First slide

Ballistic pendulum

Question

A bullet of mass $10 g$ moving horizontally with a velocity of $400 m s^{- 1}$ strikes a wood block of mass $2 k g$ which is suspended by light inextensible string of length $5 m$ . As a result, the centre of gravity of the block found to rise a vertical distance of $10 c m$ . The speed of the bullet after it emerges out horizontally from the block will be

Moderate

A

$100 m s^{- 1}$
B

$80 m s^{- 1}$
C

$120 m s^{- 1}$
D

$160 m s^{- 1}$

Solution

We can apply work energy theorem for the bullet and block before strike and after the bullet is ejected out of the block
$F r o m c o n s e r v a t i o n o f l i n e a r m o m e n t u m \frac{10}{1000} \times 400 + 0 = 2 v_{1} + \frac{10}{1000} v_{2} F r o m w o r k e n e r g y t h e o r e m W_{g r} = ∆ K . E \Rightarrow 2 g \times y_{C . G} = \frac{1}{2} \times 2 \times {v_{1}}^{2}$
solving we get $v_{1} = \sqrt{2} m / s e c a n d v_{2} = 120 m / s e c$

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