Question

A horizontal constant force $F$ is applied at the top point of uniform solid cylinder so that it starts pure rolling. Acceleration of cylinder is :

• A. $\frac{F}{3m}$
• B. $\frac{2F}{3m}$
• C. $\frac{4F}{3m}$
• D. $\frac{5F}{3m}$

Answer 1

The correct option is C $\frac{4F}{3m}$

Such question can be solved by taking instantaneous axis of Rotation about bottom most point $Q$.
Let the angular acceleration of cylinder is $\alpha$ about the instantaneous axis of rotation.


On applying $\sum T=I\alpha$ about axis passing through $Q$.
$[T=F{r}_{\perp },I=I_o+m{d}^2]$
$2FR=(\frac{m{R}^2}{2}+m{R}^2)\alpha$
$\Rightarrow 2FR=\frac{3m{R}^2}{2}\alpha$
$\Rightarrow R\alpha =\frac{4F}{3m}$
For pure Rolling, $a=\alpha R$
$\Rightarrow a=\frac{4F}{3m}$
Acceleration of cylinder is $\frac{4F}{3m}$