Q. Two spherical bodies of the same mass $M$ are moving with velocities $v_{1}$ and $v_{2}$. These collide perfectly inelastically
A) $\frac{1}{2}M\left( v_{1} - v_{2} \right)^{2}$
B) $\frac{1}{2}M\left( v_{1}^{2} - v_{2}^{2} \right)^{2}$
C) $\frac{1}{4}M\left( v_{1} - v_{2} \right)^{2}$
D) $2M(v_{1}^{2} - v_{2}^{2})$
Explanation
(c) Loss of kinetic energy $= \frac{1}{2}\frac{m_{1}m_{2}}{m_{1}{+ m}_{2}}\left( v_{1} - v_{2} \right)^{2}$
$= \frac{1}{2}\frac{M \times M}{(M + M)}\left( v_{1} - v_{2} \right)^{2}$
$= \frac{M \bullet M}{2(2M)}\left( v_{1} - v_{2} \right)^{2}$
$= \frac{M}{4}\left( v_{1} - v_{2} \right)^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.