How does the force of gravitation between two objects change when the distance between them is reduced to half?

Question

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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.,  $𝐹∝ \frac{1 }{𝑟^2 }$ If distance r becomes  $\frac{r}2$ , then the gravitational force will be proportional to $\frac1{ (\frac𝑟{2})^2}$  =  $\frac4{𝑟^2}$ Hence, if the distance is reduced to half, then the gravitational force becomes four times larger than the previous value.

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

How does the force of gravitation between two objects change when the distance between them is reduced to half?

Solution and Explanation

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