Question

Find the moment of inertia of a uniform rectangular plate of mass $M$ and edges of length $l$ and $b$ about its axis passing through the centre and perpendicular to it

• A. $\frac{M{l}^2}{12}$
• B. $\frac{M{b}^2}{12}$
• C. $\frac{M(l+b{)}^2}{12}$
• D. $\frac{M(l^2+b^2)}{12}$

Answer 1

The correct option is D $\frac{M(l^2+b^2)}{12}$

Let us consider rectangular plate lies in $x-y$ plane and $z-$axis is passing through its center perpendicular to it.

we know that for rectangular plate,
$I_Y=\frac{M{l}^2}{12}$ and $I_X=\frac{M{b}^2}{12}$
And from Perpendicular axis theorem ,
$I_Z=I_X+I_Y$
$\Rightarrow I_Z=\frac{M{b}^2}{12}+\frac{M{l}^2}{12}$
$\Rightarrow I_Z=\frac{M(l^2+b^2)}{12}$