Question
Three point masses each of mass m are placed at the vertices of an equilateral triangle of side l. What is the gravitational potential due to three masses at the centriod of the triangle?
Solution
Let three masses each of mass m be placed at the vertices of an equilateral triangle ABC of side l.
Let O be the centroid of the triangle.
The distance of centroid from each vertex is,
r = AO = BO = CO =
The gravitational potential at O due to mass m at A is,
Similarly,
and
Therefore total potential due to all the three masses is,
Let O be the centroid of the triangle.
The distance of centroid from each vertex is,
r = AO = BO = CO =
The gravitational potential at O due to mass m at A is,
Similarly,
and
Therefore total potential due to all the three masses is,
