The moment of inertia of a sphere about its diameter is proportional to the product of its mass and the square of its radius ($I \propto MR^2$). Given that both spheres have the same mass ($M_1 = M_2 = M$) and the ratio of their radii is $R_1 : R_2 = 1 : 2$. The ratio of their moments of inertia will be: $\frac{I_1}{I_2} = \frac{M_1 R_1^2}{M_2 R_2^2} = \left(\frac{R_1}{R_2}\right)^2$ $\frac{I_1}{I_2} = \left(\frac{1}{2}\right)^2 = \frac{1}{4}$ Therefore, the ratio is $1:4$.