(A) The moment of inertia $I$ of a circular disc about its geometric axis is given by $I = \int r^2 dm$. To maximize the moment of inertia for a fixed

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Aluminum on the inside and iron on the outside

(A) The moment of inertia $I$ of a circular disc about its geometric axis is given by $I = \int r^2 dm$. To maximize the moment of inertia for a fixed total mass,we need to place the maximum possible mass at the largest possible distance $r$ from the axis of rotation. Since iron is denser than aluminum,placing iron at the outer rim (the largest radius) increases the mass distribution at a greater distance from the axis. Therefore,placing iron on the outside and aluminum on the inside maximizes the moment of inertia.

Class 11 Physics System of Particles and Rotational Motion Moment of Inertia and Radius of gyration

Medium

$A$ circular disc is made using iron and aluminum. To maximize the moment of inertia about its geometric axis,which configuration is preferred?

A
Aluminum on the inside and iron on the outside
B
Iron on the inside and aluminum on the outside
C
By keeping alternate layers of iron and aluminum
D
Iron strips on both outer surfaces and aluminum strips on the inside

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Class 11

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Chapter

System of Particles and Rotational Motion

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Moment of Inertia and Radius of gyration

$A$ thin rod of length $L$ and mass $M$ is bent at the middle point $O$ at an angle of $60^{\circ}$ as shown in the figure. The moment of inertia of the rod about an axis passing through $O$ and perpendicular to the plane of the rod will be:

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Two circular loops $A$ and $B$ of radii $R$ and $NR$ respectively are made from a uniform wire. The moment of inertia of $B$ about its axis is $3$ times that of $A$ about its axis. The value of $N$ is:

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$A$ solid sphere $A$ and a hollow sphere $B$ have the same mass and the same external radius. Their moments of inertia about their diameters are $I_A$ and $I_B$ respectively. Which of the following relations is correct?

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$A$ thin rod of length $L$ and mass $M$ is bent at its midpoint $O$ at an angle of $90^{\circ}$. The moment of inertia of the bent rod about an axis passing through the point $O$ and perpendicular to the plane of the bent rod is:

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For a rectangle $ABCD$ with $BC = 2AB$,about which axis will the moment of inertia be minimum?

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$A$ circular disc is made using iron and aluminum. To maximize the moment of inertia about its geometric axis,which configuration is preferred?

Similar Questions

$A$ thin rod of length $L$ and mass $M$ is bent at the middle point $O$ at an angle of $60^{\circ}$ as shown in the figure. The moment of inertia of the rod about an axis passing through $O$ and perpendicular to the plane of the rod will be:

Two circular loops $A$ and $B$ of radii $R$ and $NR$ respectively are made from a uniform wire. The moment of inertia of $B$ about its axis is $3$ times that of $A$ about its axis. The value of $N$ is:

$A$ solid sphere $A$ and a hollow sphere $B$ have the same mass and the same external radius. Their moments of inertia about their diameters are $I_A$ and $I_B$ respectively. Which of the following relations is correct?

$A$ thin rod of length $L$ and mass $M$ is bent at its midpoint $O$ at an angle of $90^{\circ}$. The moment of inertia of the bent rod about an axis passing through the point $O$ and perpendicular to the plane of the bent rod is:

For a rectangle $ABCD$ with $BC = 2AB$,about which axis will the moment of inertia be minimum?

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