Find the acceleration of the cylinder of mass `m` and radius `R` and that of plank of mass `M` placed on smooth surface if pulled with a force `F` as shown in figure. Given that sufficient friction is present between cylinder and the plank surface to prevent sliding of cylinder.

Explanation

`F-T-f=Ma`……i
`T-f=Ma`…………ii
`alpha=(fR)/(1/2mR^(2))=(2f)/(mR)`…….iii
Constraint relation `a_("plank")=a_(P)`
`Ralpha-a=a`
or `Ralpha=2a`……iv

Solving these equations, we get
`a=F/(3m+M)`