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’
Where [M1L12 T1-2] and [M2L22 T2-2] are the dimensions in the original system of units and new system of units respectively.
Now in the original system of units M1 = 1 kg , L1 = 1 m and T1 = 1 s. In the new system of units we have M2 = α kg , L2 = β m and T2 = γ s.
Thus, 5 J of energy will measure in the new system of units.
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