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Question

If linear density of a rod of length 3 m varies as λ=1+x, then the position of the centre of mass of the rod is

A
73 m
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B
95 m
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C
72 m
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D
92 m
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Solution

The correct option is B 95 m
Linear density of the rod varies with distance
dmdx=λ[Given]dm=λdx


Position of centre of mass xCM=dm×xdm
03(λdx)×x30λdx=30(1+x)×xdx30(1+x)dx=[0.5x2+x33]30[x+x22]30
=4.5+93+92=95 m
Hence, the correct answer is option (b).

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