A calorie is a unit of heat and it equals 4.2 J, where `1 J = kg m^2 s^-2`.. A distant civilisation employs a system of units in which the units of mass, length and time are α kg, `beta` m and `gamma ` s. Also J' is their unit of energy. What will be the magnitude of calorie in their units?

Explanation

Let us write the new units as A, B and C for mass, length and time respectively. We are given
`1A = alpha kg`
`1 B = betam`
`1 C = gamma s`
`1 cal = 4.2 J = 4.2 kg m^2 s^(-2)`
` =4.2 (A/alpha)(B/beta)^2 (C/gamma)^(-2)`
` = (4.2 gamma^2)/(alphabeta^2) AB^2 C^(-2)`
`= (4.2 gamma^2)/(alphabeta^2) J.`
Thus in the new units, 1 calorie is ` = (4.2 gamma^2)/(alpha beta^2) J.`