SCE Engineering Sciences 3 — Questions and Answers
Question 1: What is the shear stress distribution in a circular shaft under torsion?
- Linear, zero at center and maximum at the surface (Correct answer)
- Uniform across the cross-section
- Maximum at the center
- Parabolic distribution
Correct answer: Linear, zero at center and maximum at the surface
In a circular shaft under torsion, shear stress varies linearly from zero at the neutral axis (center) to maximum at the outer surface: τ = Tr/J, where r is the radial distance.
Question 2: Euler's buckling load for a pin-ended column is:
- π²EI/L² (Correct answer)
- π²EI/4L²
- 4π²EI/L²
- πEI/L²
Correct answer: π²EI/L²
For a pin-ended (simply supported) column, Pcr = π²EI/L², where E is Young's modulus, I is moment of inertia, and L is the column length. This is the critical load causing elastic instability.
Question 3: The Navier-Stokes equations describe:
- The motion of viscous fluid substances (Correct answer)
- Heat conduction in solids
- Elastic deformation of beams
- Electromagnetic wave propagation
Correct answer: The motion of viscous fluid substances
The Navier-Stokes equations are the fundamental PDEs governing viscous fluid motion, expressing Newton's second law for fluids with pressure, viscous, and body forces.
Question 4: In a simple supported beam with a uniformly distributed load, the maximum bending moment occurs at:
- The midspan (Correct answer)
- The supports
- Quarter points
- One-third points
Correct answer: The midspan
For a simply supported beam with UDL, the maximum bending moment M_max = wL²/8 occurs at midspan, where the shear force is zero.
Question 5: The second law of thermodynamics states that:
- Entropy of an isolated system never decreases (Correct answer)
- Energy is always conserved
- Heat flows from cold to hot
- Work can be completely converted to heat
Correct answer: Entropy of an isolated system never decreases
The second law states that in any natural process, the total entropy of an isolated system can only increase or remain constant. This limits the efficiency of all real engines and processes.
Question 6: What is the relationship between shear modulus (G), Young's modulus (E), and Poisson's ratio (ν)?
- G = E / 2(1+ν) (Correct answer)
- G = E × 2(1+ν)
- G = E / (1-ν)
- G = E × ν
Correct answer: G = E / 2(1+ν)
For isotropic materials, G = E/[2(1+ν)]. With E = 200 GPa and ν = 0.3 for steel, G ≈ 77 GPa. This links the three elastic constants.
SCE Engineering Sciences 3
What is the shear stress distribution in a circular shaft under torsion?