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 the figure the block and the man are resting on a rough plank of mass M as shown in the figure the whole system is resting on a smooth horizontal surface the man pulls the rope pulley is massless and friction what is the displacement of the plank when the block meets the pulley ( Man does not leave his position on plank during the pull)

Options

A. `0.5m`
B. `1m`
C. zero
D. `2//3m`

Answer

A

Explanation

Since thre is no external horizontal force on whole system C.M. of wholen system need move
`Deltar_(CM)=(m_(1)Deltar_(1)+m_(2)Deltar_(2))/(m_(1)+m_(2))`
`O=(M(x-2)+3Mx)/4m`
`Mx-2M+3Mx=0`
`4x=2`
`x=0.5m`