Answer:
The force of attraction between them will be 16times as great.
Explanation:
According to the law of gravitation, the force experienced by both students is expressed as shown;
Fo = GMm/d²...(1)
M and m are the masses of the students
d is the initial distance between them
G is the gravitational constant.
If they move so that the distance between them is now one-quarter as great as it was before, the new distance between them will be 1/4 of initial distance 'd' i.e d/4
The new force that will exist between them will be;
F = GMm/(d/4)²
F = GMm/(d²/16)
F = 16GMm/d² ...(2)
Dividing equation 2 by 1, we have;
F/Fo = {16GMm/d²}/GMm/d²
F/Fo = 16GMm/d² × d²/GMm
F/Fo = 16
F = 16Fo
This shows that if the distance between them is one quarter as great ad before, the force of attraction between them will be 16times as great.
