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NEETPhysicsRotational Motion

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The radius of gyration of a rigid body of a given shape and size is independent of its total mass, but depends on the position of the axis of rotation. Reason (R): The radius of gyration is defined as the arithmetic mean of the perpendicular distances of all the constituent particles of the body fr

Options

  1. ABoth Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  2. BBoth Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
  3. CAssertion (A) is true but Reason (R) is false.
  4. DAssertion (A) is false but Reason (R) is true.

Correct answer

C. Assertion (A) is true but Reason (R) is false.

Step-by-step solution

The moment of inertia of a rigid body is given by I = MK^2 , where M is the total mass and K is the radius of gyration. For a given shape, size, and axis of rotation, I is directly proportional to M . Therefore, K = I M depends only on the mass distribution (geometry) and the position of the axis of rotation, and is independent of the total mass. Thus, Assertion (A) is true. By definition, the radius of gyration is the root mean square (RMS) distance of the constituent particles from the axis of rotation, not the s

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