Collision & Variable Mass PYQs Set 1 (PDF)

Set 1 of 4 · Questions 1-30 of 119

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Mere Teacher · Previous Year Questions JEE Main Physics · Collision & Variable Mass · Set 1 (Q1-30)
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1. $When two bodies collide elastically, then$ (1) $kinetic energy of the system along is conserved$ (2) $only momentum is conserved$ (3) $both kinetic energy and momentum is conserved$ (4) $Neither kinetic energy nor momentum is conserved$ 2. $A ball is thrown vertically downwards from a height of 20 m with an initial velocity v_{0} . It collides with the ground, loses 50 % of its energy in collision and rebounds to the same height. The initial velocity v_{0} is (Take, g = 10 ms^{- 2})$ (1) $14 ms^{- 1}$ (2) $20 ms^{- 1}$ (3) $28 ms^{- 1}$ (4) $10 ms^{- 1}$ 3. $A machine gun of mass 10 kg fires 20 g bullets at the rate of 180 bullets per minute with a speed of 100 m s^{- 1} each. The recoil velocity of the gun is:$ (1) $0.02 m/s$ (2) $2.5 m/s$ (3) $1.5 m/s$ (4) $0.6 m/s$ 4. $A moving particle collides with a stationary particle of mass times the mass of moving particle, the fraction of its kinetic energy transferred to the stationary particle is$ (1) $4 n^{2} (1+n)2$ (2) $\frac{4 n}{( 1 + n ) ^{2}}$ (3) $\frac{4 n}{1 + n ^{2}}$ (4) $4 n^{2}$ 5. $Two particles A and B, move with constant velocities v_{1} and v_{2} . At the initial moment their position vectors are r_{1} and r_{2} respectively. The condition for particles A and B for their collision is$ (1) $r_{1} \times v_{1} = r_{2} \times v_{2}$ (2) $r_{1} - r_{2} = v_{1} - v_{2}$ (3) $\frac{r _{1} - r _{2}}{\| r _{1} - r _{2} \|} = \frac{v _{2} - v _{1}}{\| v _{2} - v _{1} \|}$ (4) $r_{1} \cdot v_{1} = r_{2} \cdot v_{2}$ 6. $Two bodies of mass 1 kg and 3 kg have position vectors i + 2 j + k and - 3 i - 2 j + k, respectively. The centre of mass of this system has a position vector:$ (1) $- 2 i - j + k$ (2) $2 i - j - 2 k$ (3) $- i + j + k$ (4) $- 2 i + k$ 7. $A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 m s^{- 1} . The coefficient of friction between the surface and bock is 0.5. The distance covered by the block before coming to rest is: [use g = 9.8 m s^{- 2}]$ (1) $4.9 m$ (2) $9.8 m$ (3) $12.5 m$ (4) $19.6 m$ 8. $A 1 kg ball moving at 12 m s^{- 1} collides with a 2 kg ball moving in opposite direction at 24 m s^{- 1} . If the coefficient of restitution is 2/3, then their velocities after the collision are$ (1) $- 4 m s^{- 1}, - 28 m s^{- 1}$ (2) $- 28 m s^{- 1}, - 4 m s^{- 1}$ (3) $4 m s^{- 1}, 28 m s^{- 1}$ (4) $28 m s^{- 1}, 4 m s^{- 1}$ 9. $A ball is dropped from some height and after first collision with the ground if it reaches \frac{3}{4}^{th} of its original height, then the % loss of its energy.$ (1) $25$ (2) $75$ (3) $50$ (4) $55$ 10. $A wedge of mass M = 4 m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v . There is no friction between the particle and the plane or between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by:$ (1) $\frac{v ^{2}}{g}$ (2) $\frac{2 v ^{2}}{7 g}$ (3) $\frac{2 v ^{2}}{5 g}$ (4) $\frac{v ^{2}}{2 g}$ 11. $Two particles of masses m_{1}, m_{2} move with initial velocities u_{1} and u_{2} . On collision, one of the particles get excited to higher level, after absorbing energy ϵ If final velocities of particles be v_{1} and v_{2}, then we must have$ (1) $m_{1}^{2} u_{1} + m_{2}^{2} u_{2} - ϵ = m_{1}^{2} v_{1} + m_{2}^{2} v_{2}$ (2) $\frac{1}{2} m_{1} u_{1}^{2} + \frac{1}{2} m_{2} u_{2}^{2} = \frac{1}{2} m_{1} v_{1}^{2} + \frac{1}{2} m_{2} v_{2}^{2} - ϵ$ (3) $\frac{1}{2} m_{1} u_{1}^{2} + \frac{1}{2} m_{2} u_{2}^{2} - ϵ = \frac{1}{2} m_{1} v_{1}^{2} + \frac{1}{2} m_{2} v_{2}^{2}$ (4) $\frac{1}{2} m_{1}^{2} u_{1}^{2} + \frac{1}{2} m_{2}^{2} u_{2}^{2} + ϵ = \frac{1}{2} m_{1}^{2} v_{1}^{2} + \frac{1}{2} m_{2}^{2} v_{2}^{2}$ 12. $A body falls freely from a height of 100 m on to the ground and rebounds to a maximum height of 36 m after collision. The coefficient of restitution between ground and the body is$ (1) $0.4$ (2) $0.36$ (3) $0.6$ (4) $0.5$ 13. $A ball hits the floor and rebounds after an inelastic collision. In this case$ (1) $the momentum of the ball is conserved.$ (2) $the mechanical energy of the ball is conserved.$ (3) $the total momentum of the ball and the earth is conserved.$ (4) $the total mechanical energy of the ball and the earth is conserved.