Centre of Mass & Momentum PYQs Set 1 (PDF)

Set 1 of 4 · Questions 1-30 of 97

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Mere Teacher · Previous Year Questions NEET Physics · Centre of Mass & Momentum · Set 1 (Q1-30)
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1. $A system of two particles is having masses m_{1} and m_{2} . If the particle of mass m_{1} is pushed towards the centre of mass of particles through a distance d, by what distance the particle of mass m_{2} should be moved, so as to keep the centre of mass of particles at the original position?$ (1) $(\frac{m _{1}}{m _{1} + m _{2}} d)$ (2) $d$ (3) $(\frac{m _{1}}{m _{2}}) d$ (4) $(\frac{m _{2}}{m _{1}}) d$ 2. $Statement-1 In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. because Statement-2 In an elastic collision, the linear momentum of the system is conserved$ (1) $Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1$ (2) $Statement-1 is True,Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1$ (3) $Statement-1 is True, Statement-2 is False$ (4) $Statement-1 is False, Statement-2 is True.$ 3. $A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h . What is the speed of its centre of mass when the cylinder reaches its bottom?$ (1) $2 gh$ (2) $\frac{3}{4} gh$ (3) $\frac{4}{3} gh$ (4) $4 gh$ 4. $A circular plate A of radius 1.5 r is removed from one edge of a uniform circular plate B of radius 2 r. The distance of centre of mass of the remaining portion from the centre of the plate B is$ (1) $\frac{5 r}{12}$ (2) $\frac{9 r}{14}$ (3) $\frac{3 r}{4}$ (4) $\frac{7 r}{8}$ 5. $A circular ring of mass 10 kg rolls along a horizontal floor. The centre of mass of the ring has a speed 1.5 m / s . The work required to stop the ring is$ (1) $10 J$ (2) $- 6 J$ (3) $14.5 J$ (4) $- 22.5 J$ 6. $When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be:$ (1) $6 %$ (2) $600 %$ (3) $60 %$ (4) $500 %$ 7. $Distance of the centre of mass of a solid uniform cone from its vertex is z0. If the radius of its base is R and its height is h then z0 is equal to$ (1) $\frac{h ^{2}}{4 R}$ (2) $\frac{3 h}{4}$ (3) $\frac{5 h}{8}$ (4) $\frac{3 h ^{2}}{8 R}$ 8. $Two balls are thrown simultaneously in air. The acceleration of the centre of mass of the two balls when in air,$ (1) $is equal to g (Acceleration due to gravity)$ (2) $depends on the masses of the two balls$ (3) $depends on the direction of motion of the two balls.$ (4) $depends on the speeds of the two balls.$ 9. $A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct?$ (1) $h = R$ (2) $h = 2 R$ (3) $h = 0$ (4) $no relation between h and R.$ 10. $A solid sphere, disc and solid cylinder all of the same mass and made of the same material are allowed to roll down (from rest) on the inclined plane, then$ (1) $solid sphere reaches the bottom first$ (2) $solid sphere reaches the bottom last$ (3) $disc will reach the bottom first$ (4) $all reach the bottom at the same time$ 11. $A circular hole of radius 3 cm is cut out from a uniform circular disc of radius 6 cm . The centre of the hole is at 3 cm, from the centre of the original disc. The distance of centre of gravity of the resulting flat body from the centre of the original disc is$ (1) $0.5 cm$ (2) $1 cm$ (3) $1.5 cm$ (4) $0.75 cm$ 12. $Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg . The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the center of mass of the system shifts by$ (1) $3.0 m$ (2) $2.3 m$ (3) $zero$ (4) $0.75 m$ 13. $A ball of mass 100 g is dropped at a time t = 0 . A second ball of mass 200 g is dropped from the same point at t = 0.2 s . The distance between the centre of mass of two balls and the release point at t = 0.4 s is (Assume, g = 10 m / s^{2})$ (1) $0.4 m$ (2) $0.5 m$ (3) $0.6 m$ (4) $0.8 m$ 14. $Two blocks of masses 2 kg and 1 kg are tied to the ends of a string which passes over a light frictionless pulley.The blocks are held at rest at the same horizontal level and then released suddenly. The distance traversed by their centre of mass in 2 seconds is (acceleration due to gravity = 10 ms^{- 2})$ (1) $1.42 m$ (2) $2.22 m$ (3) $3.12 m$ (4) $3.33 m$ 15. $A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. After collision, they stick together