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Question

How does the force of gravitation between two objects change when the distance between them is reduced to half?


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Solution

Step 1: Given Data

Let the initial distance be r.

Final distance =r2

Let the mass of the two objects be m1 and m2.

Universal gravitation constant =G

Step 2: Formula used

According to Newton's law of Gravitation F=Gm1m2r2

Step 3: Change is Gravitational Force

According to Newton's law of Gravitation,

Initial force F=Gm1m2r2

Therefore, the final force F'=Gm1m2r22

=4Gm1m2r2

=4F

Hence, when the distance between the objects is reduced to half, the gravitational force increases four times.


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