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A calorie is a unit of heat or energy and it is equal to about 4.2 J where 1 J = 1 kg m² s⁻². Suppose, we employ a system of units in which 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 4.2 β⁻²α⁻¹ γ² in terms of the new units. |
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Answer» udent,◆ ANSWER -1 cal = 4.2 β⁻²α⁻¹γ² xy²z⁻²◆ Explaination -LET x, y and z be units of mass, length and time in new system of units.x = α kg, 1 kg = x/αy = β m, 1 m = y/βz = γ s, 1 s = z/γNow we know,1 cal = 4.2 J1 cal = 4.2 kgm²s⁻²Substitute values,1 cal = 4.2 × (x/α) × (y/β)² × (z/γ)⁻²z1 cal = 4.2 β⁻²α⁻¹γ² xy²z⁻²Therefore, magnitude of 1 cal in new system of units is 4.2 β⁻²α⁻¹γ².Hope this helps you... |
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