A calorie is a unit of heat or energy and it equals about 4.2 J where

A calorie is a unit of heat or energy and it equals about 4.2 J where 1 J = 1 kg m2 s-2. Suppose, we employ a system of units in which unit of mass equal α kg, the unit of length equals β m, and the unit of time is γ s. Show that a calory has a magnitude of 4.2 α-1 β-2 γ2 in terms of the new units.

Answer»

1 cal. = 4.2 = kg m²s^-2

Dimensional formulae of energy is [M¹L²T^-2]

Comparing with [M^a L^bT^c], we get

a =1, b = 2 c = -2

Now, n₂ =n₁[M₁/M₂]^a[L₁/L₂]^b [T₁/T₂]^c

= 4.2 [1 kg/α kg]¹ [1 m/β m]² [1 s/γ s]^-2

= 4.2 α^-1 β^-2 γ².