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A uniform disc (of mass M and radius a) ...

A uniform disc (of mass `M` and radius `a`) has a hole (of radius `b`) drilled through it. The centre of the hole is at a distance `c` from the centre of the original disc. What is the moment of inertia of the disc about an axis through the centre of the disc and perpendicular to its plane ?

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To find the moment of inertia of a uniform disc with a hole drilled through it, we can follow these steps: ### Step 1: Understand the Problem We have a uniform disc of mass \( M \) and radius \( a \) with a hole of radius \( b \) drilled through it. The center of the hole is at a distance \( c \) from the center of the original disc. We need to find the moment of inertia of the remaining part of the disc about an axis through its center and perpendicular to its plane. ### Step 2: Determine the Mass of the Original Disc The mass \( M \) of the original disc can be expressed in terms of its density \( \sigma \) and area: \[ ...
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