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., $F _ { \text{viscous} } = - k v ^ { 2 }$ $(k > 0)$. The terminal speed of the ball is (1) $\sqrt { \frac { Vg \left( \rho _ { 1 } - \rho _ { 2 } \right) } { k } }$ (2) $\frac { Vg \rho _ { 1 } } { k }$ (3) $\sqrt { \frac { V g \rho _ { 1 } } { k } }$ (4) $\frac { Vg \left( \rho _ { 1 } - \rho _ { 2 } \right) } { k }$
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., $F _ { \text{viscous} } = - k v ^ { 2 }$ $(k > 0)$. The terminal speed of the ball is\\
(1) $\sqrt { \frac { Vg \left( \rho _ { 1 } - \rho _ { 2 } \right) } { k } }$\\
(2) $\frac { Vg \rho _ { 1 } } { k }$\\
(3) $\sqrt { \frac { V g \rho _ { 1 } } { k } }$\\
(4) $\frac { Vg \left( \rho _ { 1 } - \rho _ { 2 } \right) } { k }$