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

Options

A. `4.18(gamma^(2))/(alpha beta^(2))`
B. `4.18(alpha beta^(2))/(gamma^(2))`
C. `4.18(gamma^(2))/(alpha)`
D. `4.18(beta^(2))/(alpha gamma^(2))`

Answer

A

Explanation

I calorie `=4.18J=4.18kg-m^(2)//s^(2)`
`=[4.18(gamma^(2))/(alphabeta^(2))]((alpha kg)(betam)^(2))/((gammas)^(2))`