Question

A block of wood of mass $9.8kg$ is suspended by a string. A bullet of mass $200gm$ strikes horizontally with a velocity of $100m{s}^{-1}$ and gets imbedded in it. To what height will the block rise?
$(g=10m{s}^{-2})$

• A. $0.1m$
• B. $0.2m$
• C. $0.3m$
• D. $0m$

Answer 1

The correct option is B $0.2m$

A block of mass $M$ is suspended by means of a rope $l$ . A bullet of mass $m$ moving with a velocity $u$ collides with the block and get embedded on it and if the block raised to a height $h$
By using law of conservation of momentum,we get,
$mu=(M+m)v$

$\Rightarrow v=\left(\frac{m}{M+m}\right)u$

By using conservation of energy, we get,

$\frac{1}{2}m{v}^2=mgh$

$\Rightarrow h=\frac{v^2}{2g}$

$\Rightarrow h={\left(\frac{m}{M+m}\right)}^2\frac{u^2}{2g}$

But $u=100$ms${}^{-1},m=200$gm$=0.2$kg$,M=9.8$kg

$\Rightarrow h={\left(\frac{0.2}{9.8+0.2}\right)}^2\frac{{100}^2}{2\times 9.8}=\frac{2}{9.8}\approx 0.2m$