First slide

Collisions

Question

A bullet of mass ‘m’ is fired with certain velocity from a gun of mass M. Gun, which is attached with one end of the spring compresses by distance ‘d’. If ‘K’ is the spring constant K, velocity of the bullet is

Moderate

A

$\frac{d}{m} \sqrt{K M}$
B

$\frac{d}{M} \sqrt{K M}$
C

$d m \sqrt{\frac{1}{M K}}$
D

$m K \sqrt{\frac{1}{d M}}$

Solution

$a p p l y l a w o f c o n s e r v a t i o n o f l i n e a r m o m e n t u m ∴ M V = m u \Rightarrow u = \frac{M V}{m} - - - (1) m a s s o f g u n = M; v e l o c i t y o f g u n = V; m a s s o f t h e b u l l e t = m; v e l o c i t y o f b u l l e t b e u a p p l y l a w o f c o n s e r v a t i o n o f l i n e a r m o m e n t u m, \frac{1}{2} M V^{2} = \frac{1}{2} K d^{2} \Rightarrow V = d \sqrt{\frac{K}{M}} - - - (2) K i s s p r i n g c o n s \tan t; d i s d i s \tan c e o f c o m p r e s s i o n o f t h e s p r i n g s u b s t i t u t e e q n (2) i n e q n (1) \Rightarrow u = \frac{M}{m} d \sqrt{\frac{K}{M}} \Rightarrow u = \frac{d}{m} \sqrt{K M}$

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