Question

Two spherical lumps of clay attract each other with some amount of gravitational force, as explained by Newton's law of universal gravitation. If I add clay to one lump and to the other so that the mass of one is 5 times as much as before and the mass of the other is 3 times as much as before, and I move the lumps (still spherical) so that their centers are now 4 times as far apart as before, how does the new gravitational force between them compare?

• A. The new force is slightly smaller.
• B. The new force is slightly greater.
• C. The new force is more than 3 times as great.
• D. The new force is less than one-third as great.
• E. We cannot answer this question without knowing the universal gravitational constant.

Answer 1

The correct option is A The new force is slightly smaller.

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

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

now given that the two masses are equal so ,

$F=km\times m/r^2$ ...........................eq1

now given that in new position , $m_1=5m,m_2=3m$ and distance between them is now $4r$ ,

therefore force will be ,

$F^{\prime }=k\times 5m\times 3m/(4r{)}^2$ ,

or $F^{\prime }=k\frac{15m^2}{16r^2}$ .....................eq2

by dividing eq2 by eq1 ,

we get $F^{\prime }/F=15/16$

or $F^{\prime }=15F/16$

it means new force $F^{\prime }$ is slightly smaller than $F$ .