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Question

Two particles of masses m and 2m moving in opposite direction collides elastically with velocities 2v and v respectively. Find their respective magnitude of velocities after the collision.


A
2v, v
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B
v, 2v
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C
v, v
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D
4v, 0
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Solution

The correct option is A 2v, v
Let the final velocities of m and 2m be v1 and v2 respectively.



By conservation of momentum in xdirection, we get:

m(2v)+2m(v)=m(v1)+2m(v2)

0=mv1+2mv2

v1+2v2=0(1)
Also the collision is elastic,
speed of separation = speed of approach

v2v1=2v+v

Or, v2v1=3v(2)
Solving the above two equations, we get

v1=2v and v2=v

Hence, mass m moves with speed 2v along ve, xdirection and mass 2m moves with speed v in the +ve xdirection.

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