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 =4πε0.R.VWhen 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 =-Q=4πε0RV∴V' = Potential of inner shell =14πε0.QR+14πε0.-Q2R⇒V'=V-V2=V2