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  4. Three masses each of mass m are placed at the vertices of an equilateral triangle ABC of side l as shown in figure. The force acting on a mass 2m placed at the centroid O of the triangle is

Q. Three masses each of mass are placed at the vertices of an equilateral triangle of side as shown in figure. The force acting on a mass placed at the centroid of the triangle is

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Solution:


Draw a perpendicular to the side .

Distance of the centroid from is .

By symmetry,
Force on mass at due to mass at is
along .
Force on mass at due to mass at is
along
Force on mass at due to mass at is
along
Draw a line parallel to passing through . Then

Resolving and into two components.
Components acting along and are equal in magnitude and opposite in direction. So, they will cancel out while the components acting along will add up.
The resultant force on the mass at is

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