Consider a thin circular ring (A), a circular disc (B), a hollow cylinder (C) and a solid cylinder (D) of the

Question

Consider a thin circular ring (A), a circular disc (B), a hollow cylinder (C) and a solid cylinder (D) of the same radii $R$ and of the same masses. If $I_A$, $I_B$, $I_C$ and $I_D$ are their moments of inertia about the axis shown, then choose the correct answer from the options given below:

Accepted Answer

The moment of inertia of various uniform bodies about their central geometric axes are given by:
1. Thin circular ring (A): $I_A = MR^2$
2. Circular disc (B): $I_B = \frac{1}{2}MR^2$
3. Hollow cylinder (C): $I_C = MR^2$
4. Solid cylinder (D): $I_D = \frac{1}{2}MR^2$

Comparing the above values, we can clearly see that:
$I_A = I_C$ (both are equal to $MR^2$) 
$I_B = I_D$ (both are equal to $\frac{1}{2}MR^2$).
Therefore, the correct relation is $I_A = I_C$ and $I_B = I_D$.

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