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

A small sphere of radius 'r' falls from rest in a viscous liquid Asa r

1.	A small sphere of radius 'r' falls from rest in a viscous liquid Asa result heat is produced due to viscous force .the rate of production of heat when the sphere attains its terminal velocity is proportional to :
Answer» `r^(1)` `r^(3)` `r^(5)` `r^(2)` Solution :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)`