Three mass points each of mass m are placed at the vertices of an equilateral triangle of side l. What is the gravitational field and potential due to three masses at the centroid of the triangle?

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Solution

Zero.
Vector addition of 3 independent forces states that, because of 3 independent point forces, the resultant will be zero or resultant force acting at the centroid will be zero.

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Three mass points each of mass m are placed at the vertices of an equilateral triangle of side l. What is the gravitational field and potential due to three masses at the centroid of the triangle?

Zero.Vector addition of 3 independent forces states that, because of 3 independent point forces, the resultant will be zero or resultant force acting at the centroid will be zero.

Zero.
Vector addition of 3 independent forces states that, because of 3 independent point forces, the resultant will be zero or resultant force acting at the centroid will be zero.