Question

Find the radius of gyration for a rectangular lamina having mass $m$ about an axis passing through C.O.M and perpendicular to the plane of lamina. (Given: $\text{length,}a=4\text{m};\text{breadth,}b=3\text{m})$

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

Answer 1

The correct option is D $\frac{5\sqrt{3}}{6}$


Using perpendicular axis theorem
$I_z=I_{com}=I_x+I_y=\frac{m{a}^2}{12}+\frac{m{b}^2}{12}=\frac{m(a^2+b^2)}{12}$

As we know,
Radius of gyration $K=\sqrt{\frac{I}{m}}$
$K=\sqrt{\frac{\frac{m(a^2+b^2)}{12}}{m}}$
$K=\sqrt{\frac{16+9}{12}}=\frac{5\sqrt{3}}{6}$