Which of the following has the smallest moment of inertia about an axis through

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Question: Which of the following has the smallest moment of inertia about an axis through its center?

Options:

Correct Answer: Solid sphere

Solution:

The solid sphere has the smallest moment of inertia compared to the other shapes for the same mass and radius.

Which of the following has the smallest moment of inertia about an axis through its center?

Which of the following has the smallest moment of inertia about an axis through its center?

Step 1: Understand what moment of inertia means. It is a measure of how difficult it is to change the rotation of an object.
Step 2: Know that different shapes have different moments of inertia even if they have the same mass and size.
Step 3: Compare the moment of inertia of a solid sphere with other shapes like a solid cylinder or a hollow sphere.
Step 4: Find the formulas for the moment of inertia for each shape. For a solid sphere, it is (2/5) * mass * radius^2.
Step 5: Calculate or look up the moment of inertia for the other shapes to see which one is smaller.
Step 6: Conclude that the solid sphere has the smallest moment of inertia compared to the other shapes.

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