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A spherical solid ball of volume \( V \) is made of a material of density \( \rho_{1} \). It is falling through a liquid of density \( \rho_{2}\left(\rho_{2}\rho_{1}\right) \). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed \( v \), i.e., \( F_{\text {viscous }}=-k v^{2}(k0) \). The terminal speed of the ball is
[AIEEE 2008]
(a) \( \frac{V g \rho_{1}}{k} \)
(b) \( \sqrt{\frac{V g \rho_{1}}{k}} \)
(c) \( \frac{\operatorname{Vg}\left(\rho_{1}-\rho_{2}\right)}{k} \)
(d) \( \sqrt{\frac{\operatorname{Vg}\left(\rho_{1}-\rho_{2}\right)}{k}} \)
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