Find the the y− coordinate of the centre of mass of the system of three rods, each of length 6m and two rods, each of length 3m as arranged in the figure shown below. (Assume all rods to be of uniform density)
A
9√38m
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B
9√316m
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C
zero
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D
8√3m
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Solution
The correct option is B9√316m Let the mass of each rod with length 6m be 2m, then the mass of rods with length 3m will be m.
Since all the triangles are equilateral, the angles will all be 60∘
Taking origin at O, the y coordinates of the COM′s of all the rods are: AB→y1=3sin60∘=3√32m BC→y2=0 CA→y3=0 FE→y4=3sin60∘2=3√34m FD→y5=3sin60∘2=3√34m
The coordinate of centre of mass of system is: yCM=m1y1+m2y2+m2y3+m4y4+m5y5m1+m2+m3+m4+m5 =(2m×3√32)+(2m×0)+(2m×0)+(m×3√34)+(m×3√34)2m+2m+2m+m+m