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 impulse generated in the string connecting the trolleys during this process.

Options

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

Answer

B

Explanation

`I+I_(1)-Mu_(0)="mu"-Mu_(0)="mu"-(M(m-M))/(m+m)u=((m^(2)+M^(2))u)/(M+m)`