Question

derive the unit of G​

Answer 1

Answer:

$\mathrm{Nm}^{2} / \mathrm{kg}^{2}$

Explanation:

We know that

$\begin{aligned}&\mathrm{F}=\mathrm{G} \times \frac{M_{1} M_{2}}{r^{2}} \\&\mathrm{~F} \times \mathrm{r}^{2}=\mathrm{G} \times \mathrm{M}_{1} \mathrm{M}_{2} \\&\mathrm{~F} \times \frac{r^{2}}{M_{1} M_{2}}=\mathrm{G} \\&\mathrm{G}=\mathrm{F} \times \frac{r^{2}}{M_{1} M_{2}}\end{aligned}$

SI Unit of

Force $=\mathrm{F}=$ Newton

Distance $=\mathrm{R}=\mathrm{m}$

Mass $=M=k g$

Now,

$\mathrm{G}=\mathrm{F} \times \frac{r^{2}}{M_{1} M_{2}}\\\mathrm{G}=\frac{\text { Newton } \text { Meter }^{2}}{\text { Kilogram }}\\\mathrm{G}=\mathrm{Nm}^{2} / \mathrm{kg}^{2}$

So, SI Unit of $\mathrm{G} is \mathrm{Nm}^{2} / \mathrm{kg}^{2}$