Question

Find the moment of inertia of a solid sphere about its diameter.

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

Hint:

Common moment of inertia results: Ring about centre \(= MR^2\), Solid cylinder/disc \(= \frac{1}{2}MR^2\), Solid sphere \(= \frac{2}{5}MR^2\).

Answer 1

The Correct Option is B

Concept: The moment of inertia of a body measures its resistance to rotational motion about a given axis. For a solid sphere, the moment of inertia about an axis passing through its centre (diameter) is a standard result.

Step 1: Recall the standard formula. The moment of inertia of a solid sphere about its diameter is \[ I = \frac{2}{5}MR^2 \] where \(M\) = mass of the sphere, \(R\) = radius of the sphere.

Step 2: Interpret the result. This means the rotational inertia of a solid sphere depends on both its mass and the square of its radius.