A rope thrown over a pulley has a ladder with a man of mass m on one of its ends and a counter balancing mass M on its other end. The man climbs with velocity $V_r$ relative to the ladder. Ignoring the masses of the pulley as well as the friction on the pulley axis, the velocity of the centre of mass of this system is

Question

$$\begin {array} {1 1} (a)\;\frac{m}{M}Vr & \quad (b)\;\frac{m}{2M}Vr \\ (c)\;\frac{M}{m}V_r & \quad  (d)\;\frac{2M}{m}Vr \end {array}$$