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 terminal 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 terminal velocity is proportional to
Answer» `2^2` `2^3` `2^4` `2^5` Solution :Rate of HEAT produced `(DQ)/(DT) = F_v xx v_r". F_v = 6 pi eta R v_t` `=6 pi eta r v_t xx v_t "" v_t = 2/9(r^2(rho - sigma))/(eta) g` `(dQ)/(dT) prop r v_1^2 "" v_T prop r^2` `(dQ)/(dt) prop r(r^2)^(2) IMPLIES (dQ)/(dT) prop r^5` Here radius of the sphere is 2 cm, so `(dQ)/(dT) prop 2^5`.