Q66 / 75 · JEE Main 2025 (22 Jan Shift 1) · Physics

Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible),

  • A
    16 E
  • Correct answer
    B
    E
  • C
    64 E
  • D
    256 E

Solution

$\begin{aligned} & \frac{\mathrm{d} \theta}{\mathrm{dt}}=\sigma \mathrm{eAT}^4 \Rightarrow \mathrm{P} \propto \mathrm{AT}^4 \\ & \frac{\mathrm{P}_{\text {smaller }}}{\mathrm{P}_{\text {larger }}}=\frac{(0.2)^2 \times 800^4}{(0.8)^2 \times 400^4} \\ & \frac{1}{16} \times 16=1 \\ & \therefore \mathrm{P}_{\text {larger }}=\mathrm{P}_{\text {smaller }}\end{aligned}$

Hence, the correct answer is option: 'B'.

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