Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

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:

$I_A = I_C$ and $I_B = I_D$

$I_A = 2I_B$ and $2I_C = I_D$

$2I_A = I_C$ and $I_B = 2I_D$

$I_A = I_B = I_C = 2I_D$

Step-by-Step Solution

The moment of inertia of various uniform bodies about their central geometric axes are given by:

Thin circular ring (A): $I_A = MR^2$
Circular disc (B): $I_B = \frac{1}{2}MR^2$
Hollow cylinder (C): $I_C = MR^2$
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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