A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m2s–2. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2 α–1 β–2 γ2 in terms of the new units.

A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m2s–2. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time is γ s.  Show that a calorie has a magnitude 4.2 α–1 β–2 γ2 in terms of the new units.
Answer:
Given that,
1 calorie = 4.2 (1 kg) (1 m2) (1 s–2)
New unit of mass = α kg
Hence, in terms of the new unit,
1 kg =

In terms of the new unit of length,

And, in terms of the new unit of time,

∴1 calorie = 4.2 (1 α^–1) (1 β^–2) (1 γ^2) = 4.2 α^–1 β^–2 γ^2