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

At terminal velocity, the net force on the falling sphere is zero. The viscous drag force ($F_v$) exactly balances the effective weight of the sphere (actual weight minus buoyant force).

$F_v = W - F_B$
$F_v = \dfrac{4}{3}\pi r^3 \sigma g - \dfrac{4}{3}\pi r^3 \rho g$
$F_v = \dfrac{4}{3}\pi r^3 (\sigma - \rho) g$

For a given material (constant $\sigma$) and liquid (constant $\rho$), the viscous drag force at terminal velocity is directly proportional to the volume of the sphere, and hence to the cube of its radius ($F_v \propto r^3$).

Therefore, Reason (R) is correct.

Using this proportionality for spheres of radii $r$ and $2r$:
$\dfrac{F_{v2}}{F_{v1}} = \left(\dfrac{2r}{r}\right)^3 = 8$

The drag force on the larger sphere is 8 times that on the smaller sphere. Thus, Assertion (A) is correct.

Since Reason (R) provides the exact mathematical relationship used to derive Assertion (A), it is the correct explanation.

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