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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 :

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 $I_{3} + I_{4}$
According to perpendicular axis theorem, if $I_{x}, I_{y}$ and $I_{z}$ be moments of inertia about axis $x$ , $y$ and $z$ respectively, the perpendicular axis theorem states that $I_{x} + I_{y} = I_{z}$
Here $I_{z}$ be moment of inertia about an axis passing through the center O and perpendicular to the plane of the plate.
So, when $I_{x} = I_{1}, I_{y} = I_{2},$ then $I_{z} = I_{1} + I_{2}$
When $I_{x} = I_{3}, I_{y} = I_{4},$ then $I_{z} = I_{3} + I_{4}$
So we get $I_{1} = I_{2} = I_{3} = I_{4}$
Thus we get the required answers.

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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}

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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

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

and

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are respectively the moments of inertia about axis

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

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

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is a square plate with centre

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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 can NOT be given by :

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