Question

Как изменится сила притяжения между двумя телами, если а) расстояние между их центрами удвоить, б) массу каждого из тел уменьшить в 3 раза?

Answer 1

А) Уменьшится в 4 раза, т.к квадрат расстояния обратно пропорционален силе притяжения между телами.
б) уменьшиться в 9 раз, т.к произведение масс тел прямо пропорционально силе притяжения между телами

Answer 2

Changes in the Force of Gravity

When the distance between the centers of two bodies is doubled, the force of gravity between them will decrease by a factor of four. This is because the force of gravity is inversely proportional to the square of the distance between the centers of the two bodies.

Let's denote the initial distance between the centers of the two bodies as "d" and the initial force of gravity between them as "F".

a) If the distance between the centers of the two bodies is doubled, the new distance will be "2d". According to the inverse square law, the new force of gravity, denoted as "F'", can be calculated using the formula:

F' = F / (2^2) = F / 4.

b) If the mass of each body is reduced to one-third of its initial value, the new mass will be "m/3" for each body. According to Newton's law of universal gravitation, the force of gravity between two bodies is directly proportional to the product of their masses. Therefore, the new force of gravity, denoted as "F''", can be calculated using the formula:

F'' = (F / 3) * (F / 3) = F / 9.

To summarize: - If the distance between the centers of the two bodies is doubled, the force of gravity between them will decrease by a factor of four. - If the mass of each body is reduced to one-third of its initial value, the force of gravity between them will decrease by a factor of nine.

Please note that these calculations assume that the bodies are point masses and that there are no other significant gravitational influences present.

I hope this explanation helps! Let me know if you have any further questions.