Question

When the mases are doubled and the separation is halved, what effect do they have on the gravitatinal force between the mases?

Answer 1

Answer:

According to Universal Law of gravitation , the gravitational force of attrection between any two objects of mass

$M$ and $m$ is proportional to the product of their masses

and inversly proportional to the square of distance $r$ between them

So, force $F$ is given by

$F = G\frac{{M \times m}}{{{r^2}}}$

Now when the distance $r$ is reduced to half then force between two masses becomes

$F’=G\frac{M\times m}{\left ( \frac{r}{2} \right )^2}$

or,

$F’=4F$

Clearly , if distance between two objects is reduced to half then the gravitational force becomes four times larger than its previous value.