Question 99 of 130

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 :

A$3:1$B$2:1$C$1:2$D$1:1$

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Answer: (A) $3:1$

${m}_{1}{v}_{1}=-{m}_{1}v+{m}_{2}v$
${v}_{1}=-v+\dfrac{{m}_{2}}{{m}_{1}}v$
$\dfrac{\left({v}_{1}+v\right)}{v}=\dfrac{{m}_{2}}{{m}_{1}}$
$e=\dfrac{2v}{{v}_{1}}=1$
$v=\dfrac{{v}_{1}}{2}$
$\dfrac{{v}_{1}+{v}_{1}/2}{{v}_{1}/2}=\dfrac{{m}_{2}}{{m}_{1}}$
$3=\dfrac{{m}_{2}}{{m}_{1}}$