Physics

Calorie is a unit of heat or energy whose value is $$4.2J$$, where $$J=1\;kgm^2s^{-2}$$. If one uses a unit system in which units of mass, length and time are taken as $$\alpha\;kg,\;\beta\;metre$$ and $$\gamma\;second$$ respectively, then the value of calorie in this system will be


ANSWER

$$\;4.2\alpha^{-1}\beta^{-2}\gamma^{2}$$


SOLUTION

$$\because\,1\;cal=4.2\;J\;\;\;\therefore\,1\;cal=4.2\;kgm^2s^{-2}$$

$$\;\;\;\;\;\;\;\;\;\;\;\;=(4.2\,\alpha^{-1}\beta^{-2}\gamma^2)(\alpha kg)(\beta m)^2(\gamma s)^{-2}$$

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