Question

Two metallic spheres $A$ and $B$ are made of same material and have got an identical surface finish. The mass of sphere $A$ is four times that of $B$ . Both the spheres are heated to the same temperature and placed in a room having a lower temperature but thermally insulated from each other.

• A. The ratio of heat loss of A to that of $B$ is $2^{4/3}$
• B. The ratio of heat loss of A to that of B is $2^{2/3}$
• C. The ratio of the initial rate of cooling of $A$ to that of $B$ is $2^{2/3}$ .
• D. The ratio of the initial rate of cooling of $A$ to that of $B$ is $2^{-1/3}$

Answer 1

Answer: (A)

The ratio of heat loss of A to that of $B$ is $2^{4/3}$

$\begin{array}{c}Heatloss,asperstephanboltzmanlawisgivenbytherefraction:\\ q^{\prime }=e\sigma A{T}^4\\ q^{\prime }=e\sigma T^4\left(4\pi r^2\right)\\ Also,\frac{4}{3}\pi r^3=\frac{m}{\rho }\\ r=k{m}^{1/3}\\ Hence,\frac{q_1^{{}^{\prime }}}{q_2^{{}^{\prime }}}=\frac{r_1^2}{r_2^2}={\left(\frac{m_1}{m_2}\right)}^{2/3}=4^{2/3}=2^{4/3}\end{array}$

Hence,

option $\left(A\right)$ is correct answer.