Question

Radius of gyration of a thin uniform rod of length \( L \) about an axis passing through its centre and perpendicular to its length is:

• A. \( \frac{L}{\sqrt{12}} \)
• B. \( \frac{L}{12} \)
• C. \( L\sqrt{12} \)
• D. \( 12L \)

Hint:

For objects with a known moment of inertia, use: \[ k = \sqrt{\frac{I}{m}} \] to compute the radius of gyration.

Answer 1

The Correct Option is A

Step 1: Defining the Radius of Gyration The radius of gyration \( k \) is related to the moment of inertia \( I \) and mass \( m \) by: \[ I = m k^2 \] For a thin uniform rod rotating about its centre, the moment of inertia is: \[ I = \frac{1}{12} m L^2 \] Thus, \[ k = \sqrt{\frac{I}{m}} \] \[ = \sqrt{\frac{L^2}{12}} \] \[ = \frac{L}{\sqrt{12}} \] Conclusion Thus, the correct answer is: \[ \frac{L}{\sqrt{12}} \]