$ 14. $The coefficient of restitution e for a perfectly elastic collision is$ (1) $1$ (2) $0$ (3) $\infty$ (4) $-1$ 15. $A body of mass M at rest explodes into three pieces, in the ratio of masses 1:1:2. Two smaller pieces fly off perpendicular to each other with velocities of 30 m s^{- 1} and 40 m s^{- 1} respectively. The velocity of the third piece will be:$ (1) $15 m s^{- 1}$ (2) $25 m s^{- 1}$ (3) $35 m s^{- 1}$ (4) $50 m s^{- 1}$ 16. $A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate \frac{dM ( t )}{dt} = bv^{2} (t) where v (t) is its instantaneous velocity. The instantaneous acceleration of the satellite is$ (1) $- b v^{3} (t)$ (2) $- \frac{2 b v ^{3}}{M ( t )}$ (3) $- \frac{b v ^{3}}{M ( t )}$ (4) $- \frac{b v ^{3}}{2 M ( t )}$ 17. $A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body?$ (1) $1.0 kg$ (2) $1.5 kg$ (3) $1.8 kg$ (4) $1.2 kg$ 18. $A moving block having mass m, collides with another stationary block having mass 4 m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be (NEET2018)$ (1) $0.5$ (2) $0.25$ (3) $0.8$ (4) $0.4$ 19. $If the total energy transferred to a surface in time t is 6.48 \times 10^{5} J, then the magnitude of the total momentum delivered to this surface for complete absorption will be :$ (1) $2.46 \times 10^{- 3} kg m / s$ (2) $2.16 \times 10^{- 3} kg m / s$ (3) $1.58 \times 10^{- 3} kg m / s$ (4) $4.32 \times 10^{- 3} kg m / s$ 20. $Statement-1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement-2 : Principle of conservation of momentum holds true for all kinds of collisions.$ (1) $Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.$ (2) $Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1$ (3) $Statement-1 is false, Statement-2 is true.$ (4) $Statement-1 is true, Statement-2 is false.$ 21. $Collision takes place between two solid spheres denoted as 1 and 2. The initial velocities of the sphere are u_{1} = 3 m / s and u_{2} = 1.5 m / s and the final velocities are v_{1} = 2.5 m / s and v_{2} = 3.5 m / s . The coefficient of restitution between the materials of the sphere is nearly$ (1) $0.67$ (2) $0.78$ (3) $0.83$ (4) $0.96$ 22. $A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of 2 gh . If they collide head-on completely in elastically, the time taken for the combined mass to reach the ground, in units of \frac{h}{g} is$ (1) $\frac{3}{2}$ (2) $\frac{1}{2}$ (3) $3$ (4) $\frac{1}{5}$ 23. $A bullet of mass 0.1 kg moving horizontally with speed 400 m s^{- 1} hits a wooden block of mass 3. 9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block and the surface is_______.$ (1) $0.90$ (2) $0.50$ (3) $0.65$ (4) $0.25$ 24. $A moving body of mass m and velocity 3 km/hour collides with a rest body of mass 2 m and sticks to it. Now the combined mass starts to move. What will be the combined velocity?$ (1) $3 km/hour$ (2) $4 km/hour$ (3) $1 km/hour$ (4) $2 km/hour.$ 25. $A 1 kg ball moving with a speed of 6 ms^{- 1} collides headon with a 0.5 kg ball moving in the opposite direction with a speed of 9 ms^{- 1} . If the coefficient of restitution is \frac{1}{3}, then the energy lost in the collision is$ (1) $303.4 J$ (2) $66 : 7 J$ (3) $33.3 J$ (4) $67.8 J$ 26. $A ball of mass 0.2 kg is thrown vertically down from a height of 10 m . It collides with the floor and loses 50 % of its energy and then rises back to the same height. The value of its initial velocity is$ (1) $zero$ (2) $14 m s^{- 1}$ (3) $196 m s^{- 1}$ (4) $20 m s^{- 1}$ 27. $Particle A moving with a velocity v = 10 m / s experienced a head on collision with a stationary particle B of the same mass. As a result of collision, the kinetic energy of the system decreased by 1 % . The speed of particle A after collision in$ (1) $10 m / s$ (2) $0.05 m / s$ (3) $5 m / s$ (4) $102 m / s$ 28. $A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m . The impulse of force imparted by the ground to the body is given by: (given g = 9.8 m / s^{2})$ (1) $4.32 kg ms^{- 1}$ (2) $43.2 kg ms^{- 1}$ (3) $23.9 kg ms^{- 1}$ (4) $2.39 kg ms^{- 1}$ 29. $A body A, of mass m = 0.1 kg has an initial velocity of 3 i^m s^{- 1} . It collides elastically with another body, B of the same mass which has an initial velocity of 5 j m s^{- 1} . After collision, A moves with a velocity v \to= 4 (i^+ j^) . The energy of B after collision is written as \frac{x}{10} j . The value of x is$ 30. $A body of mass 2kg moving with a speed of 4m/s. makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is \frac{x}{10} m / s . Then the value of x is$