A small spherical ball of radius r falls from rest in a long column of a viscous liquid. After it reaches terminal velocity, the rate of heat production due to viscous friction is proportional to r^n . The value of n is:

Step-by-step solution

The rate of heat production is equal to the mechanical power dissipated by the viscous drag force. Power P = F v , where F is the viscous drag force and v is the terminal velocity. According to Stokes' law, the viscous drag force at terminal velocity is F = 6 r v . Therefore, the rate of heat production is: P = (6 r v) v = 6 r v^2 The terminal velocity v of a spherical ball of radius r is given by: v = 2r^2( - )g 9 This shows that v r^2 . Substituting v r^2 into the power equation: P r (r^2)^2 P r r^4 = r^5 Thus, t