A uniform solid cylinder with radius R and length L has moment of inertia $I_1$ about the axis of the cylinder. A concentric solid cylinder of radius $R/2$ and length $L/2$ is carved out of the original cylinder. If $I_2$ is the moment of inertia of the carved out portion of the cylinder then $I_1/I_2$ is (Both $I_1$ and $I_2$ are about the axis of the cylinder)

Question

A thin circular disc of mass $ M $ and radius $ R $ is rotating in a horizontal plane about an axis passing through its center and perpendicular to its plane with angular velocity $ \omega $. If another disc of the same dimensions but of mass $ M/2 $ is placed gently on the first disc co-axially, then the new angular velocity of the system is:

Answer 1

Step 1: Scaling argument
For similar solids, $I\propto m r^2$. Here mass falls by $8$ and $r^2$ falls by $4$.

Step 2: Result
$I_2 = I_1/(8\times4) = I_1/32$, so $I_1:I_2 = 32:1$. Option (D).

Final Answer:
32:1. \[ \boxed{\text{(D)}\ 32:1} \]

Show Hint

The Correct Option is D

Solution and Explanation

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