and continue to move together with velocity$ (1) $\frac{v}{3}$ (2) $\frac{v}{4}$ (3) $v$ (4) $\frac{v}{2}$ 16. $Two bodies of mass 1 kg and 3 kg have position vectors i + 2 j + k and‐3 i - 2 j + k, respectively. The centre of mass of this system has a position vector$ (1) $- 2 i - j + k$ (2) $2 i - j - 2 k$ (3) $- i + j + k$ (4) $- 2 i + 2 k$ 17. $A stone of mass 1 kg is tied to a string 2 m long and is rotated at constant speed of 40 m s^{- 1} in a vertical circle. The ratio of the tension at the top and the bottom is [Take g = 10 m s^{- 2}]$ (1) $\frac{81}{79}$ (2) $\frac{79}{81}$ (3) $\frac{19}{12}$ (4) $\frac{12}{19}$ 18. $A ring and a disc roll on the horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is 4 J then total kinetic energy of the disc is$ (1) $3 J$ (2) $4 J$ (3) $5 J$ (4) $6 I$ 19. $Three bodies A, B and C have equal kinetic energies and their masses are 400 g . 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is:$ (1) $2; 3; 1$ (2) $1 : 3 : 2$ (3) $1 : 3 : 2$ (4) $3 : 2 : 1$ 20. $A solid cylinder of mass m and radius R rolls down an inclined plane of height 30 m without slipping. The speed of its centre of mass when the cylinder reaches the bottom is [use g = 10 m / s^{2}]$ (1) $10 m / s$ (2) $20 m / s$ (3) $30 m / s$ (4) $40 m / s$ 21. $Three masses are placed on the x-axis : 300 g at origin, 500g at x = 40 cm and 400g at x = 70 cm. The distance of the centre of mass from the origin is :$ (1) $40 cm$ (2) $45 cm$ (3) $50 cm$ (4) $30 cm$ 22. $Consider a system of two particles having masses m_{1} and m_{2} . If the particle of mass m_{1} is pushed towards the mass centre of particles through a distance d, by what distance would be particle of mass m_{2} move so as to keep the mass centre of particles at the original position?$ (1) $\frac{m _{1}}{m _{1} + m _{2}} d$ (2) $\frac{m _{1}}{m _{2}} d$ (3) $d$ (4) $\frac{m _{2}}{m _{1}} d$ 23. $Two particles of masses 5 g and 3 g are separated by a distance of 40 cm . The centre of mass of the system of these two particles$ (1) $lies at a distance of 15 cm from 5g particle$ (2) $lies at a distance of 25 cm from 5g particle$ (3) $lies at a distance of 10 cm from 3 g particle$ (4) $lies at the mid point of the line joining the two particles$ 24. $Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be$ (1) $2v$ (2) $zero$ (3) $1.5 v$ (4) $v$ 25. $The real force ' F' acting on a particle of mass ' m' performing circular motion acts along the radius of circle ' r' and is directed towards the centre of circle. The square root of magnitude of such force is (T = periodic time)$ (1) $\frac{2 π}{T} mr$ (2) $\frac{Tmr}{4 π}$ (3) $\frac{2 πT}{mr}$ (4) $\frac{T ^{2} mr}{4 π}$ 26. $A bullet of mass 10 g moving horizontally with a velocity of 400 m / s strikes a wooden block of mass 2 kg which is suspended by light inextensible string of length 5 m. As a result, the center of gravity of the block is found to rise a vertical distance of 10 cm. The speed of the bullet after it emerges out horizontally from the block will be$ (1) $100 m s^{- 1}$ (2) $80 m s^{- 1}$ (3) $120 m s^{- 1}$ (4) $160 m s^{- 1}$ 27. $The centre of mass of system of particles does not depend on$ (1) $position of the particles$ (2) $relative distances between the particles$ (3) $masses of the particles$ (4) $forces acting on the particle.$ 28. $The centre of mass of an extended body on the surface of the earth and its centre of gravity$ (1) $can never be at the same point$ (2) $are always at the same point for any size of the body$ (3) $centre of mass coincides with the centre of gravity of a body if the size of the body is negligible as compared to the size (or radius) of the earth$ (4) $are always at the same point only for spherical bodies.$ 29. $A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?$ (1) $Both together only when angle of inclination of plane is 4 5^{o}$ (2) $Both together$ (3) $Hollow cylinder$ (4) $Solid cylinder$ 30. $Masses m (\frac{1}{3})^{N} \frac{1}{N} are placed at x = N, when N = 2, 3, 4 ,\dots\dots\dots. \infty . If the total mass of the system is M, then the centre of mass is$ (1) $\frac{1}{6} \frac{m}{M}$ (2) $\frac{1}{5} \frac{m}{M}$ (3) $\frac{1}{3} \frac{m}{M}$ (4) $\frac{1}{2} \frac{m}{M}$