Question

A body moving towards a body of finite mass at rest collides with it. It is possible that :

• A. both bodies come to rest
• B. both bodies move after collision
• C. the moving body stops and the body at rest starts moving
• D. the stationary body remains stationary and the moving body rebounds

Answer 1

Answer: (B), (C)

both bodies move after collision
the moving body stops and the body at rest starts moving

Given : $m_1=m$ $m_2=M$ $u_1=u$ $u_2=0$

Let the velocities of the bodies after the collision be $v_1$ and $v_2$ respectively.

$v_1=\frac{(m_1-e{m}_2)u_1+(1+e)m_2{u}_2}{m_1+m_2}$

$v_1=\frac{(m-eM)u+(1+e)M\left(0\right)}{m+M}$ $⟹$ $v_1=\frac{(m-eM)u}{m+M}$

$v_2=\frac{(m_2-e{m}_1)u_2+(1+e)m_1{u}_1}{m_1+m_2}$

$v_2=\frac{(M-em)\left(0\right)+(1+e)m\left(u\right)}{m+M}$ $⟹$ $v_2=\frac{(M-em)u}{m+M}$

The system has some finite initial momentum, hence from conservation of momentum the system must have momentum after the collision i.e both the bodies cannot come to rest.

Also for $m=M$ and $e=1$ $⟹v_1=0$ and $v_2=u$

Thus option C is correct.

For $v_2=0$ and $v_1=-u^{\prime }$ $⟹M>>m$

But it is given that $M$ is finite. Hence option D is not true.