Question

$K$ is radius of gyration of a thin square plate about an axis perpendicular to the plane of plate and passing through its centre. The radius of gyration of plate about a parallel axis to the first and passing through a corner of plate is :

• A. $\sqrt{2}K$
• B. $\sqrt{3}K$
• C. $2K$
• D. $3K$

Answer 1

Answer: (C)

$2K$

MI about an axis perpendicular to the plane of plate and passing through its center is $I_{cm}=\frac{M{l}^2}{6}$ ,

Also $M{K}^2=M{l}^2/6\Rightarrow K^2=l^2/6$...(1)

Distance of corner from the center of plate $d=\frac{l}{\sqrt{2}}$

Using parallel axis theorem $I_1=I_{cm}+M{d}^2=\frac{2M{l}^2}{3}$

Also $M{K}_1^2=\frac{2M{l}^2}{3}\Rightarrow K_1^2=2l^2/3$...(2)

From equation 1 and 2 we get $K_1=2K$