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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Let dimension formula of energy will be

$E = A^{a} T^{b} P^{c}$
$P = M^{1} L^{1} T^{- 1}$
$A = L^{2}$
$T = T^{1}$
$M^{1} L^{2} T^{- 2} = M^{C} L^{2 a + c} T^{b - c}$
by comparison $C = 1$ $. . . . . . . . . (1)$
$2 a + c = 2$ $. . . . . . (2)$
$b - c = - 2$ $. . . . . . . . (3)$
$c = 1, a = 1 / 2, b = - 1$
$E = A^{1 / 2} T^{- 1} P^{1}$

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