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

Answer

C

Explanation

The viscous drag force, `F= 6pi eta rv`.
where v= terminal velocity
`:.` The rate of production of heat = power = force `xx` terminal velocity
`rArr` Power = `6pi eta rv.v= 6pi eta r v^(2)`
`:.` Terminal velocity `v= (2r^(2) (rho - sigma) g)/(9eta)`,
`:. v prop r^(2)`
Now, power `=6pi eta n [(4r^(4) (rho-sigma)^(2))/(81 eta^(2)) g^(2)]` or Power `prop r^(5)`