The gravitational force between objects is 10 | vedclass

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Question

(A) According to Newton's law of universal gravitation,the force $F$ is inversely proportional to the square of the distance $r$ between the objects:

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Increase by a factor of $\sqrt{2}$

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(A) According to Newton's law of universal gravitation,the force $F$ is inversely proportional to the square of the distance $r$ between the objects: $F \propto \frac{1}{r^2}$.Given initial force $F_1 = 100 \, N$ and final force $F_2 = 50 \, N$.We have the ratio: $\frac{F_2}{F_1} = \frac{r_1^2}{r_2^2}$.Substituting the values: $\frac{50}{100} = \frac{r_1^2}{r_2^2} \implies \frac{1}{2} = \frac{r_1^2}{r_2^2}$.Taking the square root on both sides: $\frac{1}{\sqrt{2}} = \frac{r_1}{r_2}$.Therefore,$r_2 = \sqrt{2} \, r_1$.Thus,the distance must be increased by a factor of $\sqrt{2}$.

The gravitational force between objects is $100 \, N$. How should the distance between these objects be changed so that the force between them becomes $50 \, N$?

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