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Question

The moment of inertia of the uniform semicircular disc of mass M and radius R about a line perpendicular to the plane of the disc through the center is


A

MR2

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B

12MR2

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C

14MR2

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D

25MR2

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Solution

The correct option is B

12MR2


Step 1: Given data

Uniform semicircular disc with mass M and radius R.

We have to find the moment of inertia about a line perpendicular to the plane of the disc through the center.

Step 2: Calculation

Since the mass of a semicircular disc is M, we can consider its moment of inertia of it as half of the moment of inertia of a circular disc of mass 2M

We know, a moment of inertia of a disc of mass 2M is

Icirculardisc=12(2M)R2=MR2

Therefore, moment of inertia of semicircular disc with mass M,

Isemicirculardisc=12Icirculardisc⇒Isemicirculardisc=12MR2

The moment of inertia of the semicircular disc with mass M and radius R about a line perpendicular to the plane of the disc through the center is 12MR2

Hence, option B is correct


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