Question

look at the data from the previous table:

$d$ (m)	$	f_a	$ (n)
20	0.1667
30	0.0741
40	0.0417

what is the relationship between the gravitational and the distance between two objects?
options: inverse square, quadratic, inverse, linear

Explanation:

To determine the relationship, we analyze the data: when \( d \) (distance) doubles from 10 m to 20 m, \( |F_A| \) (gravitational force) becomes \( \frac{0.667}{0.1667}\approx4=\frac{1}{(2)^2} \) of its original value. When \( d \) triples from 10 m to 30 m, \( |F_A| \) becomes \( \frac{0.667}{0.0741}\approx9=\frac{1}{(3)^2} \) of its original value. When \( d \) quadruples from 10 m to 40 m, \( |F_A| \) becomes \( \frac{0.667}{0.0417}\approx16=\frac{1}{(4)^2} \) of its original value. This shows \( |F_A| \propto \frac{1}{d^2} \), so the relationship is inverse square.

Answer:

inverse square