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IESL Part II Mechanical study materials
IESL Part II Mechanical study resources

IESL Part II Mechanical practice questions

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Question 1Mechanical Engineering

In a steady-flow steam turbine, steam enters at 3 MPa and 400 °C with negligible velocity and leaves at 10 kPa with a quality of 0.92. Which energy term may normally be neglected in the steady-flow energy equation for the turbine?

  1. Change in enthalpy
  2. Work output
  3. Change in kinetic energy Correct answer.
  4. Heat loss to surroundings

Explanation

Because inlet velocity is negligible and exit velocity is modest, the change in kinetic energy is small compared with the enthalpy drop across the turbine, so it is normally dropped from the steady-flow energy equation. Enthalpy change and work output are the dominant terms and cannot be neglected.

Question 2Mechanical Engineering

A simply supported beam of span 4 m carries a central point load of 20 kN. What is the maximum bending moment?

  1. 20 kN·m Correct answer.
  2. 80 kN·m
  3. 40 kN·m
  4. 10 kN·m

Explanation

For a simply supported beam with a central point load P over span L, the maximum moment is PL/4. Substituting P = 20 kN and L = 4 m gives 20 × 4 / 4 = 20 kN·m at midspan.

Question 3Mechanical Engineering

A steel shaft transmits 15 kW at 300 rev/min. What is the torque carried by the shaft?

  1. 50 N·m
  2. 477 N·m Correct answer.
  3. 955 N·m
  4. 95.5 N·m

Explanation

Power equals torque times angular velocity, with angular velocity in rad/s. At 300 rev/min the angular velocity is 31.4 rad/s, so torque is 15 000 / 31.4 ≈ 477 N·m.

Question 4Mechanical Engineering

Which material property is most directly measured by a standard Charpy V-notch impact test?

  1. Creep rupture strength
  2. Notch toughness Correct answer.
  3. Yield strength
  4. Fatigue endurance limit

Explanation

The Charpy V-notch test measures the energy absorbed in fracturing a notched specimen under impact loading, which characterises notch toughness and the ductile-to-brittle transition. It does not measure strength, fatigue, or creep properties.

Question 5Mechanical Engineering

In a four-stroke diesel engine, the volumetric efficiency is defined as the ratio of which two quantities?

  1. Compression ratio to expansion ratio
  2. Actual air mass inducted to theoretical air mass at inlet conditions Correct answer.
  3. Indicated power to brake power
  4. Fuel mass to air mass

Explanation

Volumetric efficiency compares the actual mass of air drawn into the cylinder per cycle with the theoretical mass that would fill the swept volume at inlet density. It is a breathing-performance measure, not a ratio of powers or of fuel to air.

Question 6Mechanical Engineering

A pump delivers 0.02 m³/s of water through a pipe of 100 mm internal diameter. What is the mean flow velocity?

  1. 5.09 m/s
  2. 0.25 m/s
  3. 1.27 m/s
  4. 2.55 m/s Correct answer.

Explanation

The pipe cross-sectional area is π(0.1)²/4 ≈ 0.00785 m². Dividing the volumetric flow by this area gives 0.02 / 0.00785 ≈ 2.55 m/s.

Question 7Mechanical Engineering

Which dimensionless group is used to characterise whether flow in a pipe is laminar or turbulent?

  1. Reynolds number Correct answer.
  2. Nusselt number
  3. Mach number
  4. Prandtl number

Explanation

The Reynolds number compares inertial forces with viscous forces and determines the laminar-turbulent transition. The other groups characterise heat transfer, momentum diffusivity relative to thermal diffusivity, and compressibility respectively.

Question 8Mechanical Engineering

A Carnot engine operates between a source at 600 K and a sink at 300 K. What is its thermal efficiency?

  1. 60 %
  2. 50 % Correct answer.
  3. 30 %
  4. 100 %

Explanation

Carnot efficiency is 1 − T_sink/T_source with absolute temperatures. Here 1 − 300/600 = 0.5, i.e. 50 %.

Question 9Mechanical Engineering

In a bolted joint, the primary purpose of preload is to:

  1. Increase the shear strength of the bolt material
  2. Keep the joint clamped so the bolt sees reduced fluctuating load Correct answer.
  3. Eliminate the need for a gasket
  4. Reduce the coefficient of friction between mating parts

Explanation

Preload clamps the joint so that applied external loads are partly carried by the compressed members, reducing the fluctuating load on the bolt and improving fatigue life. It does not change the bolt's material strength or remove the need for sealing.

Question 10Mechanical Engineering

A gear train has a driver with 20 teeth meshing with a driven gear of 60 teeth. If the driver rotates at 900 rev/min, what is the driven gear speed?

