question_answer

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.\[{{F}_{viscous}}=-k{{v}^{2}}(k>0)\]. The terminal speed of the ball is       AIEEE  Solved  Paper-2007

A) \[\sqrt{\frac{Vg{{\rho }_{1}}}{k}}\]         

B)        \[\frac{Vg\left( {{\rho }_{1}}-{{\rho }_{2}} \right)}{k}\]

C)                                        \[\sqrt{\frac{Vg\left( {{\rho }_{1}}-{{\rho }_{2}} \right)}{k}}\]                

D)                        \[\frac{Vg{{\rho }_{1}}}{k}\]