A metallic shell of radius R is charged to a potential V. It is concentrically placed inside another shell of radius 2R, charged to a potential V. If the outer shell is earthed, potential of the inner shell will be 

Q = charge on inner cell $=4\pi {\epsilon }_0.\mathrm{R}.\mathrm{V}$

When the outer shell is earthed, the entire charge residing on its outer surface becomes zero and the charge on the inner surface of outer shell $=-\mathrm{Q}=4\pi {\epsilon }_0\mathrm{RV}$

$\therefore$V' = Potential of inner shell $=\frac{1}{4\pi {\epsilon }_0}.\frac{\mathrm{Q}}{\mathrm{R}}+\frac{1}{4\pi {\epsilon }_0}.\frac{\left(-\mathrm{Q}\right)}{2\mathrm{R}}$

$\Rightarrow \mathrm{V}\text{'}=\mathrm{V}-\frac{\mathrm{V}}{2}=\frac{\mathrm{V}}{2}$