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^(3)`
D. `r^(4)`

Answer

A

Explanation

Rate of heat produced `=F_(v) + v`
`(dQ)/(dT)= F_(v).v_(T)`
`=6pi eta r v_(T)-v_(g)`
`prop r. v_(g)^(1)`
`prop r.r^(4) [ therefore v_(1) prop r^(2)]`
`prop r^(3)`