Question

A bullet of mass $20g$ moving horizontally at a speed of $300m/s$ is fired into a wooden block of mass $500g$ suspended by a long string. The bullet crosses the block and emerges on the other side. If the centre of mass of the block rises through a height of $20.0cm$, find the speed of the bullet as it emerges from the block.

Answer 1

let m is the mass of bullet, $m=0.02Kg$

mass of block is $M=0.5Kg$

velocity of bullet with which it strikes $u=300m/s$

Bullet comes out with velocity V and velocity of block$=v^{{}^{\prime }}$

$h=0.2m$

According to work- energy theorem(for the block after the collision):

$0-\frac{1}{2}M\times {v^{{}^{\prime }}}^2=mgh$

Put all the values and we get $v^{\prime }=2m/s$

On applying conservation of momentum

$mu=M{v}^{\prime }+mv$

$0.02\times 300=0.5\times 2+0.02\times v$

$v=250m/s$