Question #17474

Three rods of the same mass are placed like a triangle.What will be the coordinate of centre of mass of the system?

Expert's answer

The geometric centroid (center of mass) of the polygon vertices of a triangle is the point which is also the intersection of the triangle's three triangle medians. The point is therefore sometimes called the median point. The centroid is always in the interior of the triangle.

The centroid of the triangle with trilinear vertices& for& pi:qi:ri, i=1,2,3 is given by

& [p1/(a*p1+b*q1+c*r1) + p2/(a*p2+b*q2+c*r2) + p3/(a*p3+b*q3+c*r3)]

: [q1/(a*p1+b*q1+c*r1) + q2/(a*p2+b*q2+c*r2) + q3/(a*p3+b*q3+c*r3)]

: [r1/(a*p1+b*q1+c*r1) + r2/(a*p2+b*q2+c*r2) + r3/(a*p3+b*q3+c*r3)].

The centroid of the triangle with trilinear vertices& for& pi:qi:ri, i=1,2,3 is given by

& [p1/(a*p1+b*q1+c*r1) + p2/(a*p2+b*q2+c*r2) + p3/(a*p3+b*q3+c*r3)]

: [q1/(a*p1+b*q1+c*r1) + q2/(a*p2+b*q2+c*r2) + q3/(a*p3+b*q3+c*r3)]

: [r1/(a*p1+b*q1+c*r1) + r2/(a*p2+b*q2+c*r2) + r3/(a*p3+b*q3+c*r3)].

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