Question

# Three identical metal balls each of radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed. When the centre of the three balls are joined, centre of mass of the system is located at

A
horizontal surface.
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B
centre of one of the balls.
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C
line joining centre of any two balls.
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D
point of intersection of the medians of the triangle
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Solution

## The correct option is D point of intersection of the medians of the triangle Balls are identical & of same radius, so, volume and density of the balls are the same. ∵ Mass = density × volume Masses of the balls will be the same i.e m1=m2=m3=m xcm=mx1+mx2+mx3m+m+m=(x1+x2+x33) ycm=my1+my2+my3m+m+m=(y1+y2+y33) Hence (xcm,ycm) is the centroid of the equilateral triangle. i.e the point of intersection of the medians of the equilateral triangle.

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