Question

A uniform hollow cylinder has a density \( \rho \), a length \( L \), an inner radius \( a \), and an outer radius \( b \). Its moment of inertia about the axis of the cylinder is (Mass of the cylinder is \( M \)):

• A. \( M(b^2 + a^2) \)
• B. \( 2M(b^2 + a^2) \)
• C. \( \frac{M}{2} (b^2 + a^2) \)
• D. \( \frac{3}{4} M(b^2 + a^2) \)

Hint:

The moment of inertia of a hollow cylinder involves both the inner and outer radii and is influenced by the mass distribution.

Answer 1

The Correct Option is A

For a hollow cylinder, the moment of inertia about its central axis is given by: \[ I = \frac{1}{2} M (b^2 + a^2) \] Since the cylinder is hollow, the moment of inertia is directly related to the mass and the square of both the inner and outer radii. Therefore, the moment of inertia is \( M(b^2 + a^2) \).