Given that ,
1 calorie =4.2 (1 kg ) `(1m^(2)) (1s^(-2))`
New unit of mass `=alpha kg`
Hence, in terms of the new unit `1kg =1/(alpha) =alpha^(-1)`
in terms of the new unit of length,
`1m =1/(beta) =beta^(-1) ` or `1m^(2)=beta^(-2)`
And, in terms of the new unit of time,
`1s=1/(gamma) =gamma^(-1)`
`1s^(2) =gamma^(-2)`
`1 s^(-2) =gamma^(2)`
`:.` calorie `=4.2 (1alpha^(-1)) (1 beta^(-2)) (1 y^(2)) =4.2 alpha^(-1) beta^(-2) gamma^(2)`