Moment Of Inertia Of A Rod MCQ - Practice Questions with Answers

Let I=Moment of inertia of a ROD about an axis through its center and perpendicular to it

To calculate I (Moment of inertia of rod)

Consider a uniform straight rod   of length L, mass M and having center C

 mass per unit length of the rod = $\lambda=\frac{M}{L}$

Take a small element of mass dm with length dx at a distance x from point C.

$$
\begin{aligned}
d m & =\lambda \cdot d x=\frac{M}{L} \cdot d x \\
\Rightarrow d I & =x^2 d m
\end{aligned}
$$

Now integrate this dl between the limits $x=-\frac{L}{2}$ to $\frac{L}{2}$

$$
I=\int d I=\int x^2 d m=\int_{\frac{-L}{2}}^{\frac{L}{2}} \frac{M}{L} x^2 * d x=\frac{M}{L} \int_{\frac{-L}{2}}^{\frac{L}{2}} x^2 d x=\frac{M L^2}{12}
$$