A) \[[{{M}^{o}}{{L}^{o}}\,{{T}^{o}}]\]
B) \[[M{{L}^{4}}{{T}^{-3}}]\]
C) \[[M{{L}^{-2}}T]\]
D) \[[M{{L}^{6}}{{T}^{-3}}]\]
Correct Answer: B
Solution :
\[{{\lambda }_{m}}T=b\] or \[{{b}^{4}}=\lambda _{m}^{4}{{T}^{4}}\] and \[\frac{\text{energy}}{\text{area}-\text{time}}=\sigma {{T}^{4}}\] \[\sigma =\frac{\text{energy}}{(area-time){{T}^{4}}}\] \[\therefore \] \[\sigma {{b}^{4}}=\left( \frac{\text{energy}}{\text{area}-\text{time}} \right)\lambda _{m}^{4}\] \[[\sigma {{b}^{4}}]=\frac{[M{{L}^{2}}{{T}^{-2}}]}{[{{L}^{2}}][T]}[{{L}^{4}}]\] \[=[M{{L}^{4}}{{T}^{-3}}]\]
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