Question

If the distance between two asteroids is halved, the gravitational force they exert on each other will

a) Also be doubled
b) Be half as great
c) Be one fourth as great
d) Will be 1/16 as great
e) Be four times greater

Answer 1

e) Be four times greater

Step-by-step explanation:

Here we have to use Newton's gravitational law that relates the gravitational force between two objects with their masses (
`m_(1)` &
`m_(2)`) and the distance between them (
`r`) in the next way:

`F=G(m_(1)m_(2))/(r^(2))` (2)

Now if distance between asteroids is halved:

`F_(2)=G(m_(1)m_(2))/(((r)/(2))^(2))`

`F_(2)=G(m_(1)m_(2))/((r^(2))/(4))`

`F_(2)=G(4m_(1)m_(2))/(r^(2))=4G(m_(1)m_(2))/(r^(2))`

Note that
`G(m_(1)m_(2))/(r^(2))` because (1) is F so:

`F_(2)=4F`

It's four times greater!