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

Options

A. `(5v)/(3)`
B. `(3v)/(3)`
C. `(2v)/(3)`
D. none of these

Answer

D

Explanation

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_(1) + (m)/(2) v_(1)`
or `2v_(1) + v_(2) = 0` ....(1)
`e = 1 = (v_(2) - v_(1))/(v + 2v) implies v_(2) - v_(1) = 3v` ....(2)
Solving (1) and (2) , we get `v_(1) = v`.