Question

A uniform solid cylindrical roller of mass 'm' is being pulled on a horizontal surface with force 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:

• A. 2 ma
• B. $\frac{3}{2}$ma
• C. ma
• D. $\frac{5}{3}$ma

Answer 1

The correct option is B $\frac{3}{2}$ma

from figure ma=F-f

but$\frac{m{R}^2}{2}\times \alpha =f\times R⟹\frac{m{R}^2}{2}\times \frac{a}{R}=fR$

we know $\frac{ma}{2}=f$

now $ma=F-\frac{ma}{2}⟹F=\frac{3ma}{2}$