How does the force of gravity between two objects change when the distance between them is 3 times larger?

Option 3 : One ninth of previous force

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The correct answer is option 3) i.e. One-ninth of the previous force

CONCEPT:

Newton's universal law of gravitation: Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them i.e.

\(F = \frac{Gm_{1}m_{2}}{r^{2}}\)

Where, F = Force of gravitation between the objects m1 = Mass of one of the objects m2 = Mass of the second object, r = Distance between the centres of the two objects, G = Universal gravitational constant

EXPLANATION:

The gravitational force between two objects is inversely proportional to the square of the distance between them.
If the distance is increased, the force reduces.

CALCULATION:

Let, the mass of the two bodies be m1 and m2 respectively and the distance between their centers be r.

Then, the gravitational force between them is given by:

\(F = \frac{Gm_{1}m_{2}}{r^{2}}\)

Now, when the distance between them is made three times, the gravitational force will be:

\(F^{'} = \frac{Gm_{1}m_{2}}{(3r)^{2}}\)

⇒\(F^{'} = \frac{Gm_{1}m_{2}}{9r^{2}}\)

⇒\(F^{'} = \frac{F}{9}\)

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