Question

A uniform rectangular lamina is shown in figure. Find the moment of inertia $I_{\text{com}}$ about $z$ axis which passes through its centre and perpendicular to its plane. Here $b=10\text{m}$, $l=20\text{m}\&M=12\text{kg}$.

• A. $100{\text{kg-m}}^2$
• B. $1200{\text{kg-m}}^2$
• C. $400{\text{kg-m}}^2$
• D. $500{\text{kg-m}}^2$

Answer 1

The correct option is D $500{\text{kg-m}}^2$

For a rectangular lamina, the moment of inertia about an axis passing through its $\text{COM}\&$ $\perp$ to the plane of lamina is given by:
$I_{\text{com}}=\frac{M{l}^2}{12}+\frac{M{b}^2}{12}$
Putting the given values,
$I_{\text{com}}=\frac{12\times {20}^2}{12}+\frac{12\times {10}^2}{12}$
$\therefore I_{\text{com}}=500{\text{kg-m}}^2$