If the unit of mass is $α kg$ , the unit of length is $β$ meter and the unit of time is $' γ'$ second,
The magnitude of calorie in the new system is $(1cal = 4.2J)$

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$4.2 α^{- 1} β^{- 2} γ^{2} n e w u n i t s$

$α^{- 1} β^{- 2} γ^{2} n e w u n i t s$

$4.2 α^{2} β^{2} γ^{2} n e w u n i t s$

$\frac{1}{4.2} α^{- 1} β^{- 2} γ^{2} n e w u n i t s$

answer is B.

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Detailed Solution

$1cal = 4.2 \frac{kg - m^{2}}{s^{2}} 1 cal = \frac{4.2 {(\frac{kg}{α})}^{1} . {(\frac{m}{β})}^{2}}{{(\frac{s^{1}}{r})}^{2}} = 4.2 α^{- 1} β^{- 1} γ^{2} {Kg}^{1} m^{2} s^{- 2} 1cal = 4.2 α^{- 1} β^{- 2} γ^{2} newunits$

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