Question

The moment of inertia of uniform semi-cicular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is [AIEEE 2005]​

Answer 1

• Explanation:- The moment of inertia of disc about the given axis is I = 2Mr²/2 = Mr²

• Let the moment of inertia of semi - circular disc be I₁.

Thu disc may be assumed as combination of two semi - circular parts .

Thus, I₁ = I- I₁

Or, ∴ I₁ = I/2 = Mr²/2 Answer.

Answer 2

Answer:

A circular disc will have 2 times the mass of the semicircular disc.

Moment of inertia of circular disc of mass 2M is

Icirculardisc = 1/2(2M)R^2 = MR^2.

Moment of inertia of semi-circular disc is half of the Moment of inertia of circular disc due to symmetry.

∴Isemicirculardisc = 1/2 Icirculardisc = 1/2 MR^2.

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