$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ (where $\rho_2 < \rho_1$). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{viscous} = -kv^2$ (where $k > 0$). Then the terminal speed of the ball is:
- A$\sqrt{\frac{Vg(\rho_1 - \rho_2)}{k}}$
- B$\frac{Vg\rho_1}{k}$
- C$\sqrt{\frac{Vg\rho_1}{k}}$
- D$\frac{Vg(\rho_1 - \rho_2)}{k}$
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If $a = \frac{1-i \sqrt{3}}{2}$,then the correct matching of List-$I$ with List-$II$ is:
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| $(iv) \ \operatorname{Im}\left(\frac{4}{3a}\right)$ | $(D) 1$ |
| $(E) \frac{\pi}{3}$ | |
| $(F) \frac{2}{\sqrt{3}}$ |
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