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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.

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Answer Text

Solution :
Given that , <br> 1 calorie =4.2 (1 kg ) `(1m^(2)) (1s^(-2))` <br> New unit of mass `=alpha kg` <br> Hence, in terms of the new unit `1kg =1/(alpha) =alpha^(-1)` <br> in terms of the new unit of length, <br> `1m =1/(beta) =beta^(-1) ` or `1m^(2)=beta^(-2)` <br> And, in terms of the new unit of time, <br> `1s=1/(gamma) =gamma^(-1)` <br> `1s^(2) =gamma^(-2)` <br> `1 s^(-2) =gamma^(2)` <br> `:.` calorie `=4.2 (1alpha^(-1)) (1 beta^(-2)) (1 y^(2)) =4.2 alpha^(-1) beta^(-2) gamma^(2)`

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