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Byju's Answer

Standard XII

Physics

Parallel Axis Theorem

The moment of...

Question

The moment of inertia of a thin square plate ABCD (shown in the figure) of uniform thickness about an axis passing through the centre O perpendicular to the plane of plate is

I_{1} + I_{2}

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I_{3} + I_{4}

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I_{1} + I_{3}

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All of the above is correct

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Solution

The correct options are
A $I_{1} + I_{3}$
B All of the above is correct
C $I_{1} + I_{2}$
D $I_{3} + I_{4}$
The axis of $I_{1}$ and $I_{2}$ and that of $I_{3}$ and $I_{4}$ are perpendicular to each other. Using perpendicular axis theorem $I = I_{1} + I_{2} = I_{3} + I_{4}$
$\Rightarrow I = 2 I_{1} = 2 I_{2} = 2 I_{3} = 2 I_{4}$
$\Rightarrow I_{1} = I_{2} = I_{3} = I_{4}$

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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}

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))

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)

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.

Q. The moments of inertia of a thin square plate

A B C D

of uniform thickness an axis passing through the centre

O

and perpendicular to the plate are
(where

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

are respectively, the moments of inertia about axes 1,2,3,4 where axes are in the plane of the plate)

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The moment of inertia of a thin square plate ABCD (shown in the figure) of uniform thickness about an axis passing through the centre O perpendicular to the plane of plate is

The correct options are A I1+I3 B All of the above is correct C I1+I2 D I3+I4The axis of I1 and I2 and that of I3 and I4 are perpendicular to each other. Using perpendicular axis theorem I=I1+I2=I3+I4⇒I=2I1=2I2=2I3=2I4⇒I1=I2=I3=I4