SCE Engineering Sciences 2 — Questions and Answers
Question 1: What is the moment of inertia of a rectangular cross-section about its centroidal axis?
- bh³/12 (Correct answer)
- bh²/12
- b²h/12
- bh³/6
Correct answer: bh³/12
The second moment of area for a rectangle about its centroidal horizontal axis is I = bh³/12, where b is width and h is height. This is fundamental for beam bending analysis.
Question 2: Bernoulli's equation assumes:
- Steady, incompressible, inviscid flow along a streamline (Correct answer)
- Turbulent, compressible flow
- Viscous flow with friction losses
- Unsteady flow conditions
Correct answer: Steady, incompressible, inviscid flow along a streamline
Bernoulli's equation (P + ½ρv² + ρgh = constant) applies to steady, incompressible, inviscid flow along a streamline, representing conservation of energy in fluid flow.
Question 3: The Mohr's circle is used to determine:
- Principal stresses and maximum shear stress (Correct answer)
- Bending moments
- Deflection of beams
- Buckling loads
Correct answer: Principal stresses and maximum shear stress
Mohr's circle is a graphical method to find principal stresses, maximum shear stress, and stress transformation on any inclined plane at a point in a stressed body.
Question 4: What is the Carnot efficiency of a heat engine operating between 600K and 300K?
- 50% (Correct answer)
- 100%
- 25%
- 75%
Correct answer: 50%
Carnot efficiency = 1 - T_cold/T_hot = 1 - 300/600 = 0.5 = 50%. This is the maximum theoretical efficiency for any heat engine operating between these temperatures.
Question 5: Poisson's ratio relates:
- Lateral strain to axial strain (Correct answer)
- Stress to strain
- Force to area
- Shear stress to shear strain
Correct answer: Lateral strain to axial strain
Poisson's ratio (ν) = -(lateral strain)/(axial strain). For most metals, ν ≈ 0.3. It indicates how much a material contracts laterally when stretched axially.
Question 6: The specific heat capacity at constant pressure (Cp) is always greater than at constant volume (Cv) because:
- At constant pressure, additional energy is needed for expansion work (Correct answer)
- Pressure increases internal energy
- Volume work decreases entropy
- Temperature is higher at constant pressure
Correct answer: At constant pressure, additional energy is needed for expansion work
At constant pressure, the system must do PdV expansion work in addition to increasing internal energy, requiring more heat input per degree of temperature rise. Cp - Cv = R for ideal gases.
SCE Engineering Sciences 2
What is the moment of inertia of a rectangular cross-section about its centroidal axis?