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

Answer 1

Answer: (C)

$\frac{3}{2}$ ma

Answer 2

$F-f=m a$...(1)
$f^{r}=\left(\frac{m r^{2}}{2}\right)\left(\frac{a}{r}\right)$...(2)
$f=\frac{m a}{2}.$ Therefore, $F=\frac{3 m a}{2}$