A boy of mass m stands on one end of a wooden plank of length I and mass M. The plank is floating on water. If
the boy walks from one end of the plank to the other end at a constant speed, the resulting displacement of the plank is given by

detailed solution

Correct option is C

. Initially, when the body stands on the plank, the momentum o f boy-plank system is zero because they are at rest. Let the boy walks with a speed v on the plank. As a result, let the speed of the plank in the opposite direction be y. Now the total momentum of the system is mv−(M+m)VAccording to the law of consecrations of momentum mv−(M+m)V=0∴ VV=m(M+m) As the distance moved is proportional to the speed, the displacement L' of the plank is givea by L′L=VV=m(M+m)L′=mLM+m