Question
Three point masses each of mass m are placed at the vertices of an equilateral triangle of side 1. What is the gravitational field due to three masses at the centriod of triangle?
Solution
Let three masses each of mass m be placed at the vertices of an equilateral triangle ABC of side 1 unit.
Let O be the centroid of the triangle.
The distance of the centroid from each vertex is,
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The gravitational field at O due to mass m at A is,
Similarly,
and
Here, the three coplanar vectors
and 
are equal in magnitude and make an angle of 
with the preceding vector.
Therefore, the resultant field is zero.
Let O be the centroid of the triangle.
The distance of the centroid from each vertex is,
The gravitational field at O due to mass m at A is,
Similarly,
and
Here, the three coplanar vectors
and are equal in magnitude and make an angle of with the preceding vector.Therefore, the resultant field is zero.
