A small sphere of radius 2 cm falls from rest in a viscous liquid. Heat is produced due to viscous force. The rate of production of heat when the sphere attains its teminal velocity is proportional to:

A small sphere of radius 2 cm falls from rest in a viscous liquid. Hea

1.	A small sphere of radius 2 cm falls from rest in a viscous liquid. Heat is produced due to viscous force. The rate of production of heat when the sphere attains its teminal velocity is proportional to:
Answer» `2^(2)` `2^(3)` `2^(4)` `2^(5)` Solution :TERMINAL velocity`v_(t)=(2r^(2)(rho-sigma)g)/(9eta)` `v_(t)propr^(2)` The rate of production of heat is `(DeltaH)/(Deltat)=Fv_(t)^(2)` `F=6pietar` `THEREFORE(DeltaH)/(Deltat)=6pietar[(2(rho-sigma)R^(2)g)/(9eta)]^(2)` `=6pietar[(4(rho-sigma)^(2)r^(4)g^(2))/(81eta^(2))]` `=(24pieta(rho-sigma)^(2)g^(2)r^(5))/(81eta^(2))` `=[(8pi(rho-sigma)^(2)g^(2))/(27eta)]r^(5)` `therefore(DeltaH)/(Deltat)propr^(5)` But r = 2 cm `therefore(DeltaH)/(Deltat)prop2^(5)`