Consider a disc of mass `m` and radius `R` placed on a rough plank of mass `M` which is turn is place on a smooth horizontal surface. Now plank is pulled by a force `F` and disc starts to roll on the plank.
If there is no friction any where then find
`(a)` Fricition force acting on the disc
`(b)` Angular acceleration of the disc

Explanation

Let us apply Newton's laws on disc in horizontal direction

`f=ma`……..`(i)`
For plank
`F-f=Ma_(1)`……….`(ii)`
Applying torque equation on disc about centre of mass
`tau=l alpha`
`impliesfR=(mR^(2))/(2)alpha`........`(iii)`
For pure rolling
`a_(1)=a+Ralpha`.......`(iv)`
Solving the four equations, we get
`f=(Fm)/(m+3M)`, `alpha=(2F)/((m+3M)R)`