A body of mass 1 kg makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to $1/5th$ of its original velocity. Find the mass of the second body.

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\frac{3}{2} kg

\frac{2}{5} kg

\frac{2}{3} kg

\frac{5}{2} kg

answer is A.

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Detailed Solution

m_{1} = 1 kg, m_{2} = m

$u_{1} = u, u_{2} = 0$

$v_{1} = \frac{1}{5} u$

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

$\frac{1}{5} u = \frac{(1 - m) u}{1 + m}$

$1 + m = 5 - 5 m$

$6m = 4$

$m = \frac{2}{3}$

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