Question

If a thin uniform circular ring and a thin uniform circular disc have the same mass and radius, then the ratio of their moments of inertia about their central axes normal to their planes is}

• A. \(3 : 2\)
• B. \(2 : 3\)
• C. \(1 : 4\)
• D. \(1 : 2\)
• E. \(2 : 1\)

Hint:

Standard formulas: \[ I_{\text{ring}}=MR^2,\qquad I_{\text{disc}}=\frac12 MR^2 \] These are very important rotational motion results.

Answer 1

Answer: (E)

Moment of inertia of a thin circular ring about its central axis is: \[ I_{\text{ring}}=MR^2 \] Moment of inertia of a thin circular disc about its central axis is: \[ I_{\text{disc}}=\frac{1}{2}MR^2 \] So the ratio is: \[ I_{\text{ring}} : I_{\text{disc}} = MR^2 : \frac12 MR^2 \] \[ = 1 : \frac12 = 2:1 \]
Hence, the correct answer is: \[ \boxed{(E)\ 2:1} \]