A spherical ball of radius r and density d is dropped from rest in a viscous fluid having density `rho` and coefficient of viscosity `eta`.
(a) Calculate the power `(P_(1))` of gravitational force acting on the ball at a time t after it is dropped. (b) Calculate the rate of heat generation `(P_(2))` due to rubbing of fluid molecules with the ball, at time t after it is dropped. (c) How do `P_(1)` and `P_(2)` change if the radius of the ball were doubled? (d) Find `P_(1)` and `P_(2)` when both become equal.

Answer

(a)`P_(1)=(8pi)/(27)(d(d-rho)g^(2)r^(5))/(eta)[1-e^((9etat)/(2dr^(2)))]`
(b) `P_(1)=(8pi)/(27)((d-rho)^(2)g^(2)r^(5))/(eta)[1-e^((9etat)/(2dr^(2)))]`
(c) `P_(1)=P_(2)` become 32 times.
(d) `P_(1)=P_(2)=(8pi)/(27)((d-rho)^(2)g^(2)r^(5))/(eta)`