Question

Two particles of masses $m$ and $3m$ approach each other with different velocities. After collision, the particle of mass $m$ has velocity $\overset{ \rightarrow }{v}$ in their centre of mass frame. Velocity of particle of mass $3m$ in the centre of mass frame is

• A. $-2\overset{ \rightarrow }{v}$
• B. $-\frac{\overset{ \rightarrow }{v}}{2}$
• C. $-\frac{\overset{ \rightarrow }{v}}{3}$
• D. $-\frac{\overset{ \rightarrow }{v}}{4}$

Answer 1

Answer: (C)

In the centre of mass frame, the total linear momentum of the system is zero.
Hence, $m\overset{ \rightarrow }{v}+3m\overset{ \rightarrow }{v}^{'}=0$
or $\overset{ \rightarrow }{v}^{'}=-\frac{\overset{ \rightarrow }{v}}{3}$