Question

A ball of mass $m$ moving with speed $u$ undergoes a head on collision with a stationary ball of mass $3m$. If collision is perfectly inelastic, find the loss of kinetic energy.

• A. $\frac{1}{4}m{u}^2$
• B. $\frac{1}{8}m{u}^2$
• C. $\frac{1}{16}m{u}^2$
• D. $\frac{3}{8}m{u}^2$

Answer 1

The correct option is D $\frac{3}{8}m{u}^2$

For inelastic collision, both ball will move together with speed $v$ after collision.
Now, applying momentum conservation,
$mu+0=(m+3m)v$
$\Rightarrow v=\frac{u}{4}$
Initial kinetic energy $=\frac{1}{2}m{u}^2$
Final kinetic energy $=\frac{1}{2}(m+3m)v^2$
$=\frac{1}{2}\left(4m\right){\left(\frac{u}{4}\right)}^2$
$=\frac{1}{8}m{u}^2$
So, Loss in KE = Initial KE - Final KE
$=\frac{1}{2}m{u}^2-\frac{1}{8}m{u}^2$
$=\frac{3}{8}m{u}^2$