Question

Two metallic spheres S₁ and S₂ are made of same material and have identical surface finish. The mass of S₁ is thrice that of S₂ . Both the spheres are heated to the same high temperature and placed in same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of S₁ to that of S₂ is

(1) 1/3

(2) 1/√3

(3) √3/1

(4) (1/3)^1/3

Answer 1

(4) (1/3)^1/3

Let ε be the degree of blackness of each sphere. The temperature of each sphere is TK. Let the room temperature be T₀K (T₀ < T). Let M and R denote mass and radius of sphere of density p . Then

Also dQ = M x s x dT; where s is specific heat of sphere