How will the force of gravitational interaction between two material points change if the distance

| June 15, 2021 | education

How will the force of gravitational interaction between two material points change if the distance between them is increased by 3 times?

Given:

m1, m2 is the mass of two interacting bodies;

r2 = 3 * r1 – the distance between the two bodies was increased by 3 times.

It is required to determine F2 / F1 – how the force of gravitational interaction will change with increasing distance by 3 times.

The force of gravitational interaction in the first case will be equal to:

F1 = G * m1 * m2 / r1 ^ 2, where G is the gravitational constant.

In the second case, the force of interaction will be equal to:

F2 = G * m1 * m2 / r2 ^ 2 = G * m1 * m2 / (r1 * 3) ^ 2 = G * m1 * m2 / (9 * r1 ^ 2).

Then:

F2 / F1 = (G * m1 * m2 / (9 * r1 ^ 2)) / (G * m1 * m2 / r1 ^ 2) = 1/9, that is, it will decrease by 9 times.

Answer: with an increase in the distance between bodies by 3 times, the force of gravitational interaction will decrease by 9 times (there are no correct answers among those indicated in the condition of the problem).



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