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 propoertional to the square of its speed $v$ , i.e., ${F_{{\rm{viscous}}}} = - k{v^2}\left( {k > 0} \right)$. Then terminal speed of the bal 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 ${\rho _2}\left( {{\rho _2} < {\rho _1}} \right)$. Assume that the liquid applies a viscous force on the ball that is propoertional to the square of its speed $v$ , i.e., ${F_{{\rm{viscous}}}} = - k{v^2}\left( {k > 0} \right)$. Then terminal speed of the bal 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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