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Rotational Motion

JEE Main level, single correct, medium

56 of 280

Question 56 of 280

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:

Show answer and solution

Answer: (B) A is not correct but R is correct.

{I}_{z}={I}_{x}+{I}_{y}

(using perpendicular axis theorem)
and

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

and

z

will not be same, hence assertion A is not correct reason R is correct statement (property of a rigid body).

JEE Main question paper PDF

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JEE Main 2025 Apr 2 Shift 1 question paper

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