Question

A body of mass $m_1$ having a velocity $u_1$, makes a collision with a body of mass $m_2$ travelling with a velocity $u_2$ in same direction. After the collision, the velocity of the mass $m_1$ becomes lesser than $2u_2$. If the collision is perfectly elastic and $m_2<<m_1$, then which of the flowing statements is correct?

• A. $u_1=0$
• B. $u_1\ne 0$
• C. $u_1=u_2$
• D. $u_2>>u_1$

Answer 1

The correct option is B $u_1\ne 0$

The final velocity of the mass $m_1$ is $v_1$,
From the concept of collision, we know
$v_1=\left(\frac{m_1-m_2}{m_1+m_2}\right)u_1+\frac{2m_2{u}_2}{m_1+m_2}$
$[\text{As}\frac{m_2}{m_1}<<1]$
$\Rightarrow v_1=-u_1+2u_2$
Condition that the final velocity of the mass $m_1$ becomes less than $2u_2$ is only possible when $u_1\ne 0$.