Question

A solid sphere of mass $M$ and radius $R$ is rotating about its diameter. What is its moment of inertia about the same axis?

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

Hint:

For a rotating sphere, the moment of inertia about its diameter is \(\frac{2}{5} MR^2\), a standard result in rotational dynamics.

Answer 1

The Correct Option is B

The moment of inertia \(I\) of a solid sphere rotating about its diameter is given by the formula: \[ I = \frac{2}{5} MR^2 \] This formula is derived from the definition of the moment of inertia and the distribution of mass in a sphere. Thus, the moment of inertia of a solid sphere about its diameter is \(\frac{2}{5} MR^2\).
Final answer
Answer: \(\boxed{\frac{2}{5} MR^2}\)