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A mass m1 m...

Question

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

m_{1} > m_{2}

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m_{1} < m_{2}

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m_{1} = m_{2}

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there is no relation between

m_{1}

and

m_{2}

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Solution

The correct option is B $m_{1} < m_{2}$
Let the velocity of the colliding mass before and after collision be $u$ and $v_{1}$
$∴$ $u_{1} = u$ $u_{2} = 0$
Using $v_{1} = \frac{(m_{1} - e m_{2}) u_{1} + (1 + e) m_{2} u_{2}}{m_{1} + m_{2}}$
$v_{1} = \frac{(m_{1} - e m_{2}) u + (1 + e) m (0)}{m_{1} + m_{2}}$

$v_{1} = \frac{(m_{1} - e m_{2}) u}{m_{1} + m_{2}}$
For $v_{2} < 0$ , $⟹ e m_{2} > m_{1}$
But $0 \leq e \leq 1$
Hence $m_{2} > m_{1}$ so that the colliding particle can recoil

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