Q 11-10-053JEE MainJEE Main 2025 (22 Jan, Shift 1)Easy
Two spherical bodies of same material having radii $0.2\ \text{m}$ and $0.8\ \text{m}$ are placed in same atmosphere. The temperature of the smaller body is $800\ \text{K}$ and temperature of the bigger body is $400\ \text{K}$. If the energy radiated from the smaller body is $E$, the energy radiated from the bigger body is (assume the effect of the surrounding temperature to be negligible)
Answer: (B) $E$
By the Stefan–Boltzmann law, power radiated $P = e\sigma A T^4 \propto r^2T^4$ (same material, so same emissivity).
$$\frac{E_{big}}{E_{small}} = \left(\frac{0.8}{0.2}\right)^2\left(\frac{400}{800}\right)^4 = 16\times\frac{1}{16} = 1$$
So the bigger body radiates $E$.
Solution by Sreeraj P, M.Sc Physics