If mass is measured in unit of `alpha` kg, length in `beta` m and time in `gamma ` s, then calorie would be

Options

A. `4.2 alpha beta^2 gamma^(-2)`
B. `4.2 alpha^(-1) beta^2 gamma^(2)`
C. `4.2 alpha^(-1) beta^(-2) gamma^(2)`
D. `4.2 alpha^(-2) beta^(-1) gamma^(-2)`

Answer

C

Explanation

1 cal = 4.2 J `=4.2 "kgm"^2 s^(-2)`

`implies n_2=(n_1[M_1L_1^2T_1^2])/([M_2L_2^2T_2^(-2)])`
`=4.2 ((1kg)/(alphakg))^(1)((1m)/(betam))^2 ((1s)/(gammas))^(-2)`
`=4.2alpha^(-1) beta^(-2) gamma^2`