Question

1 при увеличении массы одного из взаимодействующих тел в 5 раз сила всемирного тяготения1) увеличется в 5 раз2)уменьшится в 5 раз3)увеличится в 55 раз4)уменьшится в 25 раз 2 при увеличении массы каждого из взаимодействующих тел в 2 раза сила всемирного тяготения 1) увеличится в 5 раз2)уменьшится в 5 раз3)увеличится в 4 раза4)уменьшится в 4 раза3 при увеличении в 3 раза расстояния между центрами шарообразных тел сила гравитационного притяжения1)увеличится в 3 раза2)уменьшится в 3 раза3)увеличится в 9 раз4)уменьшается в 9 раз4если массу одного тела увеличить в 4 раза, а расстояние между телами уменьшить в 2 раза то сила всемирного тяготения1)увеличится в 2 раза2)уменьшится в 2 раза3)увеличится в 8 раз4)не изменится

Answer 1

$\bf F=G \frac{m_1m_2}{r^2}$
1. 1
2. 3
3. 4
4. 4

Answer 2

Newton's Law of Universal Gravitation

According to Newton's Law of Universal Gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, it can be expressed as:

F = G * (m1 * m2) / r^2

Where: - F is the force of gravity between the two objects, - G is the gravitational constant, - m1 and m2 are the masses of the two objects, and - r is the distance between their centers.

Let's analyze each scenario mentioned in the question and determine the change in the force of gravity.

Scenario 1: Increasing the mass of one object by 5 times

If the mass of one of the interacting objects is increased by 5 times, the force of gravity between them will also increase by 5 times. This is because the force of gravity is directly proportional to the product of the masses of the objects [[1]].

Scenario 2: Increasing the mass of both objects by 2 times

If the masses of both interacting objects are increased by 2 times, the force of gravity between them will also increase by 4 times. This is because the force of gravity is directly proportional to the product of the masses of the objects [[2]].

Scenario 3: Increasing the distance between the centers of the objects by 3 times

If the distance between the centers of the spherical objects is increased by 3 times, the force of gravitational attraction between them will decrease by 9 times. This is because the force of gravity is inversely proportional to the square of the distance between the objects [[3]].

Scenario 4: Increasing the mass of one object by 4 times and decreasing the distance between the objects by 2 times

If the mass of one object is increased by 4 times and the distance between the objects is decreased by 2 times, the force of gravity between them will remain unchanged. This is because the increase in mass is offset by the decrease in distance, resulting in a cancellation of the effects on the force of gravity [[4]].

In summary: 1. When the mass of one object is increased by 5 times, the force of gravity between the objects will also increase by 5 times. 2. When the mass of both objects is increased by 2 times, the force of gravity between the objects will increase by 4 times. 3. When the distance between the centers of the objects is increased by 3 times, the force of gravity between the objects will decrease by 9 times. 4. When the mass of one object is increased by 4 times and the distance between the objects is decreased by 2 times, the force of gravity between the objects will remain unchanged.

Please let me know if you need any further clarification.