1.

to a rigid support carries a rope whose one end is tied to a ladder with a man andm climbs up a distance h withA pulley fixedthe other end to the counterweight of mass M. The man of massrespect to the ladder and then stops. If the mass of the rope and the friction in the pulley axle arnegligible, find the displacement of the centre of mass of this system.

Answer»

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)

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.



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