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Standard XII

Physics

Rotational Inertia

The moment of...

Question

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 (where $I_{1}, I_{2}, I_{3} a n d I_{4}$ are respectively moments of inertia about axis 1,2,3, and 4 which are in the plane of the plate)

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_{1} + I_{2} + I_{3} + I_{4}

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Solution

The correct options are
A $I_{1} + I_{2}$
B $I_{3} + I_{4}$
C $I_{1} + I_{3}$
$\begin{matrix} We know that moment of inertia of a square blate about any axis parallel to its fau passing through is centre is always equal \Rightarrow I_{1} = I_{2} = I_{3} = I_{4} \Rightarrow For an axis perpendicular to the face of plate- By perpendicular axis theorem- I_{⊥} = I_{1} + I_{2} = I_{3} + I_{4} = I_{1} + I_{3} Henu, option (a), (b), (c) are correct. \end{matrix}$

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Similar questions

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))

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}

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 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 (where I1,I2,I3 and I4 are respectively moments of inertia about axis 1,2,3, and 4 which are in the plane of the plate)

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 (where $I_{1}, I_{2}, I_{3} a n d I_{4}$ are respectively moments of inertia about axis 1,2,3, and 4 which are in the plane of the plate)