Question

The radius of gyration of a circular disc of radius \( R \), rotating about its diameter is:

• A. \( R \)
• B. \( \frac{R}{2} \)
• C. \( \frac{R}{4} \)
• D. \( \frac{R}{\sqrt{12}} \)
• E. \( \frac{R}{3} \)

Hint:

The radius of gyration represents an equivalent distance from the axis where the total mass of the body could be concentrated to produce the same moment of inertia.

Answer 1

The Correct Option is B

The radius of gyration \( k \) is related to the moment of inertia and mass distribution of the object about the given axis of rotation. 
The formula for the radius of gyration of a circular disc rotating about its diameter is: \[ k = \frac{R}{2} \] This result is obtained by considering how mass is spread relative to the axis of rotation.