A small sphere falls from rest in a viscous liquid. Due to frication, heat is produced. Find the relation between the rate of production of heat and the radius of the sphere at terminal velocity.

Options

A. `r^(5)`
B. `r^(2)`
C. `r^(3)`
D. `r^(4)`

Answer

A

Explanation

Force of viscosity when sphere moves with terminal velocity `v_(v)`.
`F_(v)=6pieta rv_(c)`
Here `eta` is coefficent of viscosity.
Rate of heat generation `="force of visocity "xx "velocity"`
`-Gpi eta v_(t).t_(t)=6pi eta rv_(t)^(2)`
Terminal velocity can be proveed to be proportional to square of radius `v_(t) alpha r^(2)`
Power `=6pietar r^(4) alpha r^(54)`