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A pulley fixed to a rigid support carries a rope whose one end is tied to a ladder and a man and the other end to the counterweight of mass M. The man of mass m climbs up a distance of 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 center of mass of the system.

A pulley fixed to a rigid support carries a rope whose one end is tied to a ladder and a man and the other end to the counterweight of mass M. The man of mass m climbs up a distance of 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 center of mass of the system.



Grade:11

2 Answers

Abhijeet Kant
29 Points
13 years ago

Assumption: No object touches the ground.

Answer: Displacement of center of mass is zero.

Reason: On height gain of man relative to the ladder, ladder as well as stone of mass M adjust their respective heights according to:

F(ext.)*disp. of C.O.M.=ext. work done on the system

and ext. work done=0.

Gandharv
14 Points
8 years ago
To find the displacement in centre of mass of the system find end displacement of man with respect to ground. Let X be the displacement of ladder so displacement of man with respect to ground is       h-X (we take downward direction as negative). Displacement of centre of mass = [Mx-x(M-m)+m(h-x)]/(M+M-m+m)= mh/2M.
(Mass of ladder is M-m the system was initially at rest)
 

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