Find the x coordinate of the centre of mass of the non-uniform rod of length L given below. The origin is taken at the left end of the rod. The density of the rod as a function of its x-coordinate is ρ=ax2+bx+c, where a, b and c are constants.

Question

Find the $x$ coordinate of the centre of mass of the non-uniform rod of length $L$ given below. The origin is taken at the left end of the rod. The density of the rod as a function of its $x$ -coordinate is $ρ = {ax}^{2} + bx + c$ , where $a$ , $b$ and $c$ are constants.

\frac{(2 {aL}^{2} + 3 {bL}^{2} + 6 cL)}{2 (3 {aL}^{2} + 4 bL + 8 c)}

\frac{(4 {aL}^{3} + 3 {bL}^{2} + 2 cL)}{2 (3 {aL}^{2} + 2 bL + c)}

\frac{(3 {aL}^{2} + 4 {bL}^{2} + 6 cL)}{(4 {aL}^{2} + 6 bL + 8 c)}

\frac{(3 {aL}^{3} + 4 {bL}^{2} + 6 cL)}{2 (2 {aL}^{2} + 3 bL + 6 c)}

Solution

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