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  4. A thin uniform rectangular plate of mass 2 kg is placed in X-Y plane as shown in figure. The moment of inertial about x-axis is Ix = 0.2 kg m2 and the moment of inertia about y-axis is Iy = 0.3 kg m2 . The radius of gyration of the plate about the axis passing through O and perpendicular to the plane of the plate is

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

KCETKCET 2020System of Particles and Rotational Motion

Solution:

By perpendicular axis theorem we know that,
$I _{ z }= I _{ x }+ l _{ y }=0.3+0.2=0.5 \,kgm ^{2}$
as we know that MOI
$I = mK ^{2} \Rightarrow 0.5=2 \times K ^{2}$
$K =1 / 2=0.5 m =50 \,cm$