The linear mass density of a rod of length 5m varies with distance from its end fixed at the origin as represented in the graph shown below:
Then find the position of centre of mass of the rod w.r.t origin.
A
2516m
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B
59m
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C
259m
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D
516m
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Solution
The correct option is C259m From the graph of linear mass density of rod, writing it in y=mx+c format:
λ=(5+x)kg/m
Let us consider a small element of length dx and mass dm, which is at a distance x from the origin.
Let xCM be the position of COM of rod, so by applying basic formula and integrating with proper limits: xCM=∫xdm∫dm...(i)
λ=dmdx=5+x ⇒dm=(5+x)dx....(ii)
Substituting dm in Eq (i) and setting the values of limits as x=0 to x=5: