$A$ 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.,$F_{viscous} = -kv^2$ $(k > 0)$. The terminal speed of the ball is:

  • A
    $\frac{Vg(\rho_1 - \rho_2)}{k}$
  • B
    $\sqrt{\frac{Vg(\rho_1 - \rho_2)}{k}}$
  • C
    $\frac{Vg\rho_1}{k}$
  • D
    $\sqrt{\frac{Vg\rho_1}{k}}$

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