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Show that the centre of gravity of three...

Show that the centre of gravity of three equal weights suspended from three vertices of a triangle coincide with the centre of mass of the triangle.

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Let a median of the triangle ABC be AD Fig. Identical weights W are hung from each of the vertices A,B and C. Resultant of the weights suspended from B and C = 2W and it acts from the point D. Resultant of the forces 2W at D and W at A is 3W. Suppose this resultant acts at G. Hence `WxxAG=2WxxDG`
or, AG=2DG
Thus, G is the point of intersection of the medians of the triangle, which is the centre of mass.
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