10ms−1.10m{s}^{-1}. The second piece starts moving at an angle of 30∘30^{\circ} with respect to the xx -axis. The velocity of the ball moving at 30∘30^{\circ} with xx -axis is xms−1.xm{s}^{-1}. The configuration of pieces after the collision is shown in the figure below. The value of xx to the nearest integer is
    JEE Main/Numerical/Medium/Collisions/With diagram
  101. 101A rubber ball is released from a height of 5m5m above the floor. It bounces back repeatedly, always rising to 81100\dfrac{81}{100} of the height through which it falls. Find the average speed of the ball. (Take g=10ms−2g=10{ms}^{-2})JEE Main/MCQ/Medium/Collisions
  102. 102Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
    Assertion A : Body     PP having mass MM moving with speed uu has head-on collision elastically with another body QQ having mass mm initially at rest. If m≪Mm≪M, body QQ will have a maximum speed equal to 2u2u after collision.
    Reason R : During elastic collision, the momentum and kinetic energy are both conserved.
    In the light of the above statements, choose the most appropriate answer from the options given below:    JEE Main/MCQ/Medium/Collisions
  103. 103A ball with a speed of 9ms−19m{s}^{-1} collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30∘30^{\circ} with the original direction. If the ratio of velocities of the balls after the collision is x:yx:y, then what is the value of xx?JEE Main/Numerical/Medium/Collisions
  104. 104Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial velocities of the two bodies (in degree) is -JEE Main/Numerical/Medium/Collisions
  105. 105A particle of mass 200MeVc−2200MeV{c}^{-2} collides with a hydrogen atom at rest. Soon after the collision, the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eVeV) is N4.\dfrac{N}{4}. The value of NN is: (Given the mass of the hydrogen atom to be 1GeVc−21GeV{c}^{-2}).........JEE Main/Numerical/Medium/Collisions
  106. 106Blocks of masses m,2m,4m\text{m}, 2\text{m}, 4\text{m} and 8m8\text{m} are arranged in a line of a frictionless floor. Another block of mass mm , moving with speed υυ along the same line (see figure) collides with mass mm in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8m8\text{m} starts moving the total energy loss is \text{p%} of the original energy. Value of ‘p\text{p} ’ is close to:
    JEE Main/MCQ/Medium/Collisions/With diagram
  107. 107A block of mass 1.9kg1.9kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1kg0.1kg collides with the block and sticks to it. If the velocity of the bullet is 20ms−120m{s}^{-1} in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take g=10ms−2g=10m{s}^{-2}. Assume there is no rotational motion and loss of energy after the collision is negligible.]JEE Main/MCQ/Medium/Collisions
  108. 108A particle of mass mm is moving along the xx-axis with initial velocity ui^u\hat{i}. It collides elastically with a particle of mass 10m10m at rest and then moves with half its initial kinetic energy (see figure). If sin⁡θ1=nsin⁡θ2\sin {\theta }_{1}=\sqrt{n}\sin {\theta }_{2} then value of n is ________.
    JEE Main/Numerical/Medium/Collisions/With diagram
  109. 109A particle of mass mm with an initial velocity ui^u\hat{i} collides perfectly elastically with a mass 3m3m at rest. It moves with a velocity vj^v\hat{j} after collision, then, vv is given byJEE Main/MCQ/Medium/Collisions
  110. 110A particle of mass m is projected with a speed u from the ground at an angle θ=π3\theta =\dfrac{\pi }{3} w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity ui^.u\hat{i}. The horizontal distance covered by the combined mass before reaching the ground is:JEE Main/MCQ/Medium/Collisions
  111. 111Two particles of equal mass mm have respective initial velocities ui^u\hat{i} and u(i^+j^2)u\left(\dfrac{\hat{i}+\hat{j}}{2}\right) . They collide completely inelastically. The energy lost in the process is:JEE Main/MCQ/Medium/Collisions
  112. 112A particle of mass mm is dropped from a height hh above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of 2gh.\sqrt{2gh}. If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of hg\sqrt{\dfrac{h}{g}} is:JEE Main/MCQ/Medium/Collisions
  113. 113A body AA of mass m=0.1kgm=0.1kg has an initial velocity of 3i^ms−13\hat{i}m{s}^{-1}. It collides elastically with another body BB of the same mass which has an initial velocity of 5j^ms−15\hat{j}m{s}^{-1}. After the collision, AA moves with a velocity v⃗=4(i^+j^)ms−1\vec{v}=4\left(\hat{i}+\hat{j}\right)m{s}^{-1}. The energy of BB after the collision is written as x10J\dfrac{x}{10}J. The value of xx isJEE Main/Numerical/Medium/Collisions
  114. 114Two particles of masses MM and 2Mare2M aremoving with speeds of 10ms−110m{s}^{-1} and 5ms−15m{s}^{-1}, as shown in the figure. They collide at the origin and after that they move along the indicated directions with speeds v1{v}_{1} and v2{v}_{2}, respectively. The values of v1{v}_{1} and v2{v}_{2} are, nearly

