How will you convert a physical quantity from one unit system to … - Vidyadip

Question

How will you convert a physical quantity from one unit system to another by method of dimensions?

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Answer

If a given quantity is measured in two different unit system,
then Q = n₁u₁ = n₂u₂
Let the dimensional formula of the quantity be [M^aL^bT^c)
Then we have:
$\text{n}_1[\text{M}_1^{\text{a}}\text{L}_1^{\text{b}}\text{T}_1^{\text{c}}]=\text{n}_2[\text{M}_2^{\text{a}}\text{L}^{\text{b}}_2\text{T}^{\text{c}}_2]$
Here M₁,L₁,T₁ are the fundamental unit of mass, length and time in first unit system and M₂,L₂,T₂ in the second unit system.
$\text{Hence},\text{n}_2=\text{n}_1\Big[\frac{\text{M}_1}{\text{M}_2}\Big]^\text{a}\Big[\frac{\text{L}_1}{\text{L}_2}\Big]^\text{b}\Big[\frac{\text{T}_1}{\text{T}_2}\Big]^\text{c}$
This relation helps us to convert a physical quantity from one unit system to another.

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