Question

There are two spherical balls $A$ and $B$ of the same material with same surface, but the diameter of $A$ is half that of $B$. If $A$ and $B$ are heated to the same temperature and then allowed to cool, then

• A. Rate of cooling is same in both
• B. Rate of cooling of $A$ is four times that of $B$
• C. Rate of cooling of $A$ is twice that of $B$
• D. Rate of cooling of $A$ is $\frac{1}{4}$ times that of $B$

Answer 1

The correct option is B Rate of cooling of $A$ is four times that of $B$

Rate of heat transfer by radiation = A x T4 Temperature is same for both spheres A = Surface area Surface area of sphere = π d2 Cooling rate of big sphere / Cooling rate of small sphere = d2 big / d2small

Hence cooling rate will takes place in the ratio of 4 : 1