A sphere of radius 1 cm and mass 100 g is sinking at a steady speed of 1 mm per second down through a fluid with viscosity of 300 Pa s. Assuming that Stokes' law applies, what is the density of the viscous fluid?
A) 500 kg m-3.
B) 1000 kg m-3.
C) 1500 kg m-3.
D) 2000 kg m-3.
E) 5000 kg m-3.ANS

Question

Quizplus · Accepted Answer

Stokes' law states that the drag force on a sphere in a viscous fluid is given by F = 6πηrv, where η is the viscosity of the fluid, r is the radius of the sphere, and v is the velocity of the sphere.

In equilibrium, the drag force is equal and opposite to the weight of the sphere, given by F = mg, where m is the mass of the sphere and g is the acceleration due to gravity.

We can use these equations to solve for the density of the fluid:

F = 6πηrv = mg

η = mg/6πrv

ρ = m/V = m/(4/3πr^3)

Substituting for m, V, and η, we get:

ρ = (4/3πr^3)/(mg/6πrv)

ρ = 2gr/(9vη)

Plugging in the given values, we get:

ρ = 2(9.8 m/s^2)(0.01 m)/(9(10^-4 m/s)(300 Pa s))

ρ ≈ 1000 kg/m^3

Therefore, the answer is choice B.

A Sphere of Radius 1 Cm and Mass 100 G