Explanation (Complete Step-by-Step)

According to Stokes' law, terminal velocity of a spherical body in a viscous fluid is:

\[ v_t = \frac{2}{9} \frac{r^2 (\rho - \sigma) g}{\eta} \]

For the same material and same fluid, \( \rho \), \( \sigma \), \( g \) and \( \eta \) remain constant.

Therefore,

\[ v_t \propto r^2 \]

So the ratio of terminal velocities is:

\[ \frac{v_1}{v_2} = \frac{r_1^2}{r_2^2} \]

Given:

\[ r_1 = 6 \text{ mm}, \quad v_1 = 20 \text{ cm/s} \]

\[ r_2 = 3 \text{ mm} \]

\[ \frac{20}{v_2} = \frac{6^2}{3^2} \]

\[ = \frac{36}{9} \]

\[ = 4 \]

\[ v_2 = \frac{20}{4} \]

\[ v_2 = 5 \text{ cm/s} \]

Therefore, required terminal velocity = 5 cm/s

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