A uniform solid cylindrical roller of mass 'm' is being pulled on a horizontal surface F parallel to the surface and applied at its centre. If the acceleration of the cylinder is 'a' and it is rolling without slipping then the value of 'F' is?

Writing equation of motion of center of mass of cylinder
F−f=ma
Centerofmass=ma.. (i)
Writing torque equation for cylinder about center:
fR=ICenterofmassα.. (ii)
where α is angular acceleration and ICenterofmass=MR²/2
substituting value of f in equation (i)
F=ma+MRα/2.. (iii)
As the cylinder is rolling without slipping, the acceleration of point of contact will be zero
aCenterofmass−Rα=0
⇒α=aCenterofmass/R=a/R
substituting value of α in equation (iii)
F=ma+MRa/R2
F=32ma