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Byju's Answer

Standard XII

Physics

Moment of Inertia of an Annular Disc

The moments o...

Question

The moments of inertia of a thin square plate $A B C D$ of uniform thickness about an axis passing through the centre $O$ and perpendicular to the plate are

I_{1} + I_{2}

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I_{3} + I_{4}

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I_{1} + I_{3}

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I_{2} + I_{3}

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Solution

The correct options are
A $I_{1} + I_{2}$
B $I_{3} + I_{4}$
C $I_{1} + I_{3}$
Perpendicular Axis theorem: For a planar object, the moment of inertia about an axis perpendicular to the plane is the sum of the moments of inertia of two perpendicular axes through the same point in the plane of the object.
$∴ I_{z} = I_{1} + I_{2} = I_{3} + I_{4}$
By geometry: $I_{1} = I_{2} & I_{3} = I_{4} ∴ I_{1} = I_{2} = I_{3} = I_{4} = I_{z} / 2$
Therefore $I_{1} + I_{3} = \frac{I_{z}}{2} + \frac{I_{z}}{2} = I_{z}$

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Similar questions

Q. The moment of inertia of a thin square plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is:
a)

I_{1} + I_{3}

I_{2} + I_{4}

2 I_{1} + I_{3}

I_{1} + 2 I_{3}

The moment of inertia of thin square plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is not equal to (Given $I_{1}, I_{2}, I_{3} a n d I_{4}$ respectively, are the moments of inertia about axes 1,2,3and 4 which are in the plane of the plate)

Q. A thin square plate

A B C D

of uniform thickness is shown in the figure.

I_{1}, I_{2}, I_{3}

and

I_{4}

are respectively the moments of inertia about axis

1, 2, 3

and

4

which are in the plane of the square plate. Then, the moment of inertia

I_{0}

of the plate about an axis passing through its centre

O

and perpendicular to the plane of the plate will be equal to : (Choose the correct option(s))

A B C D

is a square plate with centre

O

. The moment of inertia of the plate about the axes

1, 2, 3

and

4

are

I_{1}, I_{2}, I_{3} & I_{4}

respectively. It follows that

The moment of inertia of a thin square plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate can NOT be given by :

where, $I_{1}, I_{2}, I_{3}, I_{4}$ are the moments of inertia of the plates about axes 1,2,3,4 respectively.

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The moments of inertia of a thin square plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plate are

The moments of inertia of a thin square plate $A B C D$ of uniform thickness about an axis passing through the centre $O$ and perpendicular to the plate are