Question

What happens to the force between two objects, if the mass of one object is doubled?

Answer 1

Law of gravitation

According to the universal law of gravitation, every item inside the universe attracted more or less every entity by a force of attraction that is directly proportional to the product of the entities' masses and inversely proportional to the square of such distances between them.

Mathematically, this can be represented as:

$\Rightarrow \mathrm{F}=\mathrm{G}\left(\frac{\mathrm{mM}}{{\mathrm{d}}^2}\right)$

Here,

1. F is the force of the gravitational pull.
2. G is the constant known as the gravitational constant
3. M is the mass of the first object.
4. m is the mass of the second object.
5. d is the distance between both objects.

Calculate if the mass of one object is doubled

The force between two objects is proportional to their respective mass and reciprocally proportional to the square of their distance.

$\Rightarrow \mathrm{F}=\mathrm{G}\left(\frac{2\mathrm{mM}}{{\mathrm{d}}^2}\right)$

If the mass is doubled for one object, then

$\mathrm{F}=2\mathrm{F}$

So the force is also doubled.