State the universal law of gravitation. Write the $SI$ unit of $G$. The gravitational force between two objects is $100 \, N$. How should the distance between the objects be changed so that the force between them becomes $50 \, N$?

(N/A) The universal law of gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The $SI$ unit of the universal gravitational constant $G$ is $N \, m^2 \, kg^{-2}$.
Given:
Initial force $F_1 = 100 \, N$
Final force $F_2 = 50 \, N$
We know that the gravitational force $F$ is given by $F = \frac{G m_1 m_2}{r^2}$,which implies $F \propto \frac{1}{r^2}$.
Therefore,$\frac{F_1}{F_2} = \left(\frac{r_2}{r_1}\right)^2$.
Substituting the values:
$\frac{100}{50} = \left(\frac{r_2}{r_1}\right)^2$
$2 = \left(\frac{r_2}{r_1}\right)^2$
$\frac{r_2}{r_1} = \sqrt{2}$
Thus,the distance between the objects should be increased by a factor of $\sqrt{2}$ (approximately $1.414$ times the original distance) to make the force $50 \, N$.