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Question

Two identical uniform rods EF and GH, each of length L=6 cm 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
(0 m,0 m)
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B
(0 m,1 m)
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C
(0 m,1.5 m)
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D
(0 m,2 m)
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Solution

The correct option is B (0 m,1.5 m)
Let the masses of both rod EF and GH be M kg


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=0 m
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)=(0 m,1.5 m)

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