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.

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Aicharya · Accepted Answer

&#8747; 0 L ( ax 2 + bx + c ) x dx &#8747; 0 L ( ax 2 + bx + c ) dx &#8747; 0 L ( ax 3 + bx 2 + cx ) dx &#8747; 0 L ( ax 2 + bx + c ) dx = ax 4 4 + bx 3 3 + cx 2 2 0 L ax 3 3 + bx 2 2 + cx 0 L = 3 aL 4 + 4 bL 3 + 6 cL 2 12 2 aL 2 + 3 bL 2 + 6 cL 6 = 3 aL 3 + 4 bL 2 + 6 cL 2 2 aL 2 + 3 bL + 6 c

Find the x coordinate of the centre of mass of the non-uniform rod of length L given below. The origin is…

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