1. Three particles of masses 1 kg, kg, and 2 kg are
located at the vertices of an equilateral triangle of
side a. The x, y coordinates of the centre of mass are
2a 5a
(a)
5a 2a
9'33
(b)
3139
5a 2a
(c)
(d)
973
2a 5a
9
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Answer:
a) Let the masses 1kg,32kgand2kg are located at the vertices A,BandC as shown in figure above. The coordinates or points A,BandC are (0,0),(a,0),(a2,3–√aa) respectively.
The coordinates of centre of mass are
XCm=m1x1+m2y2+m3x3m1+m2+m3
=[1×0+32×a+2×a2][a+32+2]=5a2
YCM=m1+y1+m2y2+m3y3m1+m2+m3
=[1×0+32×0+2×3√a2][a+32+2]=23–√a9=2a33–√.
Explanation:
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