NCERT Solutions Class 11 Physics - Solved Exercise Question 2.3

Question 2.3:

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 4.2 α-1 β-2 γ2 in terms of the new units.

Solution:

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,
1 m = 1 / β = β-1  or  1 m2 = β-2
And, in terms of the new unit of time,
1 s = 1 / γ = γ-1
1 s2 = γ-2
1 s-2 = γ2

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

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