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.

Question

Physics

Baron Huber

17 April, 15:40

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.

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Answers (1)

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Gunnar Robertson · Answer 1

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.