The gravitational force between 2 objects is F . If masses of both the objects are halved without changing distance between them , then the gravitational force would be
You can figure things like this yourself as follows:
F = k(m1*m2)d^2 so let's assume m1 and m2 are 2 each and d is 2. So
F = k(2*2)/2^2 = k*1 or 1k.
Now half m1 and m2 so each is 1. Then
F = k(1*1)/4 = k*1/4 or k/4.
So the factor between 1K and k/4 is ?
To find out how the gravitational force changes when the masses are halved without changing the distance between the objects, we can make use of Newton's law of universal gravitation.
Newton's law of universal gravitation states that the force of gravitational attraction 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 = Gravitational force between the objects
G = Universal gravitational constant
m1, m2 = Masses of the objects
r = Distance between the centers of the objects
Now, if the masses of both objects are halved, then the new masses would be m1/2 and m2/2. Plugging these values into the equation:
F' = G * ((m1/2) * (m2/2)) / r^2
= (1/4) * G * (m1 * m2) / r^2
So, we can see that the new gravitational force (F') would be one-fourth (1/4) of the original gravitational force (F) when the masses are halved without changing the distance between the objects.