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

`T-f=ma` ..(i)
`a_(P)=a_(Q)`
`thereforeRalpha-a=a` ..(ii)
`alpha=(tau)/(I)=(f.R)/((1)/(1)mR^(2))=(2f)/(mR)` ..(iii)
For plank
`F-T-f=Ma` ..(iv)
We have four known `f,Ta` and `alpha`
solving the equations we get,
`a=(F)/(M+3m)`