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 respectively 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 :
Solution
I<sub>z</sub> = I<sub>x</sub> + I<sub>y</sub> (using perpendicular axis theorem) & I = mk<sup>2</sup> (K : radius of gyration)<br><br>so, mK<sub>z</sub><sup>2</sup> = mK<sub>x</sub><sup>2</sup> + mK<sub>y</sub><sup>2</sup><br><br>K<sub>z</sub><sup>2</sup> = K<sub>x</sub><sup>2</sup> + K<sub>y</sub><sup>2</sup><br><br>so radius of gyration about axes x, y & z won't be same hence assertion A is not correct reason R is correct statement (property of a rigid body)
About this question
Subject: Physics · Chapter: Rotational Motion · Topic: Centre of Mass
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