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Atoms And Molecules

Question
CBSEENSC9006061

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

Solution

According to the law of gravitation, the force of attraction between two bodies is, 
                 space straight F space equals space straight G fraction numerator straight m subscript 1 straight m subscript 2 over denominator straight r squared end fraction
When the distance is reduced to half,
                  straight r apostrophe space equals space straight r over 2 comma space so
straight F apostrophe space equals space straight G fraction numerator straight m subscript 1 straight m subscript 2 over denominator straight r apostrophe squared end fraction space equals space straight G fraction numerator straight m subscript 1 straight m subscript 2 over denominator left parenthesis straight r divided by 2 right parenthesis squared end fraction space equals space 4 straight G fraction numerator straight m subscript 1 straight m subscript 2 over denominator straight r squared end fraction space equals space 4 straight F 
Thus, graviational force becomes four times the original force.