A calorie is a unit of heat or energy and it equal about 4.2 J where `1J = 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 `beta` m, the unit of time is `gamma` s. Show that a calorie has a magnitude 4.2 `alpha^-1` `beta^-2` `gamma^2` in terms of the new units.

Explanation

we know that, `n_(2)=n_(1)[(M_(1))/(M_(2))]^(a)[(L_(1))/(L_(2))]^(b)[(T_(1))/(T_(2))]^(c )`
`1cal=4.2J=4.2kgm^(2)s^(-2)` `:.a=1, b=2, c=-2`

`:.n_(2)=4.2[(1kg)/(alphakg)]^(1)[(1m)/(betam)]^(2)[(1s)/(gammas)]^(-2)impliesn_(2)4.2alpha^(-1)beta^(-2)gamma^(2) :. 1 cal =4.2alpha^(-1)beta^(-2)gamma^(2)` in new system