A new system of units is proposed
Question:

A new system of units is proposed in which unit of mass is α kg, unit of length β m and unit of time γ s. How much will 5 J measure in this new system?

Solution:

Let Q be the physical quantity = n1u1 = n2u2

Let M1, L1, T1 and M2,L2,T2 be the units of mass, length, and time for the given two systems.

n2 = n1

[U] = [ML2T2]

M1 = 1 kg

L1 = 1 m

T1 = 1 s

M2 = α kg

L2 = β m

T1 = γ s

Substituting the values we get, n2 = 5γ2/αβ2 J

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