Dear Aditya Nijampurkar,

Ans:

Let us consider the following

a1=Acc of the cylinder towards right

a2=Acc of the plank towards right

β= clockwise angular Acc of the cylinder

f1= The force of friction at the point of contact of the bodies

f2=The force of friction at the bottommost surface

The eq of motions of the Plank and the cylinder are,

F - f1=m2 a2..........................(1)

(f1+f2)r=Iβ.............................(2)

f1 - f2=m1 a1.............................(3)

Now the conditions of non sleepping are

βr+a1 = a2........................(4)

βr=a2...............................(5)

Solving we get

a2=8F/(3m1+8m2)

a1=4F/(3m1+8m2)

f1=3m1 F/(3m1+8m2)

f2= - m1 F/(3m1+8m2)

The negative sign indicates that friction between the ground and the cylinder  acts in the forward direction.

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