Question

The moment of inertia of a rigid body about an axis

• A. does not depend on its shape.
• B. depends on the position of axis of rotation
• C. does not depend on its size.
• D. does not depend on its mass.

Answer 1

The Correct Option is B

Concept: 

The moment of inertia \( I \) of a rigid body about a given axis is given by:

\[ I = \sum m_i r_i^2 \]

where:

• \( m_i \) is the mass of each particle in the body
• \( r_i \) is the perpendicular distance of the particle from the axis of rotation

Step 1: Factors Affecting Moment of Inertia

• It depends on the mass distribution relative to the axis of rotation.
• It depends on the position of the axis of rotation.
• It depends on the shape and size of the object.
• It does not depend only on the total mass but also on how the mass is distributed.

Step 2: Correct Answer

The moment of inertia depends on the position of the axis of rotation, as changing the axis changes the distances \( r_i \) in the formula.

Answer: The correct option is B.