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
FAandFBare inclined to each other at an angle of600. If F is the resultant ofFAandF,then F=√3×Gm24R2