A) \[{{Q}_{A}}\] is maximum
B) \[{{Q}_{B}}\] is maximum
C) \[{{Q}_{C}}\] is maximum
D) \[{{Q}_{A}}={{Q}_{B}}={{Q}_{C}}\]
Correct Answer: B
Solution :
| [b] Idea The radiant power i.e., energy radiated by a body per unit time is given by \[\frac{Q}{t}=A\varepsilon \sigma {{T}^{4}}\] |
| \[\Rightarrow \] \[Q\propto A{{T}^{4}}\] |
| Also \[{{\lambda }_{m}}T=\text{constant}\] |
| \[\Rightarrow \] \[Q\propto \frac{A}{{{({{\lambda }_{m}})}^{4}}}\] |
| Power radiated, \[Q\propto A{{T}^{4}}\] and \[{{\lambda }_{m}}T=\] constant |
| Hence, \[Q\propto \frac{A}{{{({{\lambda }_{m}})}^{4}}}\] or \[Q\propto \frac{{{r}^{2}}}{{{({{\lambda }_{m}})}^{4}}}\] |
| \[{{Q}_{A}}:{{Q}_{B}}:{{Q}_{C}}=\frac{{{(2)}^{2}}}{{{(3)}^{4}}}:\frac{{{(4)}^{2}}}{{{(4)}^{4}}}:\frac{{{(6)}^{2}}}{{{(5)}^{4}}}\] |
| \[=0.05:0.0625:0.0576\] |
| i.e., \[{{Q}_{B}}\] is maximum. |
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