Moment Of Inertia Of A Rod - Practice Questions & MCQ

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

To calculate I (Moment of inertia of rod)

Consider a uniform straight rod   of length L, mass M and having centre 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 the 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

$
\begin{aligned}
& \text { Now integrate this dl between the limits } x=-\frac{L}{2} \text { 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}
\end{aligned}
$