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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Subjective Medium Published on 18th 08, 2020
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