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The linear density of a thin rod of length 1 m varies as λ = 1 + 2x , where x is the distance from its one end. Distance of centre of mass of rod from this end is :

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a
5/12 m
b
3/4 m
c
7/12 m
d
2/3 m

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detailed solution

Correct option is C

dm=λdx=(1+2x)dxxcm=∫01 (dm)x∫01 dm=∫01 x(1+2x)dx∫01 (1+2x)dx=712m

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