Question

To buckets of sand exert a gravitational force of 18 nanoNewtons 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 the question.

Answer 1

Answer: (A)

2 nanoNewtons

The gravitational force $F$ between two masses $m_1,m_2$ separated by a distance $r$ is given by ,

$F=k{m}_1{m}_2/r^2$ ,

now when $r=d$ ,

$F=k{m}_1{m}_2/d^2$ .................eq1

and when $r=3d$ ,

$F^{\prime }=k{m}_1{m}_2/(3d{)}^2$ ,

or $F^{\prime }=k{m}_1{m}_2/9d^2$ ...............eq2

dividing eq2 by eq1 ,

$F^{\prime }/F=1/9$

or $F^{\prime }=F/9$

now given $F=18nN$

therefore , $F^{\prime }=18/9=2nN$