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A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m2s–2. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2 α–1 β–2 γ2 in terms of the new units.

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Given that,

1 calorie = 4.2 (1 kg) (1 m2) (1 s–2)

New unit of mass = α kg

Hence, in terms of the new unit, 1 kg =1/α = α-1 

In terms of the new unit of length,

1 m = 1/β-1 or 1 m2 = β-2

And, in terms of the new unit of time,

1 calorie = 

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