Three point masses, 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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Answer:
Let the distance of the centroid from each vertex is r and it can be written as,
r=
3
l
The gravitational potential at centroid due to mass m at A is given as,
V
A
=
r
−Gm
=
l
−
3
Gm
The gravitational potentials at B and C are given as,
V
B
=
l
−
3
Gm
V
C
=
l
−
3
Gm
The total potential due to all the three masses is given as,
V=V
A
+V
B
+V
C
V=
l
−
3
Gm
−
l
3
Gm
−
l
3
Gm
V=
l
−3
3
Gm
Thus, the gravitational potential at the centroid of the triangle is
l
−3
3
Gm
.
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