MHT CET · Physics · Thermal Properties of Matter
respectively. If they are coated with a material of same emissivity, rate of radiation of \({ }^{\prime} \mathrm{S}_{1}{ }^{\prime}\) is \(\mathrm{E}\) then rate of radiation of \(\mathrm{S}_{2}{ }^{\prime}\) is (spheres are of the same material)
- A \(\frac{E}{6} .\)
- B \(\frac{E}{3} .\)
- C \(\frac{E}{9} .\)
- D \(\frac{E}{12} .\)
Answer & Solution
Correct Answer
(C) \(\frac{E}{9} .\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{l}
\mathrm{E}=\sigma \times 4 \pi \mathrm{R}^{2} \times \mathrm{T}^{4} \\
\mathrm{E}^{\prime}=\sigma \times 4 \pi(3 \mathrm{R})^{2} \times\left(\frac{\mathrm{T}}{3}\right)^{4} \\
\therefore \frac{\mathrm{E}^{\prime}}{\mathrm{E}}=\frac{(3)^{2}}{(3)^{4}}=9 \\
\therefore \mathrm{E}^{\prime}=9 \mathrm{E} .
\end{array}\)
\mathrm{E}=\sigma \times 4 \pi \mathrm{R}^{2} \times \mathrm{T}^{4} \\
\mathrm{E}^{\prime}=\sigma \times 4 \pi(3 \mathrm{R})^{2} \times\left(\frac{\mathrm{T}}{3}\right)^{4} \\
\therefore \frac{\mathrm{E}^{\prime}}{\mathrm{E}}=\frac{(3)^{2}}{(3)^{4}}=9 \\
\therefore \mathrm{E}^{\prime}=9 \mathrm{E} .
\end{array}\)
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