A calorie is a unit of heat or energy and it equals 4.2 J where 1J = 1 kg `m^(2)s^(-2)` . Suppose we employ a system of units in which unit of mass is `alpha` kg. unit of length is `beta` m, unit of time is `gamma` . What will be magnitude of calorie in terms of this new system?

Explanation

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