Question

How many times does the gravitaional force increase, when the distance between the two objects is reduced to one third?

• A. 3
• B. 1/3
• C. 9
• D. 1/9

Answer 1

The correct option is C 9

According to newton's law of gravitation,
$F=\frac{GMm}{r^2}$
where:
$M$ and $m$ are the two masses
$r$ is the distance between them.

When the distance between them is reduced as one-third,
$r^{\prime }=\frac{1}{3}r$

New force is:
$F^{\prime }=\frac{GMm}{(r/3{)}^2}$
$F^{\prime }=\frac{9GMm}{r^2}$
$F^{\prime }=9F$
therefore, when the distance between the two objects is reduced to one-third, the force of gravitation will increase by nine times the original force.