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Question

Two particles which are initially at rest, move towards each due to mutual attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be

A
2v
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B
1.5v
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C
0
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D
v
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Solution

The correct option is C 0
The figure shown below represents the velocity of particles moving under influence of attractive forces.

velocity of c.o.m is given by,
vcom=m1v1+m2v2m1+m2
Since particles are starting from rest, in initial case:
vc.o.m=0 and v1=v2=0
As they starts moving towards each other under the influence of mutual attraction, taking both particles as system attractive forces become internal for the system.
Fext=0
for the system of particles, applying newton's second law:
Fext=macom
Hence acom=0
vcom=constant
Therefore velocity of COM will not change.
vi=vf=0
Speed of COM of the system at any instant will be Zero.

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