Question

A ring of mass m and radius is acted upon by a force F as shown in the figure. There is sufficient friction between the ring and ground. The force of friction force necessary for pure rolling is:

• A. $\frac{F}{2}Forward$
• B. $\frac{F}{3}Forward$
• C. $zero$
• D. $\frac{F}{4}backward$

Answer 1

The correct option is C $zero$

$\begin{array}{c}F+f=ma--------\left(1\right)\\ \left(F-f\right)R=m{R}^2\cdot \alpha \\ =m{R}^2\cdot \frac{a}{R}\\ \Rightarrow F-f=ma\\ \Rightarrow 2F=2ma\\ \Rightarrow a=\frac{F}{m}\\ \therefore f=0\end{array}$

Hence,

option $\left(C\right)$ is correct answer.