If momentum (P), area (A) and time (T) are ta | vedclass

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Question

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

Vedclass · Accepted Answer

$\left[ PA ^{1 / 2} T ^{-1}\right]$

Vedclass · Answer

Let $[ E ]=[ P ]^{ x }[ A ]^{ y }[ T ]^{z}$
$ML ^{2} T ^{-2}=\left[ MLT ^{-1}\right]^{ x }\left[ L ^{2}\right] y [ T ]^{z}$
$ML ^{2} T ^{-2}= M ^{ x } L ^{ x +2 y } T ^{- x +z}$
$\rightarrow x =1$
$\rightarrow x +2 y =2$
$1+2 y =2$
$y =\frac{1}{2}$
$\rightarrow- x + z =-2$
$-1+ z =-2$
$z =-1$
$[ E ]=\left[ P A ^{1 / 2} T ^{-1}\right]$

If momentum $(P),$ area $(A)$ and time $(T)$ are taken to be the fundamental quantities then the dimensional formula for energy is :

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