Question

A squre plate of side length $\frac{a}{2}$ is removed from a uniform square plate of mass $M$ and side length $a$ as shown. Moment of inerti of remaining plate about an aixs which is passing thorugh centre $O$ and perpendicular to plane of this plate, will be

Diagram

• A. $\frac{M{a}^2}{12}$
• B. $\frac{M{a}^2}{9}$
• C. $\frac{M{a}^2}{8}$
• D. $\frac{M{a}^2}{6}$

Answer 1

The correct option is A $\frac{M{a}^2}{12}$

$l_0=l_{Total}-l_{removed}$
$=\left(\frac{M{a}^2}{6}\right)-\{\frac{M}{4}\frac{(a/2{)}^2}{6}+\left(\frac{M}{4}\right){\left(\frac{a}{2\sqrt{2}}\right)}^2\}$
$l_0=\frac{M{a}^2}{8}$