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Q.

Find the moment with respect to the diameter of the disc when the moment of inertia of the disc around the geometric axis is $I$ .

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a

I

b

2 I

c

\frac{I}{2}

d

\frac{I}{4}

answer is C.

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Detailed Solution

Concept: The moment of inertia with respect to diameter of disc is always half of the moment of inertia of disc around the geometric axis.
The moment of inertia of the disk around the geometric axis is given i.e.

I_{z}

is

I

.
According to the perpendicular axis theorem, the empty time of the plane around the axis should be equal to the total inertia times of all two axes facing each other.
i.e.

I_{z} = I_{x} + I_{y}

Considering the symmetry of the disk here, it becomes as follows.

I_{x} = I_{y}

The diameter of the disc is the same in all directions. Also,

I_{x}

and

I_{y}

are moments of inertia around the diameter of the disk.
Since

I_{z} = I

Thus,

I = I_{x} + I_{x} = 2 I_{x}

I_{x} = \frac{I}{2}

That is, the moment of inertia around the diameter of the disc is

\frac{I}{2}

where ‘

I

’ is the moment of inertia along the geometric axis of the disc.
Therefore, (3)

\frac{I}{2}

is the solution we are looking for.
Hence, the correct option is 3

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