What is the SI unit of the gravitational constant?

 

Concept: According to Newton's law of gravity, everybody in the universe attracts every other body with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

The force is directed along the line connecting the particles.

Then The gravitational attraction force is given by

The gravitational attraction force is given by

$\mathrm{F}=\frac{{\mathrm{Gm}}_1{\mathrm{m}}_2}{{\mathrm{R}}^2}$

The above equation can be written as

$\mathrm{G}=\frac{{\mathrm{FR}}^2}{{\mathrm{m}}_1 {\mathrm{m}}_2}$

- Therefore the unit of gravitational constant (G) is-

$\mathrm{G}=\frac{\mathrm{N}\times {\mathrm{m}}^2}{\mathrm{kg}\times \mathrm{kg}}$

$\mathrm{G}=\frac{\mathrm{N} {\mathrm{m}}^2}{{\mathrm{Kg}}^2}$