Question

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

Answer 1

Answer:

e) Be four times greater

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:

$F=G\frac{m_{1}m_{2}}{r^{2}}$ (2)

Now if distance between asteroids is halved:

$F_{2}=G\frac{m_{1}m_{2}}{(\frac{r}{2})^{2}}$

$F_{2}=G\frac{m_{1}m_{2}}{\frac{r^{2}}{4}}$

$F_{2}=G\frac{4m_{1}m_{2}}{r^{2}}=4G\frac{m_{1}m_{2}}{r^{2}}$

Note that $G\frac{m_{1}m_{2}}{r^{2}}$ because (1) is F so:

$F_{2}=4F$

It's four times greater!