Question

A force F is applied at the top of a ring of mass M and radius R placed on a rough
horizontal surface as shown in figure. Friction is sufficient to prevent slipping. The friction force acting on the ring is

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

Answer 1

The correct option is D $zero$

Let F’ be the friction on the ring towards right, a its linear acceleration and α the angular
acceleration about center of mass. Point of contact P is momentarily as rest i.e., ring will rotate
about P.
$\alpha =\frac{Tp}{Ip}=\frac{F\left(2R\right)}{2M{R}^2}=\frac{F}{MR}nowF+F^{\prime }=Ma=MR\alpha =For{F}^{\prime }=0$