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A particle of mass ' $\mathrm{m}$ ' collides with another stationary particle of mass ' $M$ '. Particle of mass ' $m$ ' stops just after collision. The coefficient of restitution is
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Verified Answer
The correct answer is:
$\frac{\mathrm{m}}{\mathrm{M}}$
Let $v$ be the velocity of mass $m$ and $v$ ' be the velocity of mass $M$ after collision.'
By law of conservation of momentum
$$
\begin{aligned}
& \mathrm{mv}=\mathrm{Mv} \\
& \therefore \frac{\mathrm{v}^{\prime}}{\mathrm{v}}=\frac{\mathrm{m}}{\mathrm{M}}
\end{aligned}
$$
Coefficient of restitutions,
$$
\mathrm{e}=\frac{\text { Re lative velocity after collision }}{\text { Relative velocity before collision }}=\frac{\mathrm{v}^{\prime}}{\mathrm{v}}=\frac{\mathrm{m}}{\mathrm{M}}
$$
By law of conservation of momentum
$$
\begin{aligned}
& \mathrm{mv}=\mathrm{Mv} \\
& \therefore \frac{\mathrm{v}^{\prime}}{\mathrm{v}}=\frac{\mathrm{m}}{\mathrm{M}}
\end{aligned}
$$
Coefficient of restitutions,
$$
\mathrm{e}=\frac{\text { Re lative velocity after collision }}{\text { Relative velocity before collision }}=\frac{\mathrm{v}^{\prime}}{\mathrm{v}}=\frac{\mathrm{m}}{\mathrm{M}}
$$
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