Question

The moment of inertia of a plane figure about an axis in its plane is:

• A. Directly proportional to the mass of the figure
• B. The resistance of the figure to rotation about the axis
• C. Equal to the product of mass and radius of gyration squared
• D. Inversely proportional to the square of its dimensions

Hint:

Moment of inertia measures how mass is distributed relative to an axis and governs an object’s resistance to rotational motion. It’s the rotational counterpart of mass.

Answer 1

The Correct Option is B

Step 1: The moment of inertia (MOI), also known as the second moment of area, quantifies an object's resistance to angular acceleration about a particular axis. It is a fundamental property in rotational dynamics.
Step 2: For a plane figure (a two-dimensional shape), the moment of inertia is calculated relative to an axis in the plane of the figure and reflects how the mass or area is distributed with respect to that axis.
Step 3: The greater the distance of mass elements from the axis, the higher the moment of inertia, and hence the greater the resistance to rotation. This makes MOI a rotational analog of mass in linear motion.
Why the other options are incorrect:

• (A) It’s not always directly proportional to mass alone; distribution and axis location also matter.
• (C) That formula applies to rigid bodies in mass moment of inertia calculations, not to all planar figures.
• (D) MOI generally increases with the square of dimensions, not decreases.