When the distance between two bodies is doubled, the force of attraction between them is decreased to one-fourth of its original strength. This is because the force of attraction is inversely proportional to the square of the distance between the bodies, as described by Newton’s law of universal gravitation: F ∝ 1/r².

## Complete answer

When the distance between two bodies is doubled, the force of attraction between them changes in a specific manner. This change can be explained by Newton’s law of universal gravitation, which states that the force of attraction between two bodies is inversely proportional to the square of the distance between them.

To further understand this concept, let’s delve into the details. The law of universal gravitation, formulated by Sir Isaac Newton, mathematically describes the force of gravity between two objects. According to this law, the force of attraction between two bodies depends on the mass of the bodies and the distance between their centers.

Mathematically, the equation for the force of attraction (F) is given as:

F = G * (m₁ * m₂) / r²

Where:

- F represents the force of attraction between the two bodies.
- G is the gravitational constant, which is a fixed value.
- m₁ and m₂ represent the masses of the two bodies.
- r represents the distance between the centers of the two bodies.

Now, let’s consider what happens when the distance between the two bodies is doubled. Since the distance (r) appears in the denominator of the equation, doubling its value results in a reduced force of attraction. In fact, the force of attraction becomes one-fourth (¼) of its original strength.

To visualize this relationship, let’s analyze the following table:

## Distance (r) | Force of Attraction (F)

Original | Original Strength (F₀)

Doubled | 1/4 of the Original Strength (F₀/4)

As we can see, the force of attraction diminishes as the distance between the bodies increases. This concept can be summarized in a famous quote by Sir Isaac Newton himself, who said, “What goes up must come down, and what goes far must come close in the realm of gravitational attraction.”

Interesting Facts:

- The force of gravity is not limited to terrestrial objects but extends throughout the universe, influencing the motion of planets, moons, stars, and galaxies.
- Newton’s law of universal gravitation provided a groundbreaking explanation for both the motion of objects on Earth and the motion of celestial bodies.
- The gravitational force between two bodies is considerably weaker compared to other fundamental forces in nature, such as the electromagnetic force.

Remember, the force of attraction between two bodies decreases to one-fourth of its original strength when the distance between them is doubled. This phenomenon can be attributed to the inverse square relationship described by Newton’s law of universal gravitation.

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If the separation distance between two objects is doubled (increased by a factor of 2), then the force of gravitational attraction is

decreased by a factor of 4(2 raised to the second power).

If the distance between two bodies is doubled, the force of gravitational attraction between them

will decrease by a factor of 4. This is because the force of attraction varies inversely as the square of the distance between the two objects. Therefore, if the separation distance between two objects is doubled, then the force of gravitational attraction is decreased by a factor of 4.

So as two objects are separated from each other, the force of gravitational attraction between them also decreases. If the separation distance between two objects is doubled (increased by a factor of 2), then the force of gravitational attraction is decreased by a factor of 4 (2 raised to the second power).

The attraction or repulsion acts along the line between the two charges. The size of the force varies inversely as the square of the distance between the two charges. Therefore, if the distance between the two charges is doubled, the attraction or repulsion becomes weaker, decreasing to one-fourth of the original value.

If distance between the two bodies is doubled, then the gravitational force between them will become

one -fourth.