Question

Two metallic spheres P and Q of the same surface area are taken. The weight of P is twice that of Q. Both the spheres are heated to the same temperature and left in a room to cool by radiation. The ratio of the rate of cooling of Q to P is :

• A. $\sqrt{2}$: 1
• B. 2 : 1
• C. 1 : 2
• D. 1 : (2)^1/3

Answer 1

Answer: (D)

1 : (2)^1/3

Answer 2

P and Q have same surface finish and same temperature difference. Hence rate of radiation will depend only on the surface area and mass. That is, rate of radiation will be proportional to mass per unit area m/4pr², i.e., proportional to radius r. Since the mass of P is twice that of Q, $r_{P}^{3}$ = $2r_{Q}^{3}$.

r_P = (2)^1/3 r_Q. where r_P and r_Q are the radii of spheres of P and Q respectively. Hence ratio of rates of cooling is 1 : 2^1/3