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Com in Perfectly Inelastic Collision

A mass m1 m...

Question

A mass $m_{1}$ moves with a large velocity. It strikes another mass $m_{2}$ at rest in a head on collision. It comes back along its path with lesser speed after collision. Then

A

m_{1} > m_{2}

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B

m_{1} < m_{2}

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C

m_{1} = m_{2}

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D

There is no relation between

m_{1}

and

m_{2}

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Solution

The correct option is A $m_{1} < m_{2}$
The velocity of the mass $m_{1}$ before collision be $u_{1}$ whereas the that of mass $m_{2}$ is Zero i.e $u_{2} = 0$
Let their velocities after the collision be $v_{1}$ and $v_{2}$ respectively.

Using, $v_{1} = \frac{(m_{1} - e m_{2}) u_{1} + (1 + e) m_{2} u_{2}}{m_{1} + m_{2}}$

$∴$ $v_{1} = \frac{(m_{1} - e m_{2}) u_{1}}{m_{1} + m_{2}}$ $(∵ u_{2} = 0)$
Thus for $v_{1} < 0$ , either $m_{1} < 0$ (impossible) or $e m_{2} > m_{1}$
Also as $0 \leq e \leq 1$ , $∴ e m_{2} > m_{1}$ $⟹ m_{2} > m_{1}$

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