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Question
The moment of inertia of a uniform circular disc about a tangent in its own plane is 5/4MR2 where M is the mass and R is the radius of the disc. Find its moment of inertia about an axis through its centre and perpendicular to its plane.
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Solution
- M.I. of a uniform circular disc about a tangent in its own plane, I1 = `5/4`MR2
- Applying parallel axis theorem
I1 = I2 + Mh2
∴ I2 = I1 – MR2 = `5/4`MR2 - MR2 = `("MR"^2)/4` - Applying perpendicular axis theorem,
I3 = I2 + I2 = 2I2
∴ I3 = `2 xx ("MR"^2)/4 = ("MR"^2)/2`
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