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 βm, the unit of time is yS. Show that a calorie has a magnitude 4.2 α⁻¹ β⁻² y² in terms of the new units.

Answer 1

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Answer 2

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 = 4.2 (α-1 new unit of mass) (β-1 new unit of length)2 (γ-1 new unit of time)-2

= 4.2 α-1 β-2 γ2 new unit of energy

(Proved)