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Two identical mass M moving with velocities $u_{1}$ and $u_{2}$ collide perfectly in-elastically. The loss in energy is

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$\frac{M}{2} {(2 u_{2} - 2 u_{1})}^{2}$

$\frac{M}{2} {(u_{2} - u_{1})}^{2}$

$\frac{M}{4} {(u_{1} - u_{2})}^{2}$

$\frac{M}{4} {(2 u_{1} - 2 u_{2})}^{2}$

answer is C.

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Detailed Solution

$Δ K = \frac{1}{2} \frac{m_{1} m_{2}}{(m_{1} + m_{2})} {(u_{1} - u_{2})}^{2}$

$Here, m_{1} = m_{2} = M$

$∴ Δ K = \frac{1}{2} \frac{M \times M}{(M + M)} {(u_{1} - u_{2})}^{2} = \frac{M}{4} {(u_{1} - u_{2})}^{2} .$

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