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Question

Three identical spheres of mass M each are placed at the corners of an equilateral triangle of side 2m. Taking one of the corner as the origin, the position vector of the centre of mass is:

A
3(^i^j)
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B
^i3+^j
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C
^i+^j3
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D
^i+^j3
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Solution

The correct option is D ^i+^j3
Position vector of center of mass will be position vector of the centroid,
which is on the angle bisector of the angle between any two adjacent sides and at a distance of 23×(side×32)
from that vertex.
Taking the vertex at the origin and one side along the xaxis
we get the unit vector as ^iCos(600/2)+^jSin300=12(3^i+^j) angle of an equilateral triangle is 600
multiplying it by the distance 23, we get the vector as ^i+13^j

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