A small sphere of radius 'r' falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to

Question

Question

Answer 1

Concept:

Stoke's law expresses the settling velocities of small particles in a fluid medium.

The equation of Stoke's law is,

\(F=6\pi\eta rv\)

r is radius of sphere, v is velocity of object, \(\eta\) is viscosity of fluid

Calculation:

Radius of sphere = r

Terminal velocity = \(V_T\)

Power = Rate of production of heat

Power is calculated using the formula, P = F\(V_T\)

Using Stoke's Formula,

Power = 6πηrV_T.V_T = 6πηr\(V_T^2\)

Since Terminal velocity is V_T ∝ r²

⇒ Power ∝ r⁵