EI Fundamentals of Engineering 2 — Questions and Answers
Question 1: A simply supported beam of length L carries a uniformly distributed load w. What is the maximum bending moment?
- wL²/4
- wL²/8 (Correct answer)
- wL²/2
- wL/2
Correct answer: wL²/8
For a simply supported beam with UDL, the maximum bending moment at midspan is wL²/8.
Question 2: The Laplace transform of the unit step function u(t) is:
- 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 3: In a Carnot heat engine operating between reservoirs at 800 K and 400 K, what is the maximum thermal efficiency?
- 25%
- 33%
- 50% (Correct answer)
- 75%
Correct answer: 50%
Carnot efficiency = 1 − T_L/T_H = 1 − 400/800 = 0.50 = 50%.
Question 4: Which law states that the total pressure of a gas mixture equals the sum of partial pressures of each component?
- Boyle's Law
- Dalton's Law (Correct answer)
- Henry's Law
- Raoult's Law
Correct answer: Dalton's Law
Dalton's Law of partial pressures states that total pressure equals the sum of each component's partial pressure.
Question 5: A 10 Ω resistor and a 40 Ω resistor are connected in parallel. What is the equivalent resistance?
- 50 Ω
- 25 Ω
- 8 Ω (Correct answer)
- 4 Ω
Correct answer: 8 Ω
Parallel resistance: 1/R = 1/10 + 1/40 = 5/40, so R = 8 Ω.
Question 6: The determinant of the matrix [[3, 1], [2, 4]] is:
- 10 (Correct answer)
- 14
- 12
- 6
Correct answer: 10
det = (3)(4) − (1)(2) = 12 − 2 = 10.
Question 7: A fluid flows through a pipe that narrows from 0.2 m diameter to 0.1 m diameter. If inlet velocity is 2 m/s, what is the outlet velocity (assume incompressible flow)?
- 4 m/s
- 8 m/s (Correct answer)
- 1 m/s
- 16 m/s
Correct answer: 8 m/s
By continuity: A₁V₁ = A₂V₂; (π/4)(0.2²)(2) = (π/4)(0.1²)V₂, so V₂ = 8 m/s.
EI Fundamentals of Engineering 2
A simply supported beam of length L carries a uniformly distributed load w.
What is the maximum bending moment?