Explanation

(b) Thermal capacity = Mass $\times$ Specific heat
Due to same material both spheres will have same specific heat.
Also mass = Volume $(V)$ $\times$ Density ($\rho)$
$\therefore$ Ratio of thermal capacity
$\ = \frac{m_{1}}{m_{2}} = \frac{V_{1}\rho}{V_{2}\rho} = \ \frac{\frac{4}{3}\pi r_{1}^{3}}{\frac{3}{4}\pi r_{2}^{3}} = \left( \frac{r_{1}}{r_{2}} \right)^{3}$
=$\ \left( \frac{1}{2} \right)^{3} = \frac{1}{8}$