A small spherical body of radius r and density `rho` moves with the terminal velocity v in a fluid of coefficient of viscosity `eta` and density `sigma` . What will be the net force on the body?

Options

A. `(4pi )/(3) r^3 (rho - sigma) g `
B. `6 pi eta r v `
C. 0
D. infinity

Answer

C

Explanation

Given, `rho`= Density of spherical body r= Radius of spherical body, `sigma` = Density of medium (fluid) `eta = ` Viscosity of medium
Now, when the spherical body moves downwards in the fluid medium, with terminal velocity (say, `V_("terminal")`) then, sum of the viscous drag and upthrust will be equal to the weight of the spherical body.
` therefore F_v + F_T -W`
` rArr 6pi eta r v_("terminal") + 4/3 pi r^3 sigma g = 4/3 pi r^3 rho g `
` rArr 6pi eta r v_("terminal") = 4/3 pi r^3 (rho - sigma) g `
` rArr v_("terminal") = (2r^2 (rho - sigma))/(9 eta) g `
`rArr F_("net") = 0`