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A plank of mass m moving with a velocity...

A plank of mass `m` moving with a velocity `v` along a friction less horizontal track and a body of mass `m//2` moving with `2v` collides with plank elastically. Final speed of the plank is:

A

`(5v)/(3)`

B

`(3v)/(3)`

C

`(2v)/(3)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let the velocities of plank and body of mass `(m)/(2)` move with speed `v_(1)` and `v_(2)` after collision as shown.
From conservation of momentum.

`mv-(m)/(2) 2v=mv_(1)+(m)/(2)v_(2)`
or `2v_(1)+v_(2)=0 ....(1)`
From equation of coefficient of restitution
`e=1=(v_(2)-v_(1))/(v+2v)`
`rArr v_(2)-v_(1)=3v .......(2)`
Solving 1 and 2 we get
`v_(1)=-v`
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