1 calorie=4.2 J where IJ= 1 kg `m^2s^-2`. Suppose we employ a system of units in which the unit of mass is `alpha` kg, the unit of length is `beta` m and the unit of time `gamma s`, show that a calorie has a magnitude `4.2alpha^-1beta^-2gamma^-2` in the new system.

Explanation

Here 1 calorie= `4.2J=4.2 kgm^2//s^2to (1)`
As new unit of mass =`alpha` kg
`therefore1kg=1/alpha` new unit of mass
`implies alpha^-1` new unit of mass
Similarly `1m=beta^-1` new unit of length and `1s=gamma^-1` new unit of time.
Putting these values in (1) we get
1 calorie =4.2 (`alpha^-1 n ew unit of mass) (beta^-1 n ew unit of l eng th)^2 (gamma^-1 n ew unit of time )^2`
`=4.2 alpha^-1 beta^-2 gamma^2` new unit of energy which was proved.