JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
If momentum \((P),\) area \((A)\) and time \((T)\) are taken to be the fundamental quantities then the dimensional formula for energy is :
- A \(\left[ PA ^{-1} T ^{-2}\right]\)
- B \(\left[ PA ^{1 / 2} T ^{-1}\right]\)
- C \(\left[ P ^{2} AT ^{-2}\right]\)
- D \(\left[ P ^{1 / 2} AT ^{-1}\right]\)
Answer & Solution
Correct Answer
(B) \(\left[ PA ^{1 / 2} T ^{-1}\right]\)
Step-by-step Solution
Detailed explanation
Let \([ E ]=[ P ]^{ x }[ A ]^{ y }[ T ]^{z}\) \(ML ^{2} T ^{-2}=\left[ MLT ^{-1}\right]^{ x }\left[ L ^{2}\right] y [ T ]^{z}\) \(ML ^{2} T ^{-2}= M ^{ x } L ^{ x +2 y } T ^{- x +z}\) \(\rightarrow x =1\) \(\rightarrow x +2 y =2\) \(1+2 y =2\) \(y =\frac{1}{2}\)…
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