FE Mechanical Exam questions and Correct
Answers (Verified Answers) Plus Rationales
2026 Q&A | Instant Download Pdf
1. A solid cylindrical shaft has a radius of 0.05 m and is subjected to
a torque of 500 N·m. What is the maximum shear stress in the
shaft?
A) 15.9 MPa
B) 31.8 MPa
C) 63.7 MPa
D) 127.4 MPa
Rationale: The maximum shear stress for a circular shaft is τ = Tr /
J, where J = πr^. Substituting gives τ = 63.7 MPa.
2. A 2-kg block slides down a frictionless incline of angle 30° for 4 m.
What is its velocity at the bottom?
A) 4 m/s
B) 6 m/s
C) 8 m/s
D) 10 m/s
Rationale: Using energy conservation, mgh = 0.5mv^2. Height h =
4sin(30°) = 2 m. Solving for v gives 8 m/s.*
3. A piston-cylinder device contains 0.01 m³ of air at 100 kPa and
300 K. The air is compressed isothermally to 0.005 m³. What is the
final pressure?
A) 50 kPa
B) 100 kPa
C) 200 kPa
, D) 400 kPa
Rationale: For isothermal compression, P1V1 = P2V2. So P2 =
100(0.01/0.005) = 200 kPa.*
4. The specific heat ratio (γ) for air is approximately:
A) 1.2
B) 1.4
C) 1.6
D) 1.67
Rationale: Air, a diatomic gas, has γ = Cp/Cv ≈ 1.4 at room
temperature.
5. A beam fixed at one end and free at the other has a length L and
carries a point load P at the free end. What is the deflection at the
free end?
A) PL^2 / (2EI)
B) PL^3 / (3EI)
C) PL^3 / (6EI)
D) PL^4 / (8EI)
Rationale: The deflection of a cantilever with end load is δ = PL^3 /
(3EI).
6. A gas flows through a nozzle. If the flow is adiabatic and
reversible, what kind of process occurs?
A) Isothermal
B) Isobaric
C) Isentropic
D) Isochoric
Rationale: An adiabatic, reversible process is by definition
isentropic.
7. For a laminar flow between parallel plates, the velocity profile is:
A) Parabolic
, B) Linear
C) Uniform
D) Exponential
Rationale: Laminar flow between plates yields a parabolic velocity
distribution.
8. The modulus of elasticity for steel is approximately:
A) 100 MPa
B) 200 MPa
C) 200 GPa
D) 500 GPa
Rationale: Standard modulus of elasticity for steel is 200 GPa.
9. A system has 2 kg of water at 100°C. How much energy is required
to convert it completely to steam at 100°C? (Latent heat = 2257
kJ/kg)
A) 2257 kJ
B) 4514 kJ
C) 4514 kJ
D) 1130 kJ
Rationale: Q = mL = 22257 = 4514 kJ.
10. A 10 N force acts at a point located 0.2 m from a pivot. What
is the moment about the pivot?
A) 1 N·m
B) 2 N·m
C) 5 N·m
D) 20 N·m
Rationale: Moment = Force × Distance = 100.2 = 2 N·m.*
11. For a 1-D steady heat conduction through a slab of thickness
L, the heat transfer rate is:
A) kAΔT / L
Answers (Verified Answers) Plus Rationales
2026 Q&A | Instant Download Pdf
1. A solid cylindrical shaft has a radius of 0.05 m and is subjected to
a torque of 500 N·m. What is the maximum shear stress in the
shaft?
A) 15.9 MPa
B) 31.8 MPa
C) 63.7 MPa
D) 127.4 MPa
Rationale: The maximum shear stress for a circular shaft is τ = Tr /
J, where J = πr^. Substituting gives τ = 63.7 MPa.
2. A 2-kg block slides down a frictionless incline of angle 30° for 4 m.
What is its velocity at the bottom?
A) 4 m/s
B) 6 m/s
C) 8 m/s
D) 10 m/s
Rationale: Using energy conservation, mgh = 0.5mv^2. Height h =
4sin(30°) = 2 m. Solving for v gives 8 m/s.*
3. A piston-cylinder device contains 0.01 m³ of air at 100 kPa and
300 K. The air is compressed isothermally to 0.005 m³. What is the
final pressure?
A) 50 kPa
B) 100 kPa
C) 200 kPa
, D) 400 kPa
Rationale: For isothermal compression, P1V1 = P2V2. So P2 =
100(0.01/0.005) = 200 kPa.*
4. The specific heat ratio (γ) for air is approximately:
A) 1.2
B) 1.4
C) 1.6
D) 1.67
Rationale: Air, a diatomic gas, has γ = Cp/Cv ≈ 1.4 at room
temperature.
5. A beam fixed at one end and free at the other has a length L and
carries a point load P at the free end. What is the deflection at the
free end?
A) PL^2 / (2EI)
B) PL^3 / (3EI)
C) PL^3 / (6EI)
D) PL^4 / (8EI)
Rationale: The deflection of a cantilever with end load is δ = PL^3 /
(3EI).
6. A gas flows through a nozzle. If the flow is adiabatic and
reversible, what kind of process occurs?
A) Isothermal
B) Isobaric
C) Isentropic
D) Isochoric
Rationale: An adiabatic, reversible process is by definition
isentropic.
7. For a laminar flow between parallel plates, the velocity profile is:
A) Parabolic
, B) Linear
C) Uniform
D) Exponential
Rationale: Laminar flow between plates yields a parabolic velocity
distribution.
8. The modulus of elasticity for steel is approximately:
A) 100 MPa
B) 200 MPa
C) 200 GPa
D) 500 GPa
Rationale: Standard modulus of elasticity for steel is 200 GPa.
9. A system has 2 kg of water at 100°C. How much energy is required
to convert it completely to steam at 100°C? (Latent heat = 2257
kJ/kg)
A) 2257 kJ
B) 4514 kJ
C) 4514 kJ
D) 1130 kJ
Rationale: Q = mL = 22257 = 4514 kJ.
10. A 10 N force acts at a point located 0.2 m from a pivot. What
is the moment about the pivot?
A) 1 N·m
B) 2 N·m
C) 5 N·m
D) 20 N·m
Rationale: Moment = Force × Distance = 100.2 = 2 N·m.*
11. For a 1-D steady heat conduction through a slab of thickness
L, the heat transfer rate is:
A) kAΔT / L