    JEE Main/MCQ/Medium/Collisions/With diagram
  115. 115A body of mass 2kg2kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body?JEE Main/MCQ/Medium/Collisions
  116. 116A body of mass m1{m}_{1} moving with an unknown velocity of v1i^,{v}_{1}\hat{i}, undergoes a collinear collision with a body of mass m2{m}_{2} moving with a velocity v2i^.{v}_{2}\hat{i}. After the collision, m1{m}_{1} and m2{m}_{2} move with velocities of v3i^{v}_{3}\hat{i} and v4i^,{v}_{4}\hat{i}, respectively. If m2=0.5m1{m}_{2}=0.5{m}_{1} and v3=0.5v1,{v}_{3}=0.5{v}_{1}, then v1{v}_{1} is:JEE Main/MCQ/Medium/Collisions
  117. 117A simple pendulum, made of a string of length ll and aa bob of mass m,m, is released from a small angle θ0.{\theta }_{0}. It strikes a block of mass M,M, kept on horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ1.{\theta }_{1}. Then MM is given by:JEE Main/MCQ/Medium/Collisions
  118. 118Three blocks A,BA,B and CC are lying on a smooth horizontal surface, as shown in the figure. AA and BB have equal masses, mm while CC has mass M.M. Block AA is given an initial speed vv towards BB due to which it collides with BB perfectly inelastically. The combined mass collides with C,C, also perfectly inelastically . 56th\dfrac{5}{6}\text{t}\text{h} of the initial kinetic energy is lost in the whole process. What is the value of M/mM/m?

    JEE Main/MCQ/Medium/Collisions/With diagram
  119. 119A proton of mass m\mathrm{m} collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of 90∘90^{\circ} with respect to each other. The mass of unknown particle is:JEE Main/MCQ/Medium/Collisions
  120. 120The mass of a hydrogen molecule is 3.32×10−27kg.3.32\times {10}^{-27}kg. If 1023{10}^{23} hydrogen molecules strike, per second, a fixed wall of the area 2cm22{cm}^{2} at an angle of 45o{45}^{o} to the normal, and rebound elastically with a speed of 103ms−1,{10}^{3}m{s}^{-1}, then the pressure on the wall is nearly:JEE Main/MCQ/Medium/Collisions
  121. 121It is found that if a neutron suffers an elastic collinear collision with a deuterium at rest, the fractional loss of its energy is Pd{P}_{d}, while for its similar collision with a carbon nucleus at rest, the fractional loss of energy is Pc{P}_{c}. The values of Pd{P}_{d} and Pc{P}_{c} are respectivelyJEE Main/MCQ/Medium/Collisions
  122. 122Two particles AA and BB of equal mass MM are moving with the same speed vv as shown in figure. They collide completely inelastic and move as a single particle CC. The angle θ\theta that the path of CC makes with the XX-axis is given by-

    JEE Main/MCQ/Medium/Collisions/With diagram
  123. 123A particle of mass m\text{m} moving in the xx direction with speed 2v2v is hit by another particle of mass 2m2m moving in the yy direction with speed v.v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to:JEE Main/MCQ/Medium/Collisions
  124. 124Three masses m,2 m\mathrm{m}, 2 \mathrm{~m} and 3 m3 \mathrm{~m} are moving in x−y\mathrm{x}-\mathrm{y} plane with speed 3u,2u3 \mathrm{u}, 2 \mathrm{u} and u\mathrm{u} respectively as shown in figure. The three masses collide at the same point at P\mathrm{P} and stick together. The velocity of resulting mass will be:
    JEE Main/MCQ/Medium/Collisions/With diagram
  125. 125This question has Statement−IStatement - I and Statement−IIStatement - II of the four choices given after the Statements, choose the one that best describes the two Statements.

    Statement−I:Statement - I: A point particle of mass mm moving with speed ν\nu collides with stationary point particle of mass MM. If the maximum energy loss possible is given as
    f(12mν2)f\left(\dfrac{1}{2}m{\nu }^{2}\right) then f=(mM+m)f=\left(\dfrac{m}{M+m}\right).

    Statement−II:Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.    JEE Main/MCQ/Medium/Collisions
  126. 126A moving particle of mass mm, makes a head on elastic collision with another particle of mass 2m2 m, which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close toJEE Main/MCQ/Medium/Collisions
  127. 127Two bodies AA and BB of mass mm and 2m2 m respectively are placed on a smooth floor. They are connected by a spring of negligible mass. AA third body CC of mass mm is placed on the floor. The body CC moves with a velocity v0v_0 along the line joining AA and BB and collides elastically with AA. At a certain time after the collision it is found that the instantaneous velocities of AA and BB are same and the compression of the spring is x0x_0. The spring constant kk will beJEE Main/MCQ/Medium/Collisions
  128. 128Statement-1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
    Statement-2 : Principle of conservation of momentum holds true for all kinds of collisions.
    Of the four choices given after the statements, choose the one that best describes the two statements.
    Of the four choices given after the statements, choose the one that best describes the two statements.    JEE Main/MCQ/Medium/Collisions
  129. 129A mass ' mm ' moves with a velocity vv and collides inelastically with another identical mass. After collision the 1st 1^{\text {st }} mass moves with velocity v/3v / \sqrt{3} in a direction perpendicular to the initial direction of motion. Find the speed of the 2nd 2^{\text {nd }} mass after collision
    JEE Main/MCQ/Medium/Collisions/With diagram
  130. 130A balloon and its content having mass MM is moving up with an acceleration ' aa '. The mass that must be released from the content so that the balloon starts moving up with an acceleration ' 3a′3 a^{\prime} will be
    (Take ' g ' as acceleration due to gravity)    JEE Main/MCQ/Medium/Variable mass system

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