First slide

The steps in collision

Question

A bullet of mass m is fired into a block of wood of mass M which hangs on the end of pendulum and
gets embedded into it. When the bullet strikes the wooden block, the pendulum starts to swing with
maximum rise R. Then, the velocity of the bullet is given by

Moderate

A

$\frac{M}{m + M} \sqrt{2 g R}$
B

$\frac{M + m}{m} \sqrt{2 g R}$
C

$\frac{M}{m} \sqrt{2 g R}$
D

None of these

Solution

We know that, $v' = \sqrt{2 g R}$
From conservation of linear momentum,
$m v = (M + m) v'$
$∴$ $v = \frac{M + m}{m} \cdot v^{'} = (\frac{M + m}{m}) \sqrt{2 g R}$

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