4. Two students are sitting in the cafeteria eating lunch. They move so that the distance between them is now one-quarter as great as it was before. The force of attraction between them (gravitational that is) is now times as great.

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.