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Statement-I: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement-II: Principle of conservation of momentum holds true for all kinds of collisions.
Asked in AIEEE 2010 · Perfectly inelastic collisions
- (1) Statement-I is true, Statement-II is false.
- (2) Statement-I is true, Statement-II is true; Statement-II is the correct explanation of Statement-I.
- (3) Statement-I is true, Statement-II is true; Statement-II is not the correct explanation of Statement-I.
- (4) Statement-I is false, Statement-II is true.
Answer: (2) Statement-I is true, Statement-II is true; Statement-II is the correct explanation of Statement-I.
Step-by-step solution
Momentum is conserved in every collision, so the centre of mass keeps moving and its kinetic energy (p²)/(2(m₁+m₂)) can never be lost: Statement-I is true.
Statement-II is true and is exactly the reason.
Why the other options are wrong
- (1) Comes from thinking momentum conservation fails in inelastic collisions; only kinetic energy is lost.
- (3) Comes from missing that the non-zero total momentum is precisely what forbids losing all the energy.
- (4) Comes from thinking a sticking collision can stop both bodies; it can only if their momenta cancel.
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