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Question

Three uniform spheres each having a mass M and radius a are kept in such a way that each touches the other two. Find the magnitude of the gravitational force on any one of the spheres due to the other two.

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Solution


The System can be considered at three particles located at the vertices of equilateral triangle having side 2a.
Gravitational Force between two sphere is given as
F1=GMM4a2
similarly

F2=GMM4a2
As mass and radius of all sphere is same.
So on one sphere two forces of equal magnitude are acting at angle of 60 degrees.
F=f12+f22+2f1f2cos60
F=3GMM4a2


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