how dimensional analysis use to find conversion factor between two different systems of unit. A calorie is a unit of heat and it equals 4.2 J, where 1J= kg 2 −2 . A distant civilisation employs a system of units in which the units of mass, length and time are α kg, β m, and γ s. Also J’ is their unit of energy. What will be the magnitude of calorie in their units?
Answers
Explanation:
1 cal = 4.2 kgm²s⁻²
Whenever conversion factor is required we use the rule
n₁u₁ = n₂u₂
where n refers to magnitude and u refers to units
So
4.2 kg m² s⁻² = n₂ α kg β² m² γ⁻² s⁻²
Now cancel kg m² s⁻² on both sides
n₂ = 4.2 γ² α⁻¹ β⁻² = 1 cal
Answer:
1 cal = 4.2 Kgm²s - ²
SI system. NEW system
M1 = 1Kg. M2. = aKg
L1 = 1m. L2 = βm
T1= 1 8. T2 = y8
n1 = 4. n2=?
dimensional formula energy is ( ML²T²-² )
comparing with [Ma Lb Tc]
Now ,n² = n ¹
[M1. ] [ L1] [T1]
________________
[m2] [L2] [T2]
= 4.2 [1Kg]¹ [ 1m] [1s]
___________________
[ akg] [ βm][ y8] = 4.2a -¹β-².
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