Question

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
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:

• A. Both $A$ and $R$ are correct but $R$ is NOT the correct explanation of $A$.
• B. $A$ is not correct but $R$ is correct.
• C. $A$ is correct but $R$ is not correct.
• D. Both A and R are correct and R is the correct explanation of A.

Answer 1

Answer: (B)

$I_{z}=I_{x}+I_{y}$ (using perpendicular axis theorem)
$\& I=m k^{2}(K$ : radius of gyration )
so $m K_{z}{ }^{2}=m K_{x}{ }^{2}+m K_{y}{ }^{2}$
$K_{z}^{2}=K_{x}^{2}+K_{y}^{2}$
So radius of gyration about axes $x, y$ \& $z$ won't be same hence asseration $A$ is not correct reason $R$ is correct statement (property of a rigid body)