Question

Radius of gyration \( K \) of a hollow cylinder of mass \( M \) and radius \( R \) about its long axis of symmetry is:

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

Hint:

For a hollow cylinder, the radius of gyration about its axis of symmetry is simply equal to the radius of the cylinder.

Answer 1

The Correct Option is C

Step 1: The formula for the radius of gyration \( K \) of a hollow cylinder about its central axis (the long axis of symmetry) is given by: \[ K = \sqrt{\frac{I}{M}} \] where \( I \) is the moment of inertia and \( M \) is the mass of the hollow cylinder. 
Step 2: The moment of inertia \( I \) of a hollow cylinder about its central axis is: \[ I = M R^2 \] where \( R \) is the radius of the hollow cylinder. 
Step 3: Substitute the expression for \( I \) into the formula for \( K \): \[ K = \sqrt{\frac{M R^2}{M}} = \sqrt{R^2} = R \] Thus, the radius of gyration \( K \) is equal to the radius \( R \) of the hollow cylinder.