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Displacement of COM:Application

A pulley fixe...

Question

A pulley fixed to a rigid support carries a rope whose one end is tied to a ladder with a man and the other end to the counterweight of mass $M$ . The man of mass $m$ climbs up a distance $h$ with respect to the ladder and then stops. If the mass of the rope and the friction in the pulley axle are negligible, find the displacement of the centre of mass of this system.

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Solution

Assumption: No object touches the ground. So, displacement of centre of mass is zero.
On the height gain of main relative to the ladder as well as store of mass.
M adjust their respective height according to $F (e x t) \times$ dispalcement of centreof mass $=$ ext work done on the system,
and ext work done $= 0$

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