Question

A rectangular lamina of mass $6\text{kg}$, breadth $4\text{m}$ and length $6\text{m}$ is taken as shown in figure. If $I_x$ and $I_y$ are the moments of inertia of the rectangular lamina about $x-$ axis and $y-$ axis respectively, then the value $I_y+I_x$ is

• A. $26{\text{kg-m}}^2$
• B. $10{\text{kg-m}}^2$
• C. $8{\text{kg-m}}^2$
• D. $18{\text{kg-m}}^2$

Answer 1

The correct option is A $26{\text{kg-m}}^2$

Given, mass of rectangular lamina $\left(M\right)=6\text{kg}$
Length of rectangular lamina $\left(l\right)=6\text{m}$
Breadth of rectangular lamina $\left(b\right)=4\text{m}$
Moment of inertia about $x-$ axis $\left(I_x\right)=\frac{m{b}^2}{12}=\frac{6(4{)}^2}{12}=8{\text{kg-m}}^2$
Moment of inertia about $y-$ axis $\left(I_y\right)=\frac{m{l}^2}{12}=\frac{6(6{)}^2}{12}=18{\text{kg-m}}^2$
Then,
$I_y+I_x=26{\text{kg-m}}^2$