A calorie is a unit of heat energy and its value is 4.18J, where 1J=1kg `-m^(2)//s^(2)`. Suppose we use a new system of units in which unit of mass equals of kg, the unit of length equals `beta` m and the unit of the time is `gamma` sec. Then the value of a calorie in the new system of 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)`