Question:
A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m2
s–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 4α–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 = 1/α = α-1
In terms of the new unit of length,
1m = 1/β = β-1 OR 1m2 = β-2
And, in terms of the new unit of time,
1s = 1/γ = γ-1 OR 1s2 = γ-2 OR 1s-2 = γ-2
∴1 calorie = 4.2 (1 α–1) (1 β–2) (1 γ2) = 4.2 α–1 β–2 γ2
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