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Q.

A calorie is a unit of heat and equals 4.2 J. Suppose we employ a system of units in which the unit of mass is $α k g,$ the unit of length is $β m e t r e$ and the unit of time is $γ s .$ In this new system, 1 calorie =

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a

$α^{- 1} β^{- 2} γ^{2}$

b

$4.2 α β^{2} γ^{- 2}$

c

$α β^{2} γ^{2}$

d

$4.2 α^{- 1} β^{- 2} γ^{2}$

answer is D.

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Detailed Solution

$[C a l o r i e] = [M L^{2} T^{- 2}]$

Comparing with general dimensional formula $[M^{a} L^{b} T^{c}],$ we get a =1, b = 2, c = 2

$n_{2} = 4.2 {[\frac{1 k g}{α k g}]}^{1} {[\frac{1 m}{β m}]}^{2} {[\frac{1 s}{γ s}]}^{- 2} = 4.2 α^{- 1} β^{- 2} γ^{2}$

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