Q: Two spheres of radii in the ratio 1 : 2 and densities in the ratio 2 : 1 and of same specific heat, are heated to same temperature and left in the same surrounding. Their rate of cooling will be in ratio

(a) 2 : 1

(b) 1 : 1

(c) 1 : 2

(d) 1 : 4

Ans: (b)

Sol: Rate of cooling , $\large \frac{dT}{dt} = \frac{e \sigma A}{m s}(T^4 – T_o^4 ) $

$\large \frac{(dT/dt)_1}{(dT/dt)_2} = \frac{A_1}{A_2} . \frac{m_2}{m_1} $

$\large = \frac{r_1^2}{r_2^2} . \frac{\rho_2 . \frac{4}{3}\pi r_2^3}{\rho_1 . \frac{4}{3}\pi r_1^3} $

$\large \frac{(dT/dt)_1}{(dT/dt)_2} = \frac{\rho_2}{\rho_1} . \frac{r_2}{r_1} $

$\large \frac{(dT/dt)_1}{(dT/dt)_2} = \frac{1}{2} . \frac{2}{1} $

= 1:1