A spherical solid ball of volume $V$ is made of a material of density $\rho _1$. It is falling through a liquid of density $\rho _2(\rho _2 < \rho _1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v,$ i.e., $F_{viscous} = -k\upsilon ^2 (k > 0)$. The terminal speed of the ball is
A spherical solid ball of volume $V$ is made of a material of density $\rho _1$. It is falling through a liquid of density $\rho _2(\rho _2 < \rho _1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v,$ i.e., $F_{viscous} = -k\upsilon ^2 (k > 0)$. 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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