Fundamentals of Engineering FE Knowledge 3 — Questions and Answers
Question 1: Which of the following is the correct expression for the Laplace transform of a unit step function u(t)?
- 1/s²
- 1/s (Correct answer)
- s
- e^(-s)
Correct answer: 1/s
The Laplace transform of the unit step function u(t) is 1/s.
Question 2: A hollow cylindrical pressure vessel has an inner radius of 0.5 m, wall thickness of 25 mm, and internal pressure of 2 MPa. What is the hoop stress?
- 20 MPa
- 40 MPa (Correct answer)
- 80 MPa
- 160 MPa
Correct answer: 40 MPa
Hoop stress σ_h = pr/t = (2×10⁶ × 0.5)/0.025 = 40 MPa.
Question 3: In probability theory, two events A and B are independent if:
- P(A ∩ B) = P(A) + P(B)
- P(A | B) = P(B)
- P(A ∩ B) = P(A) × P(B) (Correct answer)
- P(A ∪ B) = 1
Correct answer: P(A ∩ B) = P(A) × P(B)
Events are independent when the joint probability equals the product of individual probabilities.
Question 4: The First Law of Thermodynamics for a closed system states:
- Heat added equals work done by the system
- Change in internal energy equals heat added minus work done by system (Correct answer)
- Entropy of an isolated system always decreases
- Work done by a system equals its change in enthalpy
Correct answer: Change in internal energy equals heat added minus work done by system
ΔU = Q − W: the change in internal energy equals heat added to the system minus work done by the system.
Question 5: Which type of structural analysis method satisfies both equilibrium and compatibility?
- Force method only
- Displacement method only
- Exact (complete) structural analysis (Correct answer)
- Plastic analysis
Correct answer: Exact (complete) structural analysis
A complete structural analysis satisfies equilibrium (statics), compatibility (geometry of deformation), and constitutive relations simultaneously.
Question 6: The hydraulic radius of a circular pipe flowing full is:
- D/4 (Correct answer)
- D/2
- D
- πD/4
Correct answer: D/4
Hydraulic radius R_h = A/P = (πD²/4)/(πD) = D/4.
Question 7: An engineer receives a gift from a vendor whose company bids on the engineer's projects. According to NSPE Code of Ethics, the engineer should:
- Accept it if its value is under $50
- Accept it only after the project is awarded
- Decline the gift to avoid a conflict of interest (Correct answer)
- Disclose the gift to their manager and then accept it
Correct answer: Decline the gift to avoid a conflict of interest
Engineers must avoid gifts from parties with a vested interest in their decisions to maintain objectivity and public trust.
Fundamentals of Engineering FE Knowledge 3
Which of the following is the correct expression for the Laplace transform of a unit step function u(t)?