Three masses each of mass m are placed at the vertices of an equilateral triangle ABC of side as shown in figure. The force acting on a mass 2m placed at the centroid O of the triangle is
Text Solution
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Draw a perpendicular AD to the side BC.
Distance AO of the centroid O from A is 
By Symmetry, AO = BO = CO 
Force on mass 2m at O due to mass m at A is
Force on mass 2m at O due to mass m at B is
Force on mass 2m at O due to mass m at C is
Draw a line PQ parallel to BC passing through O. Then 
Resolving 
and 
into two components.
Resolving acting along OP and OQ are equal in magnitude and opposite in directions. So, they will cancel
out while the components acting along OD will add up.
The resultant force on the mass 2m at O is
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