### Q.3:- A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m^{2}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} γ^{2 }in terms of the new units.

**Answer:-**

Given that,

1 Calorie=4.2 J = 4.2 Kg m^{2} 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} γ^{2} new unit of energy (Proved)