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 of the spheres due to the other two.

Answer 1

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ANSWER::

Force in CB = ( Gm² cos60° î ) / 4a² - ( Gm² sin60° j  ) / 4a²

Force in CA = ( Gm² cos60° î ) / (-4a² ) - ( Gm² sin60° j  ) / 4a²

Total Force = Force in CB + Force in CA

Total Force = (-2Gm² sin60° j ) / 4a² = (-2Gm²√3 j )/2x4a² = √3Gm²/ 4a²

Hope it helps!