A object of mass $m_{1}$ collides with another object of mass m₂ , which is at rest. After the collision the objects move with equal speeds in opposite directions. The ratio of the masses $m_{2} : m_{1}$ is

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2 : 1

3 : 1

1 : 2

1 : 1

answer is B.

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Detailed Solution

From law of conservation of momentum $P_{i} = P_{f}$
$m_{1} v = (m_{2} - m_{1}) v_{1}$

$\Rightarrow v_{1} = \frac{m_{1} v}{(m_{2} - m_{1})}$ ….. (i)
If collision is elastic then,
$e = 1 = \frac{v_{1} - (- v_{1})}{v - 0}$
Also, $2 v_{1} = v$
$\Rightarrow v_{1} = \frac{v}{2}$ …..ii)
From equation (i) & (ii)
$\begin{array}{l} \frac{1}{2} = \frac{m_{1}}{m_{2} - m_{1}} \\ ∴ \frac{m_{2}}{m_{1}} = \frac{3}{1} \end{array}$