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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

  1. ABoth (A) and (R) are true and (R) is the correct explanation of (A)
  2. BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
  3. C(A) is true but (R) is false
  4. 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

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