Q118 / 150 · MHT CET 2017 · Physics

Two spherical black bodies have radii $r_{1}$ and $r_{2}$ . Their surface temperatures are $T_{1}$ and $T_{2}$ . If they radiate same power then $\frac{r_{2}}{r_{1}}$ is

A
$\frac{T_{1}}{T_{2}}$
B
$\frac{T_{2}}{T_{1}}$
Correct answer
C
${(\frac{T_{1}}{T_{2}})}^{2}$
D
${(\frac{T_{2}}{T_{1}})}^{2}$

Solution

\frac{Q}{t} = σ A T^{4}

i . e . p o w e r = σ A T^{4}

∴ f o r s a m e p o w e r

∴ A \propto \frac{1}{T^{4}}

∴ \frac{A_{2}}{A_{1}} = \frac{T_{1}^{4}}{T_{2}^{4}}

∴ \frac{{4 π r}_{2}^{2}}{{4 π r}_{1}^{2}} = \frac{T_{1}^{4}}{T_{2}^{4}}

∴ \frac{r_{2}}{r_{1}} = {(\frac{T_{1}}{T_{2}})}^{2}

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

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