Question

Two particles are placed at some distance. If the mass of each of the two particles is doubled and keeping the distance between them unchanged, the value of gravitational force between them will be

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Solution

The correct option is **D** 4 times

Force between two particles of mass m1 and m2 is given as,

F=Gm1m2r2→(1)

where G- universal gravitational constant

r- distance between two mass m1 and m2

let F′ be the new force between two masses i.e 2m1 and 2m2 and also distance is fixed

F′=G2m12m2r2→(2)

On dividing the equation 1 with equation 2 we get,

FF′=Gm1m2r2∗r2G2m12m2

⇒FF′=14

⇒F′=4F

so option d is correct.

Force between two particles of mass m1 and m2 is given as,

F=Gm1m2r2→(1)

where G- universal gravitational constant

r- distance between two mass m1 and m2

let F′ be the new force between two masses i.e 2m1 and 2m2 and also distance is fixed

F′=G2m12m2r2→(2)

On dividing the equation 1 with equation 2 we get,

FF′=Gm1m2r2∗r2G2m12m2

⇒FF′=14

⇒F′=4F

so option d is correct.

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