Given below are two statements: one is labelled as Assertion (A)...

According to Stokes' law, the viscous drag force is given by $F_v = 6\pi\eta r v$.

The terminal velocity $v_t$ of a sphere of radius $r$ and density $\rho$ falling in a liquid of density $\sigma$ and viscosity $\eta$ is given by $v_t = \dfrac{2}{9}\dfrac{r^2(\rho - \sigma)g}{\eta}$.

Therefore, the terminal velocity is directly proportional to the square of the radius ($v_t \propto r^2$).

Substituting this into Stokes' law, we get $F_v \propto r(r^2) \Rightarrow F_v \propto r^3$.

Thus, the Reason is correct.

For two spheres of radii $R$ and $2R$, the ratio of their viscous drag forces at terminal velocity will be $R^3 : (2R)^3 = 1 : 8$.

Thus, the Assertion is also correct, and the Reason is the correct explanation for the Assertion.

Answer: Both (A) and (R) are correct and (R) is the correct explanation of (A)