Question

If momentum (p), area (A) and time (T) are taken to be fundamental quantities, then energy has the dimensional formula
(a) [pA⁻¹T¹]
(b) [p²AT]
(c) [$pA^{-{1/2}}T$]
(d) [$pA^{{1/2}}T$]

Answer 1

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Answer 2

Answer:

(P^1 A^1/2 T^–1)

Explanation:

The fundamental quantities are momentum - p, area -A and time - T.

Thus,

Dimensional formula of energy = E = ML²T² and p = MLT-1

Dimensions of Energy = ML²T^-2 ( equation 1)

Momentum = MLT-1 or P = MLT-1 ( equation a)

Area = L^2  or A^1/2 = L  (equation b)

Substituting a and b equation in 1st equation , we get

Dimensions of Energy =  P ^1 A^1/2T^-1

Thus, the energy has the dimensional formula P ^1 A^1/2T^-1