The moment of inertia of a body is a measure of:
Try it first: pick an option, then read the explanation.
Correct answer: D. its resistance against rotation
Asked in SSC JE 09/10/2023 (Morning)
Detailed Explanation
In straight-line motion, mass measures inertia: F = m·a. In rotation, the equivalent is the mass moment of inertia: T = I·α, where T is torque and α angular acceleration.
\[ I = \sum m r^2 \qquad T = I\alpha \]
Unit: kg·m²; dimensions [M L²].
Why “its resistance against rotation” Is Correct
The larger I is, the larger the torque needed for the same angular acceleration. So I measures the body's resistance against rotation. Mass placed further from the axis increases I strongly, because of the r² term.
Why the Other Options Are Wrong
- A. its resistance against linear deformation: Resistance to deformation depends on stiffness (E, A), not on moment of inertia of mass.
- B. its resistance against translation: Resistance to translation is measured by mass.
- C. its resistance against shear: Resistance to shear depends on shear modulus and area.
Key Point
Mass moment of inertia = rotational inertia (T = Iα).
Key Concepts for Students
- Radius of gyration k: I = m k².
- A flywheel stores energy because of its large moment of inertia.
- Area moment of inertia (mm⁴) measures resistance of a section to bending.
Practice more: this is question 6 in Moment MCQs – Part 1. Try the whole set and check every answer instantly.