A system of men and trolley is shown in Fig. To the left, end of the string, a trolley of mass `M` is connected on which a man of mass `m` is standing. To the right end of the string another trolley of mass `m` is connected on which a man of mass `M` is standing. Initially, the system is at rest. All of a sudden both the men leap upwards simultaneously with the same velocity `u` w.r.t. ground.

Find the relative velocity of left man with respect to his trolley just after he leaps upwards.

Options

A. `("mu")/(m+M)`
B. `(Mu)/(m+M)`
C. `(2"mu")/(m+M)`
D. `(2"mu")/(m+M)`

Answer

C

Explanation

`I_(1)="mu", I_(2)=Mu,`
`I_(1)-I+Mu_(0), I-I_(2)="mu"_(0)`

Solve to get `u_(0)=((m-M)u)/(m+M)`
Relative velocity of left man w.r.t his trolley
`u+u_(0)=u((m-M)u)/(m+M)=(2"mu")/(m+M)`