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Question

Find the the y coordinate of the centre of mass of the system of three rods, each of length 6 m and two rods, each of length 3 m as arranged in the figure shown below. (Assume all rods to be of uniform density)


A
938 m
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B
9316 m
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C
zero
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D
83 m
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Solution

The correct option is B 9316 m
Let the mass of each rod with length 6 m be 2m, then the mass of rods with length 3 m will be m.

Since all the triangles are equilateral, the angles will all be 60


Taking origin at O, the y coordinates of the COMs of all the rods are:
ABy1=3sin60=332 m
BCy2=0
CAy3=0
FEy4=3sin602=334 m
FDy5=3sin602=334 m

The coordinate of centre of mass of system is:
yCM=m1y1+m2y2+m2y3+m4y4+m5y5m1+m2+m3+m4+m5
=(2m×332)+(2m×0)+(2m×0)+(m×334)+(m×334)2m+2m+2m+m+m

yCM=9316 m

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