Question

A stationary Pulley carries a ropes one end of which supports a ladder with a man and other a counter weight of mass M . The man of mass M climbs up a distance `l' w.r.t the ladder and then stops.The displacement of the centre of mass of this system is 5x, then x is

Answer 1

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)

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