1. For a small spherical body moving through a viscous fluid, the viscous drag force is given by Stokes' law:

$F = 6\pi \eta R v$

where:

• $\eta$ = coefficient of viscosity,
• $R$ = radius of the spherical ball,
• $v$ = velocity of the ball.

2. From the formula,

$F \propto \eta R v$

Since $\eta$ is the fluid property and fixed here, we get:

$F \propto Rv$

3. Therefore, the retarding viscous force is:

• directly proportional to radius $R$, and
• directly proportional to velocity $v$.

4. Checking options:

• A: inversely proportional to both $R$ and $v$ $\rightarrow$ wrong
• B: directly proportional to both $R$ and $v$ $\rightarrow$ correct
• C: directly proportional to $R$ but inversely proportional to $v$ $\rightarrow$ wrong
• D: inversely proportional to $R$ but directly proportional to $v$ $\rightarrow$ wrong

Hence, the correct option is B.