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A solid cylinder of mass 'm' and radius 'R' rests on a plank of mass '2m' lying on a smooth horizontal surface. String connecting the cylinder to the plank is passing over a massless pulley mounted on a movable light block B, and the friction between the cylinder and the plank is sufficient to prevent slipping. If the block B is pulled with a constant force 'F', find the acceleration of the cylinder and that of the plank.



Solution

The correct option is A


For the cyclinder, F2f=ma1        ...(i)

Taking moment of forces about C fR=Iα

f=mRα2( I=mR22)                 .......(ii)

For the plank, F2+f=(2m)a2               ......(iii)

And at the point of contact P, the acceleration of the two bodies must be same

a1Rα=a2                               .....(iv)

from (i)and(ii),(iii)and(iv)F=(ma1+2ma2),andF2+mRα2=2ma2

substititing value of α and solving for a1 and a2, we get acceleration of plank, a2=2F7m,and acceleration

of cyclinder, a1=3F7m

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