What happens to the magnitude of the force of gravitation between two objects if mass of both the objects as well as distance between them is doubled?

As per the universal law of gravitation, every object in the universe attracts every other object by the force of attraction which is directly proportional to the product of masses of the objects and is inversely proportional to the square of the distance between them. This is mathematically given as:

F = G(mM/d2)

Where,

• F is the force of the gravitational pull
• G is the constant known as the gravitational constant
• M is the mass of object 1
• m is the mass of the object 2
• d is the distance between object 1 and object 2

(i) The mass of one object is doubled?

According to the universal law of gravitation, the force between 2 objects (m1 and m2) is proportional to their plenty and reciprocally proportional to the sq. of the distance(R) between them.

F = G(2mM/d2)

If the mass is doubled for one object.

F = 2F, so the force is also doubled.

(ii) The distance between the objects is doubled and tripled

If the distance between the objects is doubled and tripled

If it’s doubled

Hence,

F = (GmM)/(2d)2

F = 1/4 (GmM)/d2

F = F/4

Force thus becomes one-fourth of its initial force.

Now, if it’s tripled

Hence,

F = (GmM)/(3d)2

F = 1/9 (GmM)/d2

F = F/9

Force thus becomes one-ninth of its initial force.

(iii) The masses of both objects are doubled?

If masses of both the objects are doubled, then

F = G(2mM/d2)

F = 4F, Force will therefore be four times greater than its actual value.

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