Question

A calorie is a unit of heat or energy and it equals about 4.2 J where IJ = 1 kg mºs"
Suppose we employ a system of units in which the unit of mass equals a kg, the unit
of length equals B m, the unit of time is ys. Show that a calorie has a magnitude 4.2
a'ß-2 y? in terms of the new units.​

Answer 1

Answer:

1 calorie = 4.2 j

1J = 1 kg m2s–2

put the value we get =>

1 calorie =4.2 kg m2s–2 = 4.2 × (1 kg) × (1 m2) × (1 s–2) …(1)

Given that

Unit of mass equals α kg => 1 kg mass = 1/α mass

Unit of length equals β m => 1 m length = 1/ β length

Unit of time is γs => 1 s time = 1/ γ time

Put the values in equation (1), we get

New unit of mass = α kg

=4.2 × (1 kg) × (1 m2) × (1 s–2)

= 4.2 × (1/ α ) × (1/ β ) 2 × (1/ γ) –2

= 4.2 × ( α–1 ) × (β–1 ) 2 × ( γ–1) –2

=4.2 α–1 β–2 γ2

Explanation:

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