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A calorie is a unit of heat and equal 4.2 J. Suppose we employ a system of units in which the unit of mass is $α$ kg, the unit of length is $β$ meter and the unit of time is $γ$ sec. In this new system. 1 calorie =

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${αβ}^{2} γ^{2}$

$4.2 α^{- 1} β^{- 2} γ^{2}$

$4.2 {αβ}^{2} γ^{2}$

$α^{- 1} β^{- 2} γ^{2}$

answer is D.

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Detailed Solution

[Calorie]= $[{ML}^{2} T^{- 2}]$

Comparing with general dimensional formula $[M^{a} L^{b} T^{c}],$

we get $a = 1, b = 2, c = - 2$

$n_{2} = 4.2 {[\frac{1 kg}{αkg}]}^{1} {[\frac{1 m}{βm}]}^{2} {[\frac{1 s}{γs}]}^{- 2} = 4.2 α^{- 1} β^{- 2} γ^{2}$

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