Question

A body X of mass $M$ moving with velocity $v$ hits a stationary body Y of mass $m$. If $M \gg m$ and X moves with velocity $v'$ after the collision, then the velocity of Y after an elastic collision is

• A. $2v$
• B. $v + v'$
• C. $v - v'$
• D. $2v'$

Hint:

When $M \gg m$, the lighter body moves roughly with the difference of initial and final velocities of the heavier one.

Answer 1

The Correct Option is B

Step 1: Use elastic collision formulas.
For elastic collision between masses $M$ and $m$ ($M \gg m$): Velocity of lighter mass Y after collision is: $v_Y = \dfrac{2M}{M + m} v_X - \dfrac{M - m}{M + m} v_X'$
When $M \gg m$: $\dfrac{2M}{M+m} \approx 2$, $\dfrac{M - m}{M + m} \approx 1$.
Step 2: Substitute approximations.
$v_Y \approx 2v - v'$.
Step 3: Use momentum substitution relation.
Under the given simplification, the effective relative velocity simplifies to $v_Y = v - v'$. This matches option (C).