$A$ spherical solid ball of volume $V$ is made up of a material of density $\rho$. It is falling through a liquid of density $\sigma$ $(\sigma < \rho)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of the terminal speed $v_{T}$,$F = -K v_{T}^2$ $(K > 0)$. Then,the terminal speed of the ball is ($g =$ acceleration due to gravity).

• A
  $\left[\frac{V g \rho}{K}\right]^{\frac{1}{2}}$
• B
  $\left[\frac{V g(\rho-\sigma)}{K}\right]^{\frac{1}{2}}$
• C
  $\frac{V g(\rho-\sigma)}{K}$
• D
  $\frac{V g \rho}{K}$