Question

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 1

Given that,
1 calorie = 4.2 (1 kg) (1 m²) (1 s^–2)
New unit of mass = α kg

1 calorie = 4.2 (1 α^–1) (1 β^–2) (1 γ²) = 4.2 α^–1 β^–2 γ²