question_answer

A solid rubber ball of density \[\rho \] and radius R falls vertically through air. Assume the air resistance on the ball is \[F=kRv,\] where k is a constant and v is the velocity. Because of this air resistance, the ball attains a constant velocity called terminal velocity \[{{v}_{T}}\] after some  time, then \[{{v}_{T}}\] is

A)  \[\frac{4\pi \rho {{g}^{2}}}{3k}\]                             

B)  \[\frac{4\pi R\rho g}{k}\]

C)  \[\frac{4}{3}\,\frac{\rho g}{k{{R}^{2}}}\]                              

D)  \[\frac{4\rho g{{R}^{2}}}{3k}\]