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

Answer

A

Explanation

`1j=(1kg)(1m)^(2)(1sec)^(-2)`
`1x=(alphakg)(betam)^(2)(gammasec)^(-2)`
`therefore(1j)/(1x)=((1)/(alpha))((1)/(beta))^(2)(gamma)^(2)=(gamma^(2))/(alphabeta^(2))`
`therefore1j=(gamma^(2))/(alphabeta^(2))x` or `1cal=4.18(gamma^(2))/(alphabeta^(2))`