Question

A lighter body moving with a velocity $v$ collides with a heavier body at rest. Then :

• A. the lighter body rebounces with twice the velocity of bigger body
• B. the lighter body retraces its path with the same velocity in magnitude
• C. the heavier body does not move practically
• D. both (2) and (3)

Answer 1

The correct option is D both (2) and (3)

In a collision system where $m_1$ moves with $u_1$ initially and $m_2$ is at rest with $m_2>>>m_1$.
Let the final velocity of $m_1$ be $v_1$ and $m_2$ be $v_2$.
Assumption: Let the collision be elastic. Using linear momentum conservation and equation for coefficient of restitution,
$m_1{u}_1=m_2{v}_2+m_1{v}_1$
$v_2-v_1=u_1$

We get $v_1=\frac{m_1-m_2}{m_1+m_2}{u}_1$

$v_2=\frac{2m_1}{m_1+m_2}{u}_1$

Using $m_2>>>m_1,$ we get $v_1=-u_1$ and $v_2=0$.