Question
How does the force of gravitation between two objects change when the distance between them is reduced to half $?$
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Answer
According to the universal law of gravitation, gravitational force $(F)$ acting between two objects is inversely proportional to the square of the distance $(r)$ between them, i.e.,$\text{F}\propto\frac{1}{\text{r}^2}$
If distance r becomes $r/2,$ then the gravitational force will be proportional to$\frac{1}{\big(\frac{\text{r}}{2}\big)^2}=\frac{4}{\text{r}^2}$
Hence, if the distance is reduced to half, then the gravitational force becomes four times larger than the previous value.
If distance r becomes $r/2,$ then the gravitational force will be proportional to$\frac{1}{\big(\frac{\text{r}}{2}\big)^2}=\frac{4}{\text{r}^2}$
Hence, if the distance is reduced to half, then the gravitational force becomes four times larger than the previous value.
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