Question

A uniform solid cylinder of mass $m$ and radius $R$ is placed on a rough horizontal surface A horizontal constant force $F$ is applied at the top point $P$ of the cylinder so that it starts pure rolling. The frictional force on the cylinder is :

• A. zero.
• B. $\frac{F}{3}$, towards left
• C. $\frac{2F}{3}$, towards right
• D. $\frac{2F}{3}$, towards left

Answer 1

The correct option is A zero.

Let f be the friction on the ring towards right. a be the linear acceleration and $\alpha$ be the angular acceleration about the center of mass. The point P is momentarily at rest. %That is the cylinder will rotate about P. The radius of the cylinder is R and mass m (given)

Therefore, angular momentum, $\alpha =\frac{{\tau }_P}{I_P}=\frac{F\left(2R\right)}{{2mR}^2}$

=$\frac{F}{mR}$

F= mR$\alpha$

Now, F+f= ma = mR$\alpha$ = F

Therefore f=0. Frictional force is 0.