First slide

Moment of intertia

Question

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

Moderate

A

$\frac{7 {ML}^{2}}{48}$
B

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

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

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

Solution

See fig
The distance OC $= \frac{L}{2} - \frac{L}{3} = \frac{L}{6}$
Applying the theorem of parallel axis
$\begin{array}{l} I_{C} = I_{O} + M (OC)^{2} \\ = \frac{{ML}^{2}}{12} + M {(\frac{L}{6})}^{2} = \frac{{ML}^{2}}{9} \end{array}$

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