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Q.

Three particles of masses 1 kg, 2 kg, and 3 kg are located the vertices of an equilateral triangle of side a. The x, y coordinates of the centre of mass are

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a

(7a12, 3a4)

b

(2a33, 5a9)

c

(5a9, 2a3)

d

(2a3,5a9)

answer is A.

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Detailed Solution

Let the masses 1 kg,  2 kg and 3 kg are located at the vertices A, B and C as shown in figure above. The coordinates of points A, B and C are (0, 0), (a, 0), (a2, 3a2) respectively.The coordinates of centre of mass areXCM = m1x1+m2x2+m3x3m1+m2+m3         = [1×0+2×a+3×a2][1+3+2] = 7a12YCM = m1+y1+m2y2+m3y3m1+m2+m3      = [1×0+2×0+3×3a2][1+3+2] = 3a4
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