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Q.

The moment of inertia of a thin uniform rod of length L, and mass M about an axis passing through a point at a distance L/3 from one of its ends and perpendicular to the rod is

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a

$\frac{{ML}^{2}}{9}$

b

$\frac{{ML}^{2}}{3}$

c

$\frac{{ML}^{2}}{6}$

d

$\frac{{ML}^{2}}{12}$

answer is C.

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Detailed Solution

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Distance of the axis from the center of mass is L/6 (L/2-L/3)

Using theorem of parallel axes,

$l = \frac{{ML}^{2}}{12} + M {(\frac{L}{6})}^{2} I = \frac{{ML}^{2}}{12} + \frac{{ML}^{2}}{36} = \frac{4 {ML}^{2}}{36} = \frac{{ML}^{2}}{9}$

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The moment of inertia of a thin uniform rod of length L, and mass M about an axis passing through a point at a distance L/3 from one of its ends and perpendicular to the rod is