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Question

Three uniform spheres, each having mass m and radius R, are kept in such a way that each touches the other two, the magnitude of the gravitational force on any sphere due to the other two is

A
3Gm24R2
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B
3Gm24R2
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C
3Gm2R2
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D
3Gm24R2
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Solution

The correct option is D 3Gm24R2
The given system may be regarded as a system of three particles located at the three vertices of an equilateral triangle of side 2R.
Now,
FA=FB
Gm2(2R)2=Gm24R2

FAandFB are inclined to each other at an angle of 600.
If F is the resultant of FA and F, then
F=3×Gm24R2

366153_159689_ans.JPG

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