Question

The dimension of the quantity $\frac{1}{e_0}\frac{e^2}{hc}$ is ( e= charge of electron, h= Planks constant and c= velocity of light)

• A. $\left[M^{-1}{L}^{-3}{T}^{2}A\right]$
• B. $\left[M^0{L}^0{T}^0{A}^0\right]$
• C. $\left[M{L}^3{T}^{-4}{A}^{-2}\right]$
• D. $\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$

Answer 1

The correct option is B $\left[M^0{L}^0{T}^0{A}^0\right]$

Dimensions of ${ϵ}_0=\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$

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

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

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

$\Rightarrow \frac{1}{{ϵ}_0}\times \frac{c^2}{hC}=\frac{1}{[M^{-1}{L}^{-3}{T}^4{A}^2}\times \frac{\left[A^2{T}^2\right]}{\left[M^1{L}^2{T}^{-2}\right]\left[L^1{T}^{-1}\right]}$

$=\left[M^0{L}^0{T}^0{A}^0\right]$ $\left(B\right)$ Ans