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. When the men are at the highest point of their motion, the trolleys will also be instantaneously at rest.
B. When the men are at the highest point of their motion, then the left trolley will be moving downwards.
C. Impulse acting on both the men will be same in the given process.
D. None of these

Answer

A

Explanation

Time taken for men to come to rest:
`t_(1)=u/g`
Acceleration of trolleys (after the men have jumped)
`a=((m-M))/(m+M)g`
Time taken by trolleys to come to rest:
`t_(1)=(u_(0))/a=u/g`