Question

Two particles of mass $m$ and $2m$ have a perfectly inelastic collision. Before collision velocity of $m$ is $u\hat{i}$ and velocity of $2m$ is $-\frac{u}{2}\hat{i}$. Loss of kinetic energy will be

• A. $\frac{m{u}^2}{6}$
• B. $\frac{7m{u}^2}{12}$
• C. $\frac{3m{u}^2}{4}$
• D. $\frac{m{u}^2}{12}$

Answer 1

The correct option is C $\frac{3m{u}^2}{4}$

Applying conservation of momentum
$\overrightarrow{P_i}=mu\hat{i}-2m\frac{u}{2}\hat{i}\overrightarrow{P_i}=0$

$\overrightarrow{P_f}=3m\overrightarrow{v}$

$3m\overrightarrow{v}=0$
$\overrightarrow{v}=0$

$K.E_i=\frac{1}{2}m{u}^2+\frac{1}{2}2m{(-\frac{u}{2})}^{2}K.E_i=\frac{1}{2}m{u}^2+\frac{m{u}^2}{4}=\frac{3m{u}^2}{4}$

$K.E_f=\frac{1}{2}m{v}^2=0$

$\text{Loss}=K.E_i-K.E_f=\frac{3}{4}m{u}^2-0\text{Loss}=\frac{3}{4}m{u}^2$