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Three bodies of same masses are kept at the top of an equilateral triangle with side ‘a’. What speed would the three bodies be moved in a circle so that the triangle moves in the circular orbit and there should be no change in the side of the triangle?

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The gravitational force acting between each couple of masses
F = \(\frac{G M M}{a^{2}}=\frac{G M^{2}}{a^{2}}\)
Each internal angle of equilateral triangle is of 60°. Therefore the resultant of forces acting on each mass will be directed towards the centre O of the circle and the same will the role of centripetal force for circular motion of the whole triangle.

Centripetal force = Resultant force

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