Question

A body of mass $m$ falls from a height $h$ and collides with another stationary body of same. If the two bodies combine together and move after collision, calculate the velocity of combined system.

Answer 1

The potential energy will be equal to kinetic energy so,

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

So, $v=\sqrt{2gh}$

As both the bodies combine together and move, their momentum will remain conserve

According to principle of conservation of momentum will be,

$m\left(\sqrt{2gh}\right)+m\left(0\right)=2m\left(v^{\prime }\right)$

$v^{\prime }=\sqrt{\frac{gh}{2}}$