A nonuniform rod lies along the x-axis with its left end at x = y = 0 . It has a total mass M , length L and a mass distribution of dM / dx = B (L^{2} − x^{2}), where B is a constant to be found in your analysis. What is the rotational inertia of the rod about the y-axis, pivoting about a vertical axis through its left end?

1. 1/2 ML^{2}

2. ML^{2}

3. 1/4 ML^{2}

4. 2/3 ML^{2}

5. 3/5 ML^{2}

6. 1/7 ML^{2}

7. 1/3 ML^{2}

8. 1/6 ML^{2}

9. 1/5 ML^{2}

10. 3/4 ML^{2}

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