(D) The dimensions of the given quantities are:$E = [ML^2 T^{-2}]$$L = [ML^2 T^{-1}]$$m = [M]$$G = [M^{-1} L^3 T^{-2}]$Given the formula $P = E L^2 m^

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(D) The dimensions of the given quantities are:$E = [ML^2 T^{-2}]$$L = [ML^2 T^{-1}]$$m = [M]$$G = [M^{-1} L^3 T^{-2}]$Given the formula $P = E L^2 m^{-5} G^{-2}$,we substitute the dimensions:$[P] = [ML^2 T^{-2}] \cdot [ML^2 T^{-1}]^2 \cdot [M]^{-5} \cdot [M^{-1} L^3 T^{-2}]^{-2}$$[P] = [ML^2 T^{-2}] \cdot [M^2 L^4 T^{-2}] \cdot [M^{-5}] \cdot [M^2 L^{-6} T^4]$$[P] = [M^{1+2-5+2} L^{2+4-6} T^{-2-2+4}]$$[P] = [M^0 L^0 T^0]$Thus,the dimensions of $P$ are dimensionless.

Class 11 Physics Units, Dimensions and Measurement Dimensional Analysis, Uses and Limitations

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If $E$,$L$,$m$ and $G$ denote the quantities as energy,angular momentum,mass and constant of gravitation respectively,then the dimensions of $P$ in the formula $P = EL^2 m^{-5} G^{-2}$ are

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A
$[M^0 L^1 T^0]$
B
$[M^{-1} L^{-1} T^2]$
C
$[M^1 L^1 T^{-2}]$
D
$[M^0 L^0 T^0]$

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Units, Dimensions and Measurement

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Dimensional Analysis, Uses and Limitations

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If $E$,$L$,$m$ and $G$ denote the quantities as energy,angular momentum,mass and constant of gravitation respectively,then the dimensions of $P$ in the formula $P = EL^2 m^{-5} G^{-2}$ are

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