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Question 3

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 J = 4.2 Kg m2 s-2 ...... (i)

As new unit of mass = α Kg

∴ 1 Kg = 1/α new unit of mass

Similarly,

1 m = β– 1 new unit of length

1 s = γ-1 new unit of time

Putting these values in (i), we get

1 calorie = 4.β (α-1 new unit of mass) (β– 1 new unit of length)β ( γ-1 new unit of time)-2

= 4.β α-1 β– 2 γ2 new unit of energy (Proved)

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