If the distance between two objects increases then the gravitational force between them

Gravitational force is given by

F=GMm/r2

That implies Force is inversely proportional to distance between the objects.

Therefore, If the distance between the objects increase with mass remaining same ,then the gravitational forces between the object will decrease.

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Option 4 : decrease by four times

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The correct answer is to decrease by four times.

Newton's law of gravitation explains the gravitational force.

Key Points

Newton's law of gravitation states that the two particles in the universe are attracted to each other by a force called the gravitational force which is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them.
F= G × (M1 × M2) / d2.
G is a gravitational constant.
G= 6.67 × 10-11 Newtons kg-2 m2.
This means that if the distance between the two objects is doubled and since the distance is inversely proportional to the gravitational force it will become 1/(2*2)= 1/ 4.
Also if the masses are doubled and since masses are directly proportional to the gravitational force it will become 4 times (2*2).

Additional Information

Gravitational Potential Energy:
- It is the energy possessed by a body at a certain point when work is done by the force of gravity in bringing the object from infinity to that point.
- The gravitational potential energy between two masses m1 and m2 separated by a distance d is given byU=−Gm1m2U=−Gm1m2r

EXPLANATION:

The gravitational potential (V) is the gravitational potential energy per unit mass. ⇒V=U⇒V=Um
At an infinite distance, the gravitational field is assumed to be zero and hence, it will not interact with the mass with regards to gravitational potential. Thus, when E = 0, V = 0.
We know that the gravitational field inside a spherical shell is zero. The gravitational potential inside a shell is the same as that on the shell.−GMR−GMR.

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CONCEPT:

Gravitational Potential Energy: The energy of an object due to its position in a gravitational field.

\(U=-\frac{Gm_1m_2}{r} \)

where U is the potential energy, m1 is the mass first object, m2 is the mass of the second object, r is the distance between the earth and the object, and G is the gravitational constant.

Potential energy at infinity (r = ∞) is zero (U = 0).

EXPLANATION:

Gravitational potential energy is given by

\(U=-\frac{Gm_1m_2}{r} \)

If the distance between the objects r increases, \(\frac{1}{r} \) will decrease.

If \(\frac{1}{r} \) decreases, \(\frac{Gm_1m_2}{r} \) will also decrease.

If \(\frac{Gm_1m_2}{r} \) decrease, \(U=-\frac{Gm_1m_2}{r} \) will increase due to -ve sign.

So as the distance between two objects increases, their gravitational potential energy will increase.
Hence the correct answer is option 1.

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