Question

A thin uniform rectangular plate of mass $2kg$ is placed in $X-Y$ plane as shown in figure. The moment of inertial about x-axis is $I_x=0.2kg{m}^2$ and the moment of inertia about y-axis is $I_y=0.3kg{m}^2$ . The radius of gyration of the plate about the axis passing through O and perpendicular to the plane of the plate is

• A. 38.7 cm
• B. 50 cm
• C. 38.8 cm
• D. 31.6 cm

Answer 1

Answer: (B)

By perpendicular axis theorem we know that,
$I_z=I_x+l_y=0.3+0.2=0.5kg{m}^2$
as we know that MOI
$I=m{K}^2\Rightarrow 0.5=2\times K^2$
$K=1/2=0.5m=50cm$