We know that........ F= G Mm/r^2And if distance is halved i.e r = r/2F = GmM/(r/2)^2F= 4 GmM/r^2So we get result that force will be 4 times of the initial force of the distance is reduced to half.

Distance between Objects

When the distance between two objects is halved, it means that the objects are now twice as close to each other as they were before. In the context of gravitational force, this change in distance has a significant impact on the strength of the force.

Gravitational Force

Gravitational force is the attractive force that exists between any two objects with mass. It is responsible for holding planets in their orbits around the sun, and for keeping objects grounded on Earth. The magnitude of the gravitational force between two objects is determined by their masses and the distance between them.

Relationship between Distance and Gravitational Force

According to Newton's law of universal gravitation, the gravitational force between two objects is inversely proportional to the square of the distance between their centers. This means that as the distance between two objects decreases, the gravitational force between them increases.

Mathematical Representation

The mathematical representation of this relationship can be expressed as:

F ∝ 1/d^2

Where F is the gravitational force and d is the distance between the centers of the objects.

Effect of Halving the Distance

When the distance between two objects is halved, it means that the new distance is half of the original distance. As a result, the new distance squared is one-fourth of the original distance squared.

Let's assume the original distance between the objects is represented as d, and the halved distance is represented as d/2. Substituting these values into the equation, we get:

F ∝ 1/(d/2)^2
F ∝ 1/(d^2/4)
F ∝ 4/d^2

Therefore, halving the distance leads to a four-fold increase in the gravitational force between the objects.

Explanation

The explanation for this increase in gravitational force can be attributed to the fact that as the objects move closer to each other, the gravitational field they create becomes stronger. This increased field results in a greater force of attraction between the objects.

In conclusion, when the distance between two objects is halved, the gravitational force between them increases four times. This relationship is a consequence of Newton's law of universal gravitation and showcases the inverse square relationship between distance and gravitational force.