Assertion A : moment of inertia of a circular disc of mass M and radius R about X, Y –axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be $I_x,I_{y}and{I}_z$ respectively. The respective radii of gyration about all the three axes will be the same. 

Reason (R) : A rigid body making rotational motion has fixed mass and shape. 

In the light of the above statements, choose the most appropriate answer from the options given below.

Given, $l_x,l_{y}and{l}_z$ be the moment of inertial of disc about $X_{,}YandZ-$ axes. By using perpendicular axis theorem,   $I_z=I_x+I_y$
Where, $I_z$ is the moment of inertia about its centre of mass  $=\frac{M{R}^2}{2}$
And in symmetrical body,  $I_x=I_y$ (Disc in given case)
$$\begin{gathered} \therefore I_z=2I_x \\ \Rightarrow I_x=I_y=\frac{I_z}{2}=\frac{M{R}^2}{4} \end{gathered}$$

 Now,  $I_x=I_y\ne I_z$
As, radius of gyration,  $k=\sqrt{I/M}$
So, radii of gyration about all axis will not be the same.
$\therefore$  Assertion is not correct but Reason is correct because in a rigid body making rotational motion has fixed body making rotational motion has fixed mass M and radius  $R(I_x=I_y)$