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 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
- [AIEEE 2008]
- [AIIMS 2013]
- A
$\frac{{Vg\left( {{\rho _1} - {\rho _2}} \right)}}{k}$
- B
$\sqrt {\;\frac{{Vg\left( {{\rho _1} - {\rho _2}} \right)}}{k}} $
- C
$\;\frac{{Vg{\rho _1}}}{k}$
- D
$\;\sqrt {\frac{{Vg{\rho _1}}}{k}} $
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