Question

A bullet fired horizontally with a speed of $400m/sec$. It strikes a wooden block of mass $2kg$ hanging vertically with the help of long string. After striking with bullet, block rises a height of $20cm$. If speed with which bullet emerges out from block is $10\lambda$ then find $\lambda$. Mass of bullet is $20gm$. (take $g=10m/s^2$)

Answer 1

Given mass of wooden block $M=2kg$ and mass of bullet , $m=20gm=0.02kg$

Let speed of wooden block after collision is $v$. Block rises by $h=20cm=0.2m$

Using conservation of mechanical energy, $K{E}_1+P{E}_1=K{E}_2+P{E}_2$

$\Rightarrow \frac{1}{2}m{v}^2+0=0+mgh$ $\Rightarrow v=\sqrt{2gh}=\sqrt{2\times 10\times 0.2}=2m/s$

There are no external force are acting so momentum will be conserved.

Linear momentum before collision = Linear Momentum after collision

$\Rightarrow 0.02\times 400+2\times 0=0.02\times 10\lambda +2\times 2$

$\Rightarrow \lambda =10$