Question

Two buckets of sand exert a gravitational force of $18$ nanoNetwons on each other when their centers are separated by a distance of d.
How much force do they exert on each other when they are separated by a distance of $3d$?

• A. $2$ nanoNewtons
• B. $6$ nanoNewtons
• C. $9$ nanoNewtons
• D. $54$ nanoNewtons
• E. We need to know the masses of the sand buckets to answer this question

Answer 1

The correct option is A $2$ nanoNewtons

The gravitational force exerted by two masses on each other separated by distance $d$ is given by $F=\frac{GMm}{d^2}$

Hence $\frac{F^{\prime }}{F}=\frac{d^2}{d^{\prime 2}}=\frac{d^2}{(3d{)}^2}=\frac{1}{9}$

$⟹F^{\prime }=2nN$