First slide

Motion of centre of mass

Question

Two particles of same mass are permitted to move towards each other along the line joining their centers of mass. At a particular moment of time their speeds are v and 2 v What is the speed of their common center of mass at this instant ?

Moderate

A

zero
B

0.5 v
C

v
D

3 v

Solution

L€t m be the mass of each particle. The velocity of center of mass is given by
$v_{CM} = \frac{m_{1} v_{1} + m_{2} v_{2}}{m_{1} + m_{2}} = \frac{m (- v) + m (2 v)}{m + m} = \frac{mv}{2 m} = 0 \cdot 5 V$

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