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 :
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
$e=\frac{2 v}{v_{1}}=1$
$v=\frac{v_{1}}{2}$
$\frac{v_{1}+v_{1} / 2}{v_{1} / 2}=\frac{m_{2}}{m_{1}}$
$3=\frac{m_{2}}{m_{1}}$