A bullet of mass m travelling horizontally with speed u strikes a wooden block of mass M placed on a smooth horizontal plane. The penetration is assumed uniform and the bullet comes to rest after pene

Question

A bullet of mass m travelling horizontally with speed u strikes a wooden block of mass M placed on a smooth horizontal plane. The penetration is assumed uniform and the bullet comes to rest after penetrating a distance d into the block. Ultimately the total loss of the kinetic energy is :-

TestHub · Accepted Answer

By momentum conservation, common velocity of bullet + block is $v = \frac{m u}{M + m}$ .

Loss of KE $= \frac{1}{2} m u^{2} - \frac{1}{2} (M + m) v^{2} = \frac{1}{2} m u^{2} (1 - \frac{m}{M + m}) = \frac{m M u ^{2}}{2 ( M + m )}$ .

Option (A).

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