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Asked in GUJCET 2007 · Units and dimensions
Given: the intensity of radiation, the radiant energy crossing unit area in unit time.
Idea: I=(energy)/(area×time)=(power)/(area).
[energy]=M¹L²T⁻², [area]=L² and [time]=T¹.
So [I]=(M¹L²T⁻²)/(L²·T¹)=M¹L⁰T⁻³.
The two powers of length cancel, which is why intensity carries L⁰: in SI it is W m⁻²=kg s⁻³.
So the intensity of radiation has the dimensions M¹L⁰T⁻³.
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