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Question

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

A
3GM24R2
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B
3GM22R2
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C
3GM1R2
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D
5GM24R2
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Solution

The correct option is A 3GM24R2

Force between two spheres will be

F1=F2=GMM(2R)2=GM24R2

Two forces of equal magnitude are acting at angle 60o on any of the sphere

Fnet=F21+F22+2F1F2cos60o=F3

Fnet=34GM2R2

.Hence, magnitude of force is Fnet=34GM2R2


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