Question

The moment of inertia of a uniform hollow sphere about its diameter is

• A. $MR^2$
• B. $\frac{MR^2}{2}$
• C. $\frac{2}{3}MR^2$
• D. $\frac{3}{2}MR^2$

Hint:

Remember standard results: - Solid sphere: $\frac{2}{5}MR^2$ - Hollow sphere (shell): $\frac{2}{3}MR^2$

Answer 1

The Correct Option is C

Concept: A uniform hollow sphere (thin spherical shell) has a standard moment of inertia about any diameter given by: \[ I = \frac{2}{3}MR^2 \] where $M$ is the mass and $R$ is the radius of the sphere.

Step 1: Identify the type of body.
The given object is a uniform hollow sphere, meaning mass is distributed only on its surface.

Step 2: Recall the standard formula.
For a hollow sphere about its diameter: \[ I = \frac{2}{3}MR^2 \]

Step 3: Match with given options.
The correct expression matches option (C).

Step 4: Final conclusion.
Thus, the moment of inertia is: \[ \frac{2}{3}MR^2 \]