The calorie is a unit of heat or energy and it equals about 4.2 J where `1J=1kgm^(2)s^(-2)`. Suppose we employ a system of units in which the unit of mass equals `alpha` kg, the unit of length equals `beta` m and the unit of time is`gamma` s. Show that the calorie has a magnitude of `4.2alpha^(-1) beta^(-2) gamma^(2)` in terms of the new units.

Options

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

Answer

A

Explanation

`:' 1 cal=4.2 J :. 1 cal =4.2 kgm^(2)s^(-2)`
`=(4.2 alpha^(-1)beta^(-2)gamma^(2))(alpha kg)(beta m)^(2)(gamma s)^(-2)`