A calorie is a unit of heat enegy and its value is 4.18 J where 1J=kg `m^(2)s^(-2)`. Suppose we use a new system of units in which unit of mass equals `alpha` 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 is

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))`