Given below are two statements: one is labelled as Assertion A and… | JEE Main 2021 (25 Jul, Shift 1)

Q124JEE Main 2021 · 25 JUL · SHIFT 1Easy

Moment of Inertia & Radius of Gyration

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:

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Answer: (b)

Disc: $I_x = I_y = \frac{MR^2}{4}$ , $I_z = \frac{MR^2}{2}$ .
So $k_x = k_y = \frac{R}{2}$ but $k_z = \frac{R}{\sqrt{2}}$ : radii of gyration are not all equal, A is false.
R is true: a rigid body keeps its mass and shape while rotating.
So the answer is (b).

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Moment of Inertia & Radius of Gyration question from JEE Main 2021 (25 Jul, Shift 1)

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