A spherical solild of volume V is made of a material of density `rho_(1)`. It is falling through a liquid of density `rho_(2)(rho_(2) lt rho_(1))`. Assume that the liquid applies a viscous froce on the ball that is proportional ti the its speed v, i.e., `F_(viscous)=-kv^(2)(kgt0)`. The terminal speed of the ball is

Options

A. `sqrt((Vg(rho_(1)-rho_(2)))/(k))`
B. `(Vgrho_(1))/(k)`
C. `sqrt((Vgrho_(1))/(k))`
D. `(Vg(rho_(1)-rho_(2)))/(k)`

Answer

A

Explanation

The force acting on the ball are gravity force, buoyancy force and viscous force. When ball acquires terminal speed, it is in dynamic equilibrium,let termina speed of ball is `V_(T)`.
so, `vrho_(2)g+kv_(T)^(2)=Vrho_(1)g,V_(T)=sqrt((V(rho_(1)-rho_(2))g)/(k))`