Two spheres ' \(\mathrm{S}_1\) ' and ' \(\mathrm{S}_2\) ' have radii ' \(\mathrm{R}\) ' and '3R',…

Two spheres ' \(\mathrm{S}_1\) ' and ' \(\mathrm{S}_2\) ' have radii ' \(\mathrm{R}\) ' and '3R', temperature ' \(\mathrm{T}\) ' \(\mathrm{K}\) and. \(\frac{\mathrm{T}}{3} \mathrm{~K}\) respectively. If 3 they are coated with a material of same emissivity, rate of radiation of ' \(S_1\) ' is \(E\) then rate of radiation of ' \(S_2\) ' is _______. (spheres are of the same material)
  1. $\frac{E}{6} .$
  2. $\frac{E}{3} .$
  3. $\frac{E}{9} .$
  4. $\frac{E}{12} .$

Solution

$\begin{array}{l} \mathrm{E}=\sigma \times 4 \pi \mathrm{R}^{2} \times \mathrm{T}^{4} \\ \mathrm{E}^{\prime}=\sigma \times 4 \pi(3 \mathrm{R})^{2} \times\left(\frac{\mathrm{T}}{3}\right)^{4} \\ \therefore \frac{\mathrm{E}^{\prime}}{\mathrm{E}}=\frac{(3)^{2}}{(3)^{4}}=9 \\ \therefore \mathrm{E}^{\prime}=9 \mathrm{E} . \end{array}$

Asked in: MHT CET 2020 (13 Oct Shift 2)

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