EI Fundamentals of Engineering 3 — Questions and Answers
Question 1: What is the moment of inertia of a solid circular cross-section of diameter d about its centroidal axis?
- πd⁴/32
- πd⁴/64 (Correct answer)
- πd³/32
- πd²/4
Correct answer: πd⁴/64
The area moment of inertia of a solid circle is I = πd⁴/64.
Question 2: In engineering economics, a project has a first cost of $50,000 and annual net benefits of $12,000 for 6 years at 8% interest. The benefit-cost ratio is closest to:
- 0.93
- 1.14 (Correct answer)
- 1.44
- 1.72
Correct answer: 1.14
PW of benefits = 12,000 × (P/A, 8%, 6) = 12,000 × 4.623 = $55,476; BCR = 55,476/50,000 ≈ 1.11, closest to 1.14.
Question 3: A block weighing 500 N rests on a surface with a coefficient of static friction of 0.4. What minimum horizontal force is required to start moving it?
- 125 N
- 150 N
- 200 N (Correct answer)
- 250 N
Correct answer: 200 N
F = μₛN = 0.4 × 500 = 200 N.
Question 4: Which differential equation correctly models simple harmonic motion?
- d²x/dt² + ω²x = 0 (Correct answer)
- dx/dt + ωx = 0
- d²x/dt² − ω²x = 0
- d²x/dt² + ωx = 0
Correct answer: d²x/dt² + ω²x = 0
Simple harmonic motion is described by d²x/dt² + ω²x = 0, whose solution is sinusoidal.
Question 5: The FIRST law of thermodynamics for a closed system in differential form is:
- dU = δQ − δW (Correct answer)
- dU = δQ + δW
- dH = δQ − δW
- dS = δQ/T
Correct answer: dU = δQ − δW
The first law for a closed system is dU = δQ − δW, where W is work done BY the system.
Question 6: In fluid mechanics, the Reynolds number is defined as:
- ρVL/μ (Correct answer)
- μVL/ρ
- ρV²L/μ
- μ/(ρVL)
Correct answer: ρVL/μ
Reynolds number Re = ρVL/μ, representing the ratio of inertial to viscous forces.
Question 7: The derivative of ln(x) with respect to x is:
- ln(x)/x
- 1/x (Correct answer)
- x·ln(x)
- e^x
Correct answer: 1/x
d/dx[ln(x)] = 1/x for x > 0.
EI Fundamentals of Engineering 3
What is the moment of inertia of a solid circular cross-section of diameter d about its centroidal axis?