A uniformly charged thin spherical shell of radius R carries...

Electrical force per unit area $=\frac{1}{2} \varepsilon_0 E^2$ =\frac{1}{2} \varepsilon_0$\left(\frac{\sigma}{\varepsilon_0}\right)^2=\frac{\sigma^2}{2 \varepsilon_0} Projected area $=\pi R^2 \therefore$ net electrical force =\left(\frac{\sigma^2}{2 \varepsilon_0}\right)\left(\pi R^2\right)$In equilibrium, this force should be equal to the applied force.$\therefore \quad F=\frac{\pi \sigma^2 R^2}{2 \varepsilon_0}$or$\quad F \propto \frac{\sigma^2 R^2}{\varepsilon_0}\therefore$ The correct option is (a).