Question

Find the dimensions of $G{\epsilon }_0$. (G= Universal Gravitational constant , ${\epsilon }_0$ = permittivity in vacuum)

Answer 1

Gravitational force $F_g=\frac{G{m}^2}{r^2}$

Electrostatic $F_e=\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{r^2}$

$\left[\frac{G{m}^2}{r^2}\right]=\left[\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{r^2}\right]$

$\left[G{\epsilon }_0\right]=\left[\frac{q^2}{m^2}\right]=\left[\frac{(it{)}^2}{m^2}\right]=A^2{T}^2{M}^{-2}$