If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is :
If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is :
Correct Option: , 2
Let $[\mathrm{E}]=[\mathrm{P}]^{\mathrm{x}}[\mathrm{A}]^{\mathrm{y}}[\mathrm{T}]^{\mathrm{z}}$
$\mathrm{ML}^{2} \mathrm{~T}^{-2}=\left[\mathrm{MLT}^{-1}\right]^{x}\left[\mathrm{~L}^{2}\right]^{y}[\mathrm{~T}]^{\mathrm{z}}$
$\mathrm{ML}^{2} \mathrm{~T}^{-2}=\mathrm{M}^{\mathrm{x}} \mathrm{L}^{x+2 \mathrm{y}} \mathrm{T}^{-\mathrm{x}+\mathrm{z}}$
$\rightarrow \mathrm{x}=1$
$\rightarrow \mathrm{x}+2 \mathrm{y}=2$
$1+2 y=2$
$\mathrm{y}=\frac{1}{2}$
$\rightarrow-x+z=-2$
$-1+z=-2$
$\mathrm{z}=-1$
$[\mathrm{E}]=\left[\mathrm{PA}^{1 / 2} \mathrm{~T}^{-1}\right]$
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