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 2008]

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)       \[\frac{Vg{{\rho}_{1}}}{k}\] Correct Answer: C Solution : [c]

The ball will acquire terminal speed in the state of equilibrium