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Q.
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 :
$m _{1} v _{1}=- m _{1} v + m _{2} v$
$v _{1}=- v +\frac{ m _{2}}{ m _{1}} v$
$\frac{\left( v _{1}+ v \right)}{ v }=\frac{ m _{2}}{ m _{1}}$
$e =\frac{2 v }{ v _{1}}=1$
$v =\frac{ v _{1}}{2}$
$\frac{ v _{1}+ v _{1} / 2}{ v _{1} / 2}=\frac{ m _{2}}{ m _{1}}$
$3=\frac{ m _{2}}{ m _{1}}$
