A calorie is unit of heat or energy and it equals about 4.2J, where 1J= 1 kgm2/s2. Suppose we employ a system of units in which the unit of mass α kg, the unit of length β m & the unit of time γ s. Show that a calorie has a magnitude of 4.2α-1β-2γ-1 in terms of new units.

To find the magnitude of a calorie in terms of the new units, we need to express the units of mass, length, and time in terms of α, β, and γ, respectively.

Given:
1 calorie = 4.2 J
1 J = 1 kgm^2/s^2

We also know that unit of mass α kg, unit of length β m, and unit of time γ s.

Rewriting 1 J in terms of α, β, and γ:

1 J = 1 kg(α m)^2/(γ s)^2

Now, we can substitute this expression for J back into the definition of a calorie:

1 calorie = 4.2 J
= 4.2 kg(α m)^2/(γ s)^2

To simplify this further, we can rewrite it as:

1 calorie = 4.2α^1β^2γ^(-2)

Hence, we can conclude that a calorie, in terms of the new unit system, has a magnitude of 4.2α^(-1)β^(-2)γ^(-1).