Given below are two statements: one is labeled as Assertion A and the other is labeled as Reason R.
Assertion A: Moment of inertia of 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 and respectively. The respective radii of gyration about all the three axes will be the same. , I_x I_y I_z
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.

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Both A and R are correct and R is the correct explanation of A

A is not correct but R is correct

Both A and R are correct but R is not the correct explanation of A

A is correct but R is not correct

answer is B.

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Detailed Solution

According to perpendicular axes theorem,

I_z=I_x+I_y

The moment of inertia about any axis of rotation, in general, is,

I=mK² (K→ radius of gyration)

So, m $k_{z}^{2}$ =m $k_{x}^{2}$ +m $k_{y}^{2}$

∴ $k_{z}^{2} = k_{x}^{2} + k_{y}^{2}$

From the above equation, it is clear that the radius of gyration about the x,y and z axes can't be the same. So, assertion A is not correct.

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