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Question

Two identical copper spheres with uniform density each of radius R are in contact with each other. If the gravitational attraction between them is F, then

A
FR2
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B
FR4
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C
F1R2
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D
F1R4
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Solution

The correct option is B FR4
According to the Universal law of Gravitation, the gravitational force between two bodies is directly proportional to the mass of the two bodies and inversely proportional to the square of the distance between them.
The two identical spheres with uniform density behave as point masses with all the mass concentrated at the centre.

Mass=density × volume

Let M be the mass and ρ be the density of each sphere.
Volume of each sphere =43πR3,
where R is the radius of the sphere.

So, the mass of each sphere is 43πR3ρ

The distance between their centres is 2R.

So, the force of attraction between them is F=GM2(2R)2,
where G is the universal gravitational constant.

F=G(43πR3ρ)(43πR3ρ)1(2R)2

FR6R2

FR4


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