Answer :

Given

New unit of mass = α kg

New unit of length = β m

New unit of time = γ s

Magnitude of energy in original system n = 5J

The dimensional formula for energy is given as

Now let the magnitude of U in the original system of units be n, and in the new system of unit be n’

Then

Where [M_{1}L_{1}^{2} T_{1}^{-2}] and [M_{2}L_{2}^{2} T_{2}^{-2}] are the dimensions in the original system of units and new system of units respectively.

Now in the original system of units M_{1} = 1 kg , L_{1} = 1 m and T_{1} = 1 s. In the new system of units we have M_{2} = α kg , L_{2} = β m and T_{2} = γ s.

Thus, 5 J of energy will measure in the new system of units.

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