Question

A rectangular lamina of mass $6\text{kg}$ is placed in such a way that the centre of rectangular lamina coincides with the origin($\text{O}$) as shown in figure. If $I_x$ and $I_y$ are the moment of inertia of rectangular lamina about x - axis and y - axis respectively, then find the ratio $\frac{I_x}{I_y}$.

• A. $1$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $\frac{3}{4}$

Answer 1

The correct option is C $\frac{1}{4}$


Mass of lamina, $m=6\text{kg}$
length of rectangular lamina $a=4\text{m}$
Width of rectangular lamina $b=2\text{m}$.
$\text{MOI}$ of rectangular lamina about x - axis:
$I_x=\frac{m{b}^2}{12}$
$I_x=\frac{6\times (2{)}^2}{12}={\text{2 kg-m}}^2$

Simillarly, $\text{MOI}$ of rectangular lamina about y - axis:
$I_y=\frac{m{a}^2}{12}$
$I_y=\frac{6\times 4^2}{12}={\text{8 kg-m}}^2$
So, the ratio of $I_x$ & $I_y$,
$\frac{I_x}{I_y}=\frac{2}{8}=\frac{1}{4}$