Question

If the distance between the earth and the moon is reduced to half of its original, the gravitational force between them will _________.

Answer 1

Step 1:

Given that: Radius between earth and moon is reduced to half of the original radius.

$r^1=\frac{r}{2}$

Step 2: We know that Newton's gravitational force

${\text{F}}_{}=\frac{{\text{Gm}}_1{\text{m}}_2}{{\text{r}}^2}\left(1\right)$

Now, put the value of $r^1=\frac{r}{2}$ in the equation (1), we get

${\text{F}}_{\text{new}}=\frac{{\text{Gm}}_1{\text{m}}_2}{{\left({\displaystyle \frac{r}{2}}\right)}^2}$

By solving it, we get

${\text{F}}_{\text{new}}=\frac{{\text{4Gm}}_1{\text{m}}_2}{{\text{r}}^2}$

We can write this

${\text{F}}_{\text{new}}\text{=4F}$

So, the force of attraction between the Earth and moon becomes 4 times.