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A flat disk, a solid sphere, and a hollow sphere each have the same mass m and radius r. The three objects are arranged so that an axis of rotation passes through the center of each object. The rotation axis is perpendicular to the plane of the flat disk. Which of the three objects has the largest rotational inertia?
a) The solid sphere and hollow sphere have the same rotational inertia and it is the largest.b) The hollow sphere has the largest rotational inertia.c) The solid sphere has the largest rotational inertia.d) The flat disk has the largest rotational inertia.e) The flat disk and hollow sphere have the same rotational inertia and it is the largest.

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hugoffim

Answer:

b)

Explanation:

Rotational inertia of the sphere: [tex]\frac{2}{5}mr^2[/tex]

Rotational inertia of hollow sphere: [tex]\frac{2}{3}mr^2[/tex]

Rotational inertia of flat disk: [tex]\frac{1}{2}mr^2[/tex]

The largest value is 2/3 mr², therefore, hollow sphere's inertia is largest.

Lanuel

Based on their respective formulas, the solid sphere has the largest rotational inertia.

How to calculate moment of inertia.

In this exercise, the three (3) objects have the same mass (m) and radius (r). Also, they are arranged in such a way that an axis of rotation passes through the center of each of them.

For the flat disk:

Mathematically, the moment of inertia of a flat disk is given by this formula:

[tex]I=\frac{2}{5} mr^2[/tex]

Where:

  • I is the moment of inertia.
  • m is the mass.
  • r is the radius.

For the solid sphere:

Mathematically, the moment of inertia of a solid sphere is given by this formula:

[tex]I=\frac{2}{3} mr^2[/tex]

For the hollow sphere:

Mathematically, the moment of inertia of a hollow sphere is given by this formula:

[tex]I=\frac{1}{2} mr^2[/tex]

In conclusion, the object with the largest rotational inertia is the solid sphere.

Read more on rotational inertia here: https://brainly.com/question/3406242

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