If two quantities have the same dimensions, do they represent the same physical content?
 

Suggest a way to measure:

$\left(\mathrm{a}\right)$ the thickness of a sheet of paper and

$\left(\mathrm{b}\right)$ the distance between the sun and the moon.

$\int \frac{dx}{\sqrt{2ax-x^2}}=a^{\mathrm{n}}{\sin }^{-1}\left[\frac{x}{a}-1\right]$

Find the value of $n$. (Solve using dimensional analysis)