The terminal velocity $$v_t$$ of a spherical body falling through a viscous fluid is given by Stokes' Law, which states that:

$$ v_t = \frac{2}{9}\frac{(\rho_s - \rho_f)gr^2}{\eta} $$

where:

• $ \rho_s $ is the density of the sphere
• $ \rho_f $ is the density of the fluid
• $ g $ is the acceleration due to gravity
• $ r $ is the radius of the sphere
• $ \eta $ is the dynamic viscosity of the fluid

As per Stokes' Law, the terminal velocity is proportional to the square of the radius of the sphere (since the radius term $$r^2$$ is in the numerator).

Note that Reason R states that the terminal velocity is "inversely proportional" to its radius, which is contrary to the relationship presented by Stokes' Law. Therefore, Reason R is false.

Moving on to Assertion A, we can consider the percentage error in the radius to determine the percentage error in the terminal velocity. If the radius $$r$$ has an error of $$ \pm 0.1 \mathrm{mm} $$ at $$ 5 \mathrm{mm} $$, then the relative error in the radius is:

$$ \frac{0.1}{5} = 0.02 \text{ or } 2\% $$

Since the terminal velocity varies with the square of the radius, the percentage error in the terminal velocity would be twice the percentage error in the radius.

$$ \text{Percentage error in } v_t = 2 \times \text{ (Percentage error in } r) $$

$$ \text{Percentage error in } v_t = 2 \times 2\% = 4\% $$

This is in agreement with Assertion A, making it true.

Given this analysis, the correct statement is:

Option B: A is true but $$\mathbf{R}$$ is false.