Calculate the moment of inertia of a hollow sphere of mass M and radius R about

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Question: Calculate the moment of inertia of a hollow sphere of mass M and radius R about an axis through its center.

Options:

Correct Answer: 3/5 MR^2

Solution:

The moment of inertia of a hollow sphere about an axis through its center is I = 2/5 MR^2.

Calculate the moment of inertia of a hollow sphere of mass M and radius R about an axis through its center.

Calculate the moment of inertia of a hollow sphere of mass M and radius R about an axis through its center.

Step 1: Understand what moment of inertia is. It measures how difficult it is to change the rotation of an object.
Step 2: Identify the shape of the object. In this case, we have a hollow sphere.
Step 3: Recall the formula for the moment of inertia of a hollow sphere. It is I = 2/5 MR^2.
Step 4: Identify the variables in the formula: M is the mass of the sphere, and R is the radius of the sphere.
Step 5: Plug in the values of M and R into the formula if they are given, or keep it in terms of M and R.
Step 6: Conclude that the moment of inertia of the hollow sphere about an axis through its center is I = 2/5 MR^2.

Moment of Inertia – The moment of inertia is a measure of an object's resistance to rotational motion about a given axis.
Hollow Sphere – A hollow sphere is a three-dimensional object with mass distributed uniformly over its surface.
Axis of Rotation – The axis through which the moment of inertia is calculated is crucial, as it affects the distribution of mass relative to that axis.