A calorie is a unit of heat or energy and it equals about `4.2 J, where 1 J = 1 kg m^(2) s^(-2)`. Suppose we employ a system of units in which the unit of mass equals `alpha kg`, the unit of length equals is `beta m` , the unit of time is `gamma s`. Show tthat a calorie has a magnitude `4.2 alpha^(-1) beta^(-1) gamma^(2)` in terms of the new units.

Explanation

To solve the problem, we need to express the value of a calorie in terms of a new system of units defined by \(\alpha\) (mass), \(\beta\) (length), and \(\gamma\) (time).

### Step-by-Step Solution:

1. **Understand the SI Unit of Joules**:
The SI unit of energy (or heat) is the joule (J), which is defined as:
\[
1 \text{ J} = 1 \text{ kg} \cdot \text{m}^2 \cdot \text{s}^{-2}
...