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