Question

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
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 1

Correct Answer - A
The forces acting on the ball are gravity force, buoyancy force and viscous force. When ball acquires terminal speed, it is in dynamic equilibrium, let terminal speed of ball is `v_(T) " So " V_(rho)qg+kv_(T)^(2)=V_(r_(1))g`
`"or" " "v_(T)=sqrt((V(rho_(1)-rho_(2))g)/(k))`