Question

What happens to the gravitational force between two objects when the distance between them is :

(i) doubled?
(ii) halved?

Answer 1

$\mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{r}}^2}$
where,
F − gravitational force
G − gravitational constant
M − mass of the earth
m − mass of object
r − distance

(i). r = doubled
$\mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{r}}^2}$ keeping everything constant i.e. G, M, m
$=\frac{\mathrm{GMm}}{{\left(2\mathrm{r}\right)}^2}$
$=\frac{\mathrm{GMm}}{4{\mathrm{r}}^2}$
F becomes one-fourth.

(ii). r = halved

$\mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{r}}^2}$ keeping everything constant i.e. G, M, m
$=\frac{\mathrm{GMm}}{{\left(1/2\mathrm{r}\right)}^2}$
$=\frac{\mathrm{GMm}}{{\left(1/4\mathrm{r}\right)}^2}$
$=\frac{4\mathrm{GM}\mathrm{m}}{{\mathrm{r}}^2}$
F becomes four times the original.