Question

A rectangular lamina is shown in the figure below. Find the radius of gyration about the axis passing through its COM, perpendicular to the plane of the rectangular lamina. [in $\text{metres}$]

• A. $\frac{5}{\sqrt{3}}$
• B. $5\sqrt{3}$
• C. $\frac{5\sqrt{2}}{2}$
• D. $\frac{5\sqrt{3}}{6}$

Answer 1

The correct option is A $\frac{5}{\sqrt{3}}$

As we know,
MOI of rectangular lamina about axis passing through its COM and perpendicular to its plane is
$I=\frac{M{b}^2}{12}+\frac{M{h}^2}{12}$
Here, $b=6\text{m},h=8\text{m}$
Hence, $I=\frac{M(6{)}^2}{12}+\frac{M(8{)}^2}{12}=\frac{25M}{3}$
Radius of gyration $=K=\sqrt{\frac{I}{M}}$
$K=\sqrt{\frac{\frac{25M}{3}}{M}}$
$K=\frac{5}{\sqrt{3}}\text{m}$