the gravitational force between two object is F . How will this force will change when the distance between them is reduce to half?

The force of gravity is dependent on the two masses involved,if you halved the distance then force of gravitation will becomes double of the orignal

The attraction force is inversely proportional to the SQUARE of the distance between them. Therefore it becomes four times higher.

To understand how the gravitational force changes when the distance between two objects is reduced to half, we need to apply Newton's law of universal gravitation. According to this law, the gravitational force (F) between two objects is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance between their centers (r).

Mathematically, the equation for the gravitational force is:

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

Where:
- F is the gravitational force
- G is the gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2)
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two objects

Now, suppose the initial distance between the objects is denoted as r1 and the force is denoted as F1. If the distance is reduced to half, the new distance denoted as r2 will be half of the initial distance (r2 = r1/2).

To find the new force (F2), we substitute the new distance into the equation:

F2 = (G * m1 * m2) / (r2)^2

F2 = (G * m1 * m2) / (r1/2)^2

F2 = (G* m1 * m2) / (r1^2/4)

F2 = 4 * (G * m1 * m2) / r1^2

From the equation above, we can see that the new force (F2) will be four times greater than the initial force (F1). Therefore, when the distance between two objects is reduced to half, the gravitational force between them increases by a factor of four.