Physics - Rotation Question with Solution | TestHub

The total length of the rod is L. Since, the rod is bent at the middle, so each part of it will have same length$\frac{L}{2}$and mass$\frac{M}{2}$



Moment of inertia of each part about an axis passing through its one end

$=\frac{1}{3}\left(\frac{M}{2}\right){\left(\frac{L}{2}\right)}^2$

Hence, net moment of inertia about an axis passing through its middle point$$is

$I=\frac{1}{3}\left[\frac{M}{2}\right]{\left[\frac{L}{2}\right]}^2+\frac{1}{3}\left[\frac{M}{2}\right]{\left[\frac{L}{2}\right]}^2$

$=\frac{1}{3}\left[\frac{M{L}^2}{8}+\frac{M{L}^2}{8}\right]=\frac{M{L}^2}{12}$