Q62 / 90 · JEE Main 2021 (25 Jul Shift 1) · Physics

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 Ix,Iy and Iz, 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.
  • Correct answer
    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.

Solution

Iz=Ix+Iy (using perpendicular axis theorem)

and I=mk2(K: radius of gyration) 

so mKz2=mKx2+mKy2

Kz2=Kx2+Ky2

So radius of gyration about axes x,y and z will not be same, hence assertion A is not correct reason R is correct statement (property of a rigid body).

Hence, the correct answer is option: 'B'.

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