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 $Q = n_1u_1 = n_2u_2$ 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 $M_1,L_1,T_1$ are the fundamental unit of mass, length and time in first unit system and $M_2,L_2,T_2$ 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.
Here $M_1,L_1,T_1$ are the fundamental unit of mass, length and time in first unit system and $M_2,L_2,T_2$ 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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