Question

A wooden block of mass M is suspended by a cord and it is at rest. A bullet of mass $m$ moving with a velocity of $v$ passed through the block and comes out with a velocity $\frac{v}{2}$ in the same direction. Up to what heights the block will rise?

Answer 1

Loss of Kinetic energy of bullet=$\frac{1}{2}m{v}^2-\frac{1}{2}m{\left(\frac{v}{2}\right)}^2$

$=\frac{1}{2}\left(\frac{3m{v}^2}{4}\right)$

$Mgh=\frac{1\times 3}{2\times 4}m{v}^{2}h=\left(\frac{m}{M}\right)\frac{3v^2}{8g}$

$h=\frac{3}{8}\frac{m}{M}\frac{v^2}{g}$