Question

# A mon of mass 'm' moves on a plank of mass 'M' with a constant velocity 'u' with respect to the plank (as shown in the figure). If the plank rests on a smooth horizontal surface, then determine the final velocity of the plank.

A

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B

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C

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D

u

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Solution

## The correct option is A As no external forces are acting on the system in horizontal direction , so its linear momentum remain constant in that direction.Also there will be no shift in postion of center of mass. i.e △Xcm = 0 .Let v1 and v2 are the velocties of the man and the plank with respect to ground. Then we have. [→Vman]plank = [→Vman]ground - [→Vman]ground Then [→Vman]ground = [→Vman]plank + [→Vman]ground or v1 = u - v2 Initially the system is at rest , therefore 0 = m v1 - mv2 or 0 - m(u - v2 ) - M v2 or v2 = mum+M

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