Problem 1.160

A stationary pulley carries a rope whose one end supports a ladder with a man and the other end the counterweight of mass \(M\). The man of mass \(m\) climbs up a distance \(l^{\prime}\) with respect to the ladder and then stops. Neglecting the mass of the rope and the friction in the pulley axle, find the displacement l of the centre of inertia of this system.