Conservation of Momentum - UNSOLVED PRACTICE SET
Chapter: Laws of Motion | Topic: Conservation of Momentum
CONSERVATION OF MOMENTUM - UNSOLVED PRACTICE SET
Topic: Conservation of Momentum
Multiple Choice Questions
Q1. The law of conservation of linear momentum states that:
- Momentum can be created but not destroyed
- The total momentum of an isolated system remains constant
- Momentum is conserved only in elastic collisions
- Momentum is conserved only when external forces act
Q2. In an isolated system, if two bodies collide elastically:
- Only momentum is conserved
- Only kinetic energy is conserved
- Both momentum and kinetic energy are conserved
- Neither momentum nor kinetic energy is conserved
Q3. A bullet is fired from a rifle. The momentum of the bullet is equal in magnitude to:
- The momentum of the rifle
- The recoil momentum of the rifle
- Twice the momentum of the rifle
- Half the momentum of the rifle
Q4. Two bodies of equal mass collide head-on elastically. If one was initially at rest, after collision:
- Both move with the same velocity
- The moving body stops and the stationary body moves with the initial velocity
- Both come to rest
- Both move with half the initial velocity
Q5. A bomb at rest explodes into two fragments of masses m and 2m. The ratio of their velocities is:
- 1 : 1
- 1 : 2
- 2 : 1
- 1 : 4
Q6. In an inelastic collision:
- Momentum is not conserved
- Kinetic energy is not conserved but momentum is conserved
- Both momentum and kinetic energy are conserved
- Neither momentum nor kinetic energy is conserved
Short Answer Questions
Q7. State the law of conservation of linear momentum. Under what conditions is it valid?
Q8. Prove the law of conservation of momentum using Newton's second and third laws.
Q9. A man of mass 60 kg stands on a frictionless surface and throws a ball of mass 0.5 kg horizontally at 20 m/s. Calculate the recoil velocity of the man.
Q10. In a school demonstration, two trolleys of masses 2 kg and 3 kg are placed on a frictionless track. The 2 kg trolley moves at 4 m/s and collides with the stationary 3 kg trolley. They stick together. Calculate their common velocity after collision.
Q11. Why is the law of conservation of momentum called a "universal law"? Give two examples where it applies.
Q12. A rocket at rest in space ejects fuel backward. Explain why the rocket moves forward, using conservation of momentum.
Long Answer Questions
Q13. State and prove the law of conservation of linear momentum. Discuss its validity in:
(i) Elastic collisions
(ii) Inelastic collisions
(iii) Explosions
(iv) Rocket propulsion
Give one example for each case.
Q14. Two bodies A (mass 4 kg) and B (mass 6 kg) move towards each other with velocities 5 m/s and 3 m/s respectively on a frictionless surface. After collision, body A moves in the opposite direction with velocity 2 m/s.
(a) Calculate the velocity of body B after collision.
(b) Determine whether the collision is elastic or inelastic.
(c) Calculate the loss of kinetic energy (if any).
(d) Verify that momentum is conserved.
Q15. A ballistic pendulum consists of a wooden block of mass M suspended by a string. A bullet of mass m is fired into the block with velocity v and gets embedded in it. The block rises to a height h.
(a) Write the equation for conservation of momentum during the collision.
(b) Write the equation for conservation of energy after the collision.
(c) Derive an expression for the velocity of the bullet in terms of M, m, and h.
(d) Explain why kinetic energy is not conserved during the collision but is conserved after it.
Application-Based Problems
Q16. A 10 g bullet is fired horizontally into a 2 kg wooden block resting on a frictionless surface. The bullet gets embedded in the block, and the system moves at 2.5 m/s.
(a) Calculate the initial velocity of the bullet.
(b) Calculate the kinetic energy before and after the collision.
(c) Calculate the percentage loss in kinetic energy.
(d) What type of collision is this? Explain.
Q17. A radioactive nucleus at rest decays into an alpha particle (mass 4 u) and a daughter nucleus (mass 220 u). The alpha particle is emitted with a kinetic energy of 5.5 MeV.
(a) Calculate the velocity of the alpha particle. (1 u = 1.66 × 10⁻²⁷ kg)
(b) Using conservation of momentum, calculate the velocity of the daughter nucleus.
(c) Calculate the kinetic energy of the daughter nucleus.
(d) Verify that the total kinetic energy equals the Q-value of the reaction (assume Q = 5.6 MeV).
Q18. In a school physics lab, two students perform an experiment with two gliders on an air track (frictionless). Glider A (mass 0.5 kg) moves at 0.8 m/s towards Glider B (mass 0.3 kg) moving at 0.4 m/s in the same direction. After collision, Glider A moves at 0.5 m/s.
(a) Calculate the velocity of Glider B after collision.
(b) Calculate the total kinetic energy before and after the collision.
(c) Is the collision elastic or inelastic? Justify your answer.
(d) If the collision were perfectly elastic, what would be the velocities of both gliders after collision?