Question

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

Answer 1

Consider the given equation,

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

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.