Gravitational Force and Mass

Gravitational force is the attractive force between two objects with mass. It is described by Newton's law of universal gravitation, which states that the force is directly proportional to the product of the masses of the objects and inversely proportional to the square of the distance between them.

The formula for gravitational force (F) is given by:

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

where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them.

Effect of Halving the Masses

If the masses of both objects are halved without altering the distance between them, the gravitational force between them would change.

Let's consider the original masses as m1 and m2, and the halved masses as m1/2 and m2/2. Substituting these values into the gravitational force formula, we get:

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

Simplifying the equation, we have:

F' = (1/4) * (G * (m1 * m2) / r^2)

Therefore, the new gravitational force (F') would be one-fourth (1/4) of the original gravitational force (F).

Explanation

When both masses are halved, the gravitational force between the objects decreases because the force is directly proportional to the product of the masses. Halving the masses reduces the overall gravitational pull between the objects.

The inverse square relationship between the gravitational force and the distance between the objects remains unchanged in this scenario. Only the masses are altered, while the distance remains constant. This means that the gravitational force decreases by a factor of four (1/4) when the masses are halved.

In conclusion, halving the masses of two objects without changing the distance between them results in a reduction of the gravitational force between them to one-fourth of its original value.