Q. Two identical mass $m\ $moving with velocities $u_{1}$and $u_{2}$collide perfectly inelastically. Find the loss in energy
A) $m(u_{1} - u_{2}^{2})$
B) $\frac{m}{4}\left( u_{1} - u_{2} \right)^{2}$
C) $\frac{m}{2}\left( u_{1} - u_{2} \right)^{2}$
D) $m\left( u_{1} - u_{2} \right)^{3}$
Explanation
(b) Loss in kinetic energy
$= \frac{1}{2}\frac{m_{1}m_{2}\left( u_{1} - u_{2} \right)^{2}}{\left( m_{1} + m_{2} \right)}$
$= \frac{1}{2}\ \frac{m.m\left( u_{1} - u_{2} \right)^{2}}{(m + m\ )}$
$= \frac{m}{4}\left( u_{1} - u_{2} \right)^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.