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 :

Options

A. `r^(1)`
B. `r^(3)`
C. `r^(5)`
D. `r^(2)`

Answer

c

Explanation

The rate of production of heat `(dQ)/(dt)=F_(v)v_(tau)`
where `F_(v)=` viscous force
`v_(tau)`= terminal velocity
`=6pietarv_(tau)xxv_(tau)`
`proprv_(T)^(2)[because6pieta` is constant]
But `V_(T)=(2)/(9)(r^(2)g)/(eta)(rho-sigma)`
`thereforeV_(T)propr^(2) " " [because` all other terms are constant)
`therefore(dQ)/(dt)propr(r^(2))^(2)`
`propr^(5)`