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

`n_(2)=n_(1)[(M_(1))/(M_(2))]^(a)((L_(1))/(L_(2)))^(b)((T_(1))/(T_(2)))^(c)`
`=4.2((kg)/(alphakg))^(1)((m)/(betam))^(2)((s)/(gammas))^(-2)`
`n_(2)=4.2alpha^(-1)beta^(-2)gamma^(2)`