Question

A block of mass M is tied to one end of a massless rope. The other end of the rope is in the hands of a man of mass 2M as shown in figure. The block and the man are resting on a rough wedge of mass M. The whole system is resting on a smooth horizontal surface. The man starts walking towards right while holding the rope in his hands. Pulley is massless and frictionless. Find the displacement of the wedge when the block meets the pulley. Assume wedge is sufficiently long so that man does not fall down :

• A. 1/2 m towards right
• B. 1/2 m towards left
• C. the wedge does not move at all
• D. 1 m towards left

Answer 1

The correct option is B 1/2 m towards left

As the eternal horizontal force the system is zero and initially the is at rest.

$\Delta X_{cm}=0$

$⟹m_{block}{\Delta x}_1+m_{man}{\Delta x}_2+m_{wedge}{\Delta x}_3=0$

$⟹M(l-2)+2Ml+Ml=0$

$⟹l=\frac{2M}{4M}=0.5$ towards the left