Question 1:
difficultA small sphere of radius ‘$r$’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to :
(2018)
Rate of heat production $P = F_v v_t$. We know $F_v = 6\pi\eta r v_t$ and $v_t \propto r^2$. Thus, $$P = (6\pi\eta r v_t) v_t \propto r (r^2)^2 \propto r^5$$.