If the numerical value of a physical quantity is n in a system whose fundamental units are M, L, T, and the units are changed to M′=αM, L′=βL, T′=γT, then for [Q]=[MᵃLᵇTᶜ], n′ equals:
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Question

If the numerical value of a physical quantity is n in a system whose fundamental units are M, L, T, and the units are changed to M′=αM, L′=βL, T′=γT, then for [Q]=[MᵃLᵇTᶜ], n′ equals:

G1 Physics · Accepted Answer

Q = n MᵃLᵇTᶜ = n′(αM)ᵃ(βL)ᵇ(γT)ᶜ. Therefore n′ = n α⁻ᵃβ⁻ᵇγ⁻ᶜ.