Question

A calorie is a unit of heat or energy and it is equal to about 4.2J where 1J=1ksm^2s^-2.Suppose we employ a system of units in which the unit of mass equals skg,the unit of lenght =rm,the unit of time=gs.show that a calorie has a magnitude 4.2 s^-1r^-2g^2.

Answer 1

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 =

In terms of the new unit of length,



And, in terms of the new unit of time,



∴1 calorie = 4.2 (1 α–1) (1 β–2) (1 γ2) = 4.2 α–1 β–2 γ2

Answer 2

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