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JEE Main 2006
Exam
JEE Main
Year
2006
Subject
Physics
Chapter
Thermal Properties of Matter

JEE Main 2006 · Physics · Thermal Properties of Matter

Assuming the sun to be a spherical body of radius R at a...

Assuming the sun to be a spherical body of radius R\mathrm{R} at a temperature of TK\mathrm{T} \mathrm{K}, evaluate the total radiant power, incident on Earth, at a distance rr from the Sun.

Options

  1. AR2σT4r2\frac{\mathrm{R}^2 \sigma \mathrm{T}^4}{\mathrm{r}^2}
  2. B4πr02R2σT4r2\frac{4 \pi r_0^2 R^2 \sigma T^4}{r^2}
  3. Cπr02R2σT4r2\frac{\pi r_0^2 R^2 \sigma T^4}{r^2}
  4. Dr02R2σT44πr2\frac{r_0^2 R^2 \sigma T^4}{4 \pi r^2}

Correct answer

C. πr02R2σT4r2\frac{\pi r_0^2 R^2 \sigma T^4}{r^2}

Step-by-step solution

πr024πr2(σT4⋅4πR2)=σπT4R2r02r2\frac{\pi r_0^2}{4 \pi r^2}\left(\sigma \mathrm{T}^4 \cdot 4 \pi \mathrm{R}^2\right)=\frac{\sigma \pi \mathrm{T}^4 \mathrm{R}^2 \mathrm{r}_0^2}{\mathrm{r}^2}
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