A spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_1 (\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{viscous} = -kv^2 (k > 0)$. 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 $\rho_1 (\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{viscous} = -kv^2 (k > 0)$. The terminal speed of the ball is
- A
$\sqrt {\frac{{Vg\left( {{\rho _1} - {\rho _2}} \right)}}{k}}$
- B
$\frac{{Vg{\rho _1}}}{k}$
- C
$\sqrt {\frac{{Vg{\rho _1}}}{k}}$
- D
$\frac{{Vg\left( {{\rho _1} - {\rho _2}} \right)}}{k}$
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