Q62 / 90 · JEE Main 2021 (18 Mar Shift 2) · Physics

An object of mass $m_{1}$ collides with another object of mass $m_{2}$ , which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses $m_{2} : m_{1}$ is :

Solution

$m_{1} v_{1} = - m_{1} v + m_{2} v$

$v_{1} = - v + \frac{m_{2}}{m_{1}} v$

$\frac{(v_{1} + v)}{v} = \frac{m_{2}}{m_{1}}$

$e = \frac{2 v}{v_{1}} = 1$

$v = \frac{v_{1}}{2}$

$\frac{v_{1} + v_{1} / 2}{v_{1} / 2} = \frac{m_{2}}{m_{1}}$

$3 = \frac{m_{2}}{m_{1}}$

Hence, the correct answer is option: 'A'.