A rope thrown over a pulley has a ladder with a man of mass m on one of its ends and a counter balancing mass M on its other end. The man ascends at a speed appropriate to the ladder. The velocity of the system's center of mass, disregarding the masses of the pulley and the rope as well as the friction on the pulley axis, is:

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m M v r

m 2 M v r

M m v r

2 M m v r

answer is B.

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Detailed Solution

Concept: In order to provide a solution to this problem, we must first ascertain the mass of the ladder, then apply the relative velocity concept to determine the velocity of each mass with respect to the ground, and finally apply the formula to ascertain the given system's center of mass.
Mass of Man

Man of ladder

If a man moves up, the ladder moves down and the counterbalancing man moves up.
Velocity of man relative to ladder

Velocity of ladder

Velocity of man relative to ground

The difference between the velocities of body A and body B determines the relative velocities between them.
Hence, the correct option is 2.

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