Let's consider,\\\\(r=\\\\) radius of a small sphere\\\\(V_T=\\\\)Terminal velocity\\\\(Power =\\\\) rate of production of heat\\\\(P=FV_T\\\\). . . . .. .. .(1)From Stoke's formula,\\\\(F=6\\pi \\eta V_T r\\\\). . . . . . . . . .(2)substitute equation (2) in equation (1), we get\\\\(P=6\\pi \\eta rV_T^2\\\\) . . . . . . . . .(3)we know that the, the terminal velocity is given by\\\\(V_T=\\dfrac{2r^2(\\rho-\\sigma)}{9\\eta}\\\\)\\\\(V_T\\propto r^2\\\\). . . . . . .(4)from equation (3) and equation (4), we get\\\\(P\\propto r^5\\\\)The correct option is A.