Select the correct statement regarding the first and second moments of area of a circular lamina of radius R.
Try it first: pick an option, then read the explanation.
Correct answer: C. The first moment of area may be either negative or positive depending on the chosen reference axes, but the second moment of area is always positive.
Asked in SSC JE 11/10/2023 (Morning)
Detailed Explanation
The first moment of area about an axis is Q = ∫y dA = A·ȳ. The second moment of area (area moment of inertia) is I = ∫y² dA.
Why “The first moment of area may be either negative or positive depending on the chosen reference axes, but the second moment of area is always positive.” Is Correct
In ∫y dA the distance y keeps its sign. If the area lies mostly on the negative side of the axis, Q is negative; about a centroidal axis it is exactly zero. In ∫y² dA every distance is squared, so each element adds a positive amount and I is always positive. That is statement (c).
Why the Other Options Are Wrong
- A. The first moment of area is always positive and the second moment of area is always negative.: The second moment can never be negative because distances are squared.
- B. The first and second moments of area are always positive.: The first moment can be negative or zero.
- D. The first moment of area is always negative and the second moment of area is always positive.: The first moment is not always negative; its sign depends on the axis.
Key Point
First moment: sign depends on axis (zero about centroid). Second moment: always positive.
Key Concepts for Students
- First moment about a centroidal axis = 0 — this is how the centroid is located.
- The first moment Q appears in the shear stress formula τ = VQ/Ib.
- Product of inertia ∫xy dA can also be negative.
Practice more: this is question 3 in Moment MCQs – Part 1. Try the whole set and check every answer instantly.