NEETPhysicsCenter of Mass, Momentum and Collision
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): A moving body always rebounds in the opposite direction after a head-on elastic collision with a stationary target of a different mass. Reason (R): In a one-dimensional elastic collision, a moving body of mass m transfers the exact same fraction of its initial kinetic energy to a stationary target
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- C(A) is true but (R) is false
- D(A) is false but (R) is true
Correct answer
D. (A) is false but (R) is true
Step-by-step solution
Evaluate Assertion (A): The final velocity of a moving body of mass m₁ colliding elastically with a stationary target of mass m₂ is v₁ = m₁ - m₂ m₁ + m₂ u₁ . The body only rebounds (i.e., v₁ is negative) if m₁ m₂ , it continues moving in the same direction. Therefore, it does not always rebound when the masses are different. Assertion (A) is false. Evaluate Reason (R): The fraction of kinetic energy transferred to a stationary target is f = 4m₁ m₂ (m₁ + m₂)^2 . For a target of mass 2m : f = 4(m)(2m) (m + 2m)^2 = 8m