Dimensions of Energy (F, A, T) – Rankers Physics
Topic: Unit And Dimensions
Subtopic: Dimensions

Dimensions of Energy (F, A, T)

If force \([F]\), acceleration \([A]\) and time \([T]\) are chosen as the fundamental physical quantities. Find the dimensions of energy.

[2021]

\([F] [A] [T^2]\)
\([F] [A] [T^{-1}]\)
\([F] [A^{-1}] [T]\)
\([F] [A] [T]\)

Solution:

We know \(E = ML^2T^{-2}\), \(F = MLT^{-2}\), \(A = LT^{-2}\), \(T = T\). From \(F = MA\), \(M = F/A\). Substitute \(M\) into \(E\): \(E = (F/A)L^2T^{-2}\). Also, \(L = AT^2\). So, \(E = (F/A)(AT^2)^2T^{-2} = (F/A) A^2 T^4 T^{-2} = F A T^2\).

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