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.

Answer 2

The moment of inertia \( I \) of a rigid body about an axis of rotation depends on the mass distribution relative to that axis, as well as the position of the axis. It is given by the formula: \[ I = \sum m_i r_i^2 \] where \( m_i \) is the mass of the \(i\)-th particle, and \( r_i \) is the perpendicular distance from the axis of rotation to the particle. Thus, the moment of inertia is influenced by the position of the axis of rotation, as changing the position of the axis changes the distance of the masses from the axis, altering the moment of inertia.

\(\textbf{Correct Answer:}\) (B) depends on the position of axis of rotation.