The charge Q given to outer sphere distributes as Q 1 outside and Q 2 inside which induces charge – Q 2 on outside of inner sphere, + Q 2 on inside of inner sphere which is earthed.

The inside of outer and the inner sphere constituting a spherical condenser having capacitance $4 \pi \epsilon_0 \frac{ab}{b - a}$ and the outside of the outer constitutes an isolated sphere of capacitance $4 \pi \epsilon_0 b$. $\therefore$ the effective capacitance is $4 \pi \epsilon_0 \frac{ab}{b - a} + 4 \pi \epsilon_0 b$ $= 4 \pi \epsilon_0 b \left[\frac{a}{b - a} + 1 \right]$ $= 4 \pi \epsilon_0 b \left[\frac{a + b - a}{b - a}\right]$ $C = 4 \pi \epsilon_0 \frac{b^2}{b - a}$