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A man of mass ‘m’ standing on a plank of mass ‘M’ which is placed on a smooth horizontal surface, is initially at rest. The man suddenly starts running on the plank with a speed of ‘v’ m/s with respect to the ground. Find the speed of the plank with respect to the ground.

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Let the velocity of plank be x m/s.
By law of conservation of momentum, m*0 + M*0 = m*v + M*x
=> Mx= -mv
=> x= - mv/M 

So the plank moves with speed  "mv/M"  m/s in the direction opposite to direction of motion of the man.
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ans-  mv/m+M
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ANSWER: mv/M+m

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A man of mass M is standing on a plank of equal mass M resting on a smooth surface the
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