A plank of mass m₁ is kept on top of a cylinder of mass m₂ kept on a horizontal plane................A Horizontal Force is

being applied on the plank.

a)Find the accln of the plank......

b)Find the accln of the centre of mass of the cylinder.....

c)Find the frictional forces acting in all surfaces..........(Soory dnt have the answers).........Solve with proper solution

posted with fbd................

Consider the cylinder. Let us assume that the friction force exerted by the plank on the cylinder be f1 and let the friction force exerted by the ground on the cylinder be f2.

We choose the directions arbitrarily. Let f1 be in the backward direction and f2 be in the forward direction.

Consider the free body diagram of the plank m1 .

We have F-f2 = m1(a1)..........(1)  (Where a1 is the acceleration of the plank.

Now, considering the linear acceleration of the cylinder,

f2-f1 = m2(a2) ..........(2)

As the cylinder also rotates, and assuming that this is a case of accelerated rolling, we have,

(f1+f2)R = I(k)........(3) where I= MI of cylinder about Centre of Mass and k is its angular acceleration.

Now, since it is a case of accelerated rolling, there is no relative acceleration between any two surfaces in contactand k = (a2)/R ...........(4)

further, 2a2 = a1 ...............(5)

and I = (m2)R²/2 ..............(6)

f2+f1 = (m2)(a2)/2 ...........(7)

Solve these 7 equations for f1, f2, a1, a2.