Two identical uniform rods EF and GH, each of length L=6m are joined as shown in figure. Locate the centre of mass of the frame.
[Point O, which is the point where the axes of the rods meet is the origin]
A
(0m,0m)
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B
(0m,1m)
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C
(0m,1.5m)
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D
(0m,2m)
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Solution
The correct option is C(0m,1.5m) Let the masses of both rod EF and GH be Mkg
Let the origin be at the point O. Then COM of rod GH, (x1y1)=(0,0) COM of rod EF, (x2y2)=(0,3)
Therefore, X-coordinate of centre of mass of frame xcom=m1x1+m2x2m1+m2 [∵m1=m2=M] xcom=M(0)+M(0)M+M=0m Y-coordinate of centre of mass of frame ycom=m1y1+m2y2m1+m2 ycom=M(0)+M(3)M+M=3M2M=1.5 m
COM of the frame (xcom,ycom)=(0m,1.5m)