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

Here, 1 calorie = `4.2 J = 4.2 kg m^2 s^(-2)`
As new unit of mass ` = alpha kg :. 1kg = (1)/(alpha)` new units of mass `= alpha^(-1)` new units of mass
Similarly, `1 m = beta^(-1)` new unit of time
Putting these value in (i), we obtain
1 calorie `= 4.2 (alpha^(-1) "new unit of mass ")(beta^(-1)" new unit of length")^2 (lambda^(-1) "new unit of times")^(-2)`
`=4.2 alpha^(-1) beta^(-2) lambda^2` new unit of energy, which was to be proved.