Question

A body of mass 2 kg makes an elastic collision with another body at rest and continues to move in the original direction at a speed equal to 1/3 of its original speed. The mass of the second body is

• A. $2kg$
• B. $3kg$
• C. $1kg$
• D. $4kg$

Answer 1

The correct option is C $1kg$

Let mass of second body be $m$ kg and its velocity after collision be $v$.

The collision is elastic i.e $e=1$

$\therefore$ $\frac{\frac{u}{3}-v}{u-0}=-1$ $⟹v=\frac{4u}{3}$

Applying conservation of momentum:

$m_{1}u+0=m_1\frac{u}{3}+mv$

$2u=2\times \frac{u}{3}+m\times \frac{4u}{3}$

$⟹m=1$ kg