Sphere in the figure is a spherical capacitor with inner sphere earthed. The capacitance of the system is

$\frac{4 \pi \varepsilon_0 b^2}{b-a}$

The potential on the outer sphere is V (let). Thus we can consider two capacitors between the outer sphere and inner sphere C₁ and outer sphere and earth C₂. These two capacitors are in parallel.

Thus, $C_1=4 \pi \varepsilon_0 \frac{ab}{b-a}$

$C_2=4 \pi \varepsilon_0 b$

$C_1=4 \pi \varepsilon_0 \frac{ab}{b-a}+4 \pi \varepsilon_0 b$

$\Rightarrow C=\frac{4 \pi \varepsilon_0 b^2}{b-a}$

∴ (B) is correct.