Physics

If $$ mu=A+\frac { B }{ \lambda } +\frac { C }{ \lambda ^ 2 }  $$ then find dimensions of A,B and C respectively (A,B,C are constant) where $$ \lambda $$ is wavelength of wave 


SOLUTION

Consider the given equation,

$$mu=A+\dfrac{B}{\lambda }+\dfrac{C}{{{\lambda }^{2}}}............(1)$$

Writing dimensional formula of m, u and lambda

Dimension of $$mu=\left[ ML{{T}^{-1}} \right]$$

Dimension of $$wavelength=\left[ L \right]$$

Since, dimension of same quantity adds.

Put dimensions in (1)

$$ \left[ ML{{T}^{-1}} \right]=A $$

$$ \left[ ML{{T}^{-1}} \right]\left[ L \right]=B $$

$$ \left[ M{{L}^{2}}{{T}^{-1}} \right]=B $$

$$ \left[ ML{{T}^{-1}} \right]\left[ {{L}^{2}} \right]=C $$

$$ \left[ M{{L}^{3}}{{T}^{-1}} \right]=C $$

Dimension of A,B and C are calculated.

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