Find the moment of inertia of a circular disc of radius R about its diameter

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The moment of inertia of a uniform circular disc of radius ' R ' and mass ' M ' about an axis passing from the edge of the disc and normal to the disc isA. MR 2B. 1/2 M R 2C. 3/2 MR 2D. 7/2 MR 2

Answer (Detailed Solution Below)

Option 2 : 3/2 MR2

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The correct answer is option 2) i.e. 3/2 MR2.

CONCEPT:

• ​Consider a circular disc of mass M, and Radius R such that its z-axis is along with its diameter.

The moment of inertia of the circular disc about the central axis, IZ = 

• Parallel axis theorem: The moment of inertia of a body about an axis parallel to the body passing through its center is equal to the sum of the moment of inertia of the body about the axis passing through its center and the product of the mass of the body times the square of the distance between the two axes.​

• It is given by: I = IC + Mh2

• ​Where, IC represents the moment of inertia of the body about an axis passing through its centre, I represent the moment of inertia of the body about an axis parallel to the body and passing through its centre, and h is the distance between the two axes.

CALCULATION:

We have to find the moment of inertia along the line CD which is along the edge of the disc and normal to it.

The moment of inertia of the circular disc about the central axis (AB), IZ = 

From parallel axis theorem, the moment of inertia about an axis passing from the edge of the disc, I = IC + Mh2

From the figure, h = R

⇒ IZ + MR2 =  + MR2 = MR2

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