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

Aniket Singh , 9 Months ago
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anser 1 Answers
Askiitians Tutor Team

To show that a calorie has a magnitude of 4.2α⁻¹β⁻²γ² in terms of the new units, we can start by expressing a calorie in terms of the given units and then replace the units with their new representations.

Given:
1 calorie = 4.2 J

We are provided with the following unit conversions:
1 J = 1 kg·m²·s⁻²
1 kg = α kg (new unit of mass)
1 m = β m (new unit of length)
1 s = γ s (new unit of time)

Now, let's express 1 calorie in terms of the new units:

1 calorie = 4.2 J

Substitute the value of 1 J:
1 calorie = 4.2 (1 kg·m²·s⁻²)

Now, replace the units with their new representations:
1 calorie = 4.2 (1 α kg·β m²·γ⁻² s⁻²)

Now, we can simplify this expression:
1 calorie = 4.2αβ⁻²γ² kg·m²·s⁻²

So, in terms of the new units, 1 calorie has a magnitude of 4.2α⁻¹β⁻²γ², which is the desired result:

1 calorie = 4.2α⁻¹β⁻²γ²

Last Activity: 9 Months ago
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