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1 What is the force acting on a mass m placed at the centroid G...

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1 What is the force acting on a mass m placed at the centroid G of the triangle What is the force on mass m if the mass at the vertex P is quadrupled Take PG QG RG 1 m Now FGP FGQ FGR 2m PA2m G The angle between GR and the positive x axis is 30 Similarly the angle between GQ and negative x axis is 30 G 2m m 1 m30 G 2m m icos 30 j sin 30 1 G 2m m i cos 30 sin 30 1 R By principle of superposition we get FR FGP FGQ FGR 2m X i e along positive y axis FR 2GM j 2Gm i cos 30 j sin 30 2Gm i cos 30 sin 30 0 ii By symmetry all the x component of the force will cancel out each other FR 8Gm j 2 Gm i sin 30 2Gm i sin 30 8Gm 4Gm sin 30 8Gm j 2Gm j

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