A particle is revolving in a circle of radius R . If the force...

Given that the force is inversely proportional to $R$ i.e. $\quad F \propto \frac{1}{R} or$\quad F=\frac{k}{R}$or$m R \omega^2=\frac{k}{R}$or$\quad \omega^2=\frac{k}{m R^2}\therefore \quad \omega^2 \propto \frac{1}{R^2}$\begin{array}{llrl} \Rightarrow& & \omega& \propto \frac{1}{R}\\ \Rightarrow & \frac{2 \pi}{T} \propto \frac{1}{R}\\ \Rightarrow & T & \propto R \end{array}$$