The density of a non-uniform rod of length 1m is given by

ρ(x) = a(1+ bx2)

where a and b are constants and 0 ≤ x ≤1.

The centre of mass of the rod will be at

1
\(\frac{3(2+b)}{4(3+b)}\)
2
\(\frac{4(2+b)}{3(3+b)}\)
3
\(\frac{3(3+b)}{4(2+b)}\)
4
\(\frac{4(3+b)}{3(2+b)}\)

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