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 = 4.2 J = 4.2 Kg `m^(2)s^(-1)….(1)`
`" "`As new unit of mass = 1 kg
`" "therefore 1kg =1/a` new unit of mass = `a^(-1)`
`" "`similarly, 1m = `1/b=b^(-1)`
`" "1s=1/g=g^(-1)`
Putting these values in eq(1), we obtains.
1 calorie = 4.2 (`a^(-1)` new unit of mass )
`(b^(-1)" new unit of length")^(2)`
`(g^(-1)" new unit of time")^(-2)`
calorie = `4.2a^(-1)b^(-2)g^(2)`