Question

$I$ is moment of inertia of a thin rod about an axis perpendicular to the length of rod and passing through one end of rod. If half length of this rod from free end is cut and removed, then moment of inertia of remaining rod about same axis is :

• A. $\frac{I}{2}$
• B. $\frac{I}{4}$
• C. $\frac{I}{8}$
• D. $\frac{I}{16}$

Answer 1

The correct option is C $\frac{I}{8}$

Moment of inertia about the end point $\Rightarrow \frac{M{l}^2}{3}=I$
But now length $L$ is halved so mass will be reduced to $\frac{M}{2}$
So, new $I$ $\Rightarrow \left(\frac{M}{2}\right)\frac{{\left(\frac{L}{2}\right)}^2}{3}=\frac{1}{8}\left(\frac{M{L}^2}{3}\right)$$=\frac{I}{8}$