Q. Two balls of masses $m_{1}$ and $m_{2}$ are separated from each other by a powder charge placed between them. The whole system is at rest on the ground. Suddenly the powder charge explodes and masses are pushed apart. The mass $m_{1}$ travels a distance $s_{1}$ and stops. If the coefficients of friction between the balls and ground are same, the mass $m_{2}$ stops after traveling the distance
A) $s_{2} = \frac{m_{1}}{m_{2}}s_{1}$
B) $s_{2} = \frac{m_{2}}{m_{1}}s_{1}$
C) $s_{2} = \frac{m_{1}^{2}}{m_{2}^{2}}s_{1}$
D) $s_{2} = \frac{m_{2}^{2}}{m_{1}^{2}}s_{1}$
Explanation
(c) We know that in the given condition $s \propto \frac{1}{m^{2}}$
$\therefore\frac{s_{2}}{s_{1}} = \left( \frac{m_{1}}{m_{2}} \right)^{2} \Rightarrow s_{2} = \left( \frac{m_{1}}{m_{2}} \right)^{2} \times s_{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.