Question

What is the moment of inertia of a solid sphere of mass \( M \) and radius \( R \) about its diameter?

• A. \( \frac{2}{5} M R^2 \)
• B. \( \frac{1}{2} M R^2 \)
• C. \( \frac{3}{5} M R^2 \)
• D. \( M R^2 \)

Hint:

Remember: The moment of inertia for a solid sphere about its diameter is \( I = \frac{2}{5} M R^2 \). For other geometries, the formula will differ.

Answer 1

The Correct Option is A

Given: Mass of the sphere, \( M \) 
Radius of the sphere, \( R \) 

Step 1: Formula for Moment of Inertia of a Solid Sphere The moment of inertia of a solid sphere about an axis passing through its diameter is given by the formula: \[ I = \frac{2}{5} M R^2 \] where: - \( M \) is the mass of the sphere, - \( R \) is the radius of the sphere. 

Step 2: Conclusion Thus, the moment of inertia of the solid sphere about its diameter is \( \frac{2}{5} M R^2 \). 

Answer: The correct answer is option (a): \( \frac{2}{5} M R^2 \).