An object of mass
Question:

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

1. (1) $3: 1$

2. (2) $2: 1$

3. (3) $1: 2$

4. (4) $1: 1$

Correct Option: 1

Solution:

$\mathrm{m}_{1} \mathrm{v}_{1}=-\mathrm{m}_{1} \mathrm{v}+\mathrm{m}_{2} \mathrm{v}$

$\mathrm{v}_{1}=-\mathrm{v}+\frac{\mathrm{m}_{2}}{\mathrm{~m}_{1}} \mathrm{v}$

$\frac{\left(\mathrm{v}_{1}+\mathrm{v}\right)}{\mathrm{v}}=\frac{\mathrm{m}_{2}}{\mathrm{~m}_{1}}$b

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

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

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

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