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A spherical solild of volume V is made o...

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

`(Vgrho_(1))/(k)`

B

`sqrt((Vgrho_(1))/(k))`

C

`(Vg(rho_(1)-rho_(2)))/(k)`

D

`sqrt(Vg(rho_(1) - rho_(2))/(k))`

Text Solution

Verified by Experts

The correct Answer is:
D
The forces acting on the ball are gravity force, buoyancy force and viscous force. When ball acquires terminal speed, it is in dynamic equilibrium, lt terminal 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))`
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