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Byju's Answer

Standard XII

Physics

Perpendicular Axis Theorem

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:
a) $I_{1} + I_{3}$
b) $I_{2} + I_{4}$
c) $2 I_{1} + I_{3}$
d) $I_{1} + 2 I_{3}$

a and b are true

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b and c are true

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c and d are true

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b and d are true

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Solution

The correct option is A a and b are true
We know that according to perpendicular axis theorem $I_{z} = I_{x} + I_{y}$
So $I_{z} = I_{1} + I_{3}$ ( directly putting up the variables from question and figure)
Also $I_{z} = I_{2} + I_{4}$

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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))

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)

Q. The moment of inertia of a thin square plate ABCD as shown in the fig. 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}

I_{4}

are the moments of inertia respectively about axis 1, 2, 3 and 4 which are in the plane of the plate.)

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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:a) I1+I3b) I2+I4c) 2I1+I3d) I1+2I3

The correct option is A a and b are trueWe know that according to perpendicular axis theorem Iz=Ix+Iy So Iz=I1+I3 ( directly putting up the variables from question and figure)Also Iz=I2+I4

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) $I_{1} + I_{3}$
b) $I_{2} + I_{4}$
c) $2 I_{1} + I_{3}$
d) $I_{1} + 2 I_{3}$

The correct option is A a and b are true
We know that according to perpendicular axis theorem $I_{z} = I_{x} + I_{y}$
So $I_{z} = I_{1} + I_{3}$ ( directly putting up the variables from question and figure)
Also $I_{z} = I_{2} + I_{4}$