Q. Two particles of masses $m_{1}$ and $m_{2}$ initially at rest start moving towards each other under their mutual force of attraction. The speed of the centre of mass at any time $t$, when they are at a distance $r$ apart, is
A) Zero
B) $\left( G\frac{m_{1}m_{2}}{r^{2}}.\frac{1}{m_{1}} \right)t$
C) $\left( G\frac{m_{1}m_{2}}{r^{2}}.\frac{1}{m_{2}} \right)t$
D) $\left( G\frac{m_{1}m_{2}}{r^{2}}.\frac{1}{m_{1} + m_{2}} \right)t$
Explanation
(a) As initially both the particles were at rest therefore velocity of centre of mass was zero and there is no external force on the system so speed of centre of mass remains constant $i.e.$ it should be equal to zero
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.