(B) For a planar object,the perpendicular axes theorem states that the moment of inertia about an axis perpendicular to the plane $(z-z')$ is the sum

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(B) For a planar object,the perpendicular axes theorem states that the moment of inertia about an axis perpendicular to the plane $(z-z')$ is the sum of the moments of inertia about two mutually perpendicular axes in the plane ($x-x'$ and $y-y'$).Thus,$I_{zz'} = I_{xx'} + I_{yy'}$.Since $I_{xx'}$ and $I_{yy'}$ are both positive quantities,it follows that $I_{zz'} > I_{xx'}$ and $I_{zz'} > I_{yy'}$.Therefore,the moment of inertia is maximum about the $z-z'$ axis.

Class 11 Physics System of Particles and Rotational Motion Moment of Inertia of Compound Bodies and Theorem of Moment of Inertia

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The rectangular plate shown in the figure is rotated in turn about $x-x'$,$y-y'$ and $z-z'$ axes passing through its centre of mass $O$. Its moment of inertia is

A
Same about all the three axes
B
Maximum about $z-z'$ axis
C
Equal about $x-x'$ and $y-y'$ axis
D
Maximum about $y-y'$ axis

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System of Particles and Rotational Motion

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Moment of Inertia of Compound Bodies and Theorem of Moment of Inertia

The moment of inertia of a uniform cylinder of length $l$ and radius $R$ about its perpendicular bisector is $I$. What is the ratio $l/R$ such that the moment of inertia is minimum?

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The moment of inertia of a semicircular ring of radius $R$ and mass $M$ about an axis passing through point $A$ (one end of the ring) and perpendicular to the plane of the paper is:

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Four spheres,each of mass $M$ and radius $r$,are situated at the four corners of a square of side $R$. The moment of inertia of the system about an axis perpendicular to the plane of the square and passing through its centre will be

Difficult

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The string of a simple pendulum is replaced by a uniform rod of length $L$ and mass $M$. If the mass of the bob of the pendulum is $m$,then for small oscillations its time period would be (assume radius of bob $r << L$):

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The moment of inertia of a sphere about its diameter is $40 \ kg \cdot m^2$. Find the moment of inertia about any tangent.

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The rectangular plate shown in the figure is rotated in turn about $x-x'$,$y-y'$ and $z-z'$ axes passing through its centre of mass $O$. Its moment of inertia is

Similar Questions

The moment of inertia of a uniform cylinder of length $l$ and radius $R$ about its perpendicular bisector is $I$. What is the ratio $l/R$ such that the moment of inertia is minimum?

The moment of inertia of a semicircular ring of radius $R$ and mass $M$ about an axis passing through point $A$ (one end of the ring) and perpendicular to the plane of the paper is:

Four spheres,each of mass $M$ and radius $r$,are situated at the four corners of a square of side $R$. The moment of inertia of the system about an axis perpendicular to the plane of the square and passing through its centre will be

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