  1. 450 rev/min
  2. 300 rev/min Correct answer.
  3. 900 rev/min
  4. 2700 rev/min

Explanation

Speed ratio is inversely proportional to the tooth ratio: driven speed = driver speed × (N_driver/N_driven) = 900 × 20/60 = 300 rev/min. The larger gear turns more slowly.

Question 11Mechanical Engineering

Which statement correctly describes the function of a relief valve in a hydraulic circuit?

  1. It filters contaminants from the fluid
  2. It limits the maximum system pressure by diverting flow to the reservoir Correct answer.
  3. It maintains a constant flow rate regardless of pressure
  4. It prevents reverse flow when the pump stops

Explanation

A relief valve opens when system pressure reaches its setting, diverting flow back to the tank and thereby limiting pressure. It is a pressure-limiting device, not a flow controller, check valve, or filter.

Question 12Mechanical Engineering

A plain journal bearing operates under hydrodynamic lubrication. Which condition is required to develop a full fluid film?

  1. Adequate speed, sufficient viscosity, and a converging film geometry Correct answer.
  2. Zero surface speed and high load
  3. Dry contact between shaft and bearing
  4. A perfectly circular clearance with no eccentricity

Explanation

Hydrodynamic lubrication requires the shaft to be eccentric so the film converges in the direction of rotation, together with sufficient speed and viscosity to generate pressure that separates the surfaces. Zero speed or dry contact implies boundary or no lubrication.

Question 13Mechanical Engineering

Which of the following best explains why a cast iron component may be preferred over a steel casting for a machine bed subject to vibration?

  1. Cast iron has a higher elastic modulus than steel
  2. Cast iron has better damping capacity Correct answer.
  3. Cast iron has higher tensile strength
  4. Cast iron has greater ductility

Explanation

Flake graphite in grey cast iron dissipates vibration energy, giving it superior damping compared with steel. Its modulus, tensile strength, and ductility are generally lower than those of steel, not higher.

Question 14Mechanical Engineering

In a closed-loop control system, integral action is added primarily to:

  1. Increase the speed of response
  2. Eliminate steady-state error Correct answer.
  3. Filter high-frequency noise
  4. Reduce overshoot

Explanation

Integral action accumulates the error over time and drives it to zero in the steady state for a step input. It typically slows the response and can worsen overshoot, and it does not act as a noise filter.

Question 15Mechanical Engineering

A thin-walled cylindrical pressure vessel of diameter 1 m and wall thickness 10 mm contains gas at 2 MPa. What is the hoop stress?

  1. 50 MPa
  2. 100 MPa Correct answer.
  3. 200 MPa
  4. 400 MPa

Explanation

For a thin-walled cylinder, hoop stress = pD/(2t) = (2 × 1)/(2 × 0.01) = 100 MPa. The longitudinal stress would be half of this value.

Question 16Mechanical Engineering

Which type of heat exchanger is characterised by the two fluids flowing in the same direction along the length of the exchanger?

  1. Cross-flow
  2. Counter-flow
  3. Shell-and-tube with baffles
  4. Parallel-flow Correct answer.

Explanation

In parallel-flow exchangers both fluids enter at the same end and flow in the same direction, giving a large initial temperature difference but a low exit effectiveness. Counter-flow and cross-flow arrangements differ in flow direction.

Question 17Mechanical Engineering

A component made of a material with a fatigue strength of 200 MPa at 10⁷ cycles is subjected to a fully reversed stress amplitude of 150 MPa. What does this indicate?

  1. The component is expected to survive indefinitely if no other damage occurs Correct answer.
  2. The fatigue strength is exceeded
  3. Failure will occur before 10⁷ cycles
  4. The component will yield on the first cycle

Explanation

Because the applied stress amplitude is below the fatigue strength at 10⁷ cycles, the component lies within the endurance region and is expected to survive indefinitely under that loading. Yielding and immediate failure require stresses near or above yield.

Question 18Mechanical Engineering

A cantilever of length 2 m carries a uniformly distributed load of 5 kN/m over its full length. What is the maximum bending moment at the fixed end?

  1. 40 kN·m
  2. 5 kN·m
  3. 10 kN·m Correct answer.
  4. 20 kN·m

Explanation

For a cantilever with a uniformly distributed load w over length L, the fixed-end moment is wL²/2 = 5 × 2²/2 = 10 kN·m. The total load is 10 kN acting at midspan, one metre from the support.

Question 19Mechanical Engineering

In a vapour-compression refrigeration cycle, the function of the expansion valve is to:

  1. Compress the refrigerant vapour
  2. Increase the refrigerant pressure before the condenser
  3. Remove moisture from the refrigerant
  4. Reduce refrigerant pressure and temperature before the evaporator Correct answer.

Explanation

The expansion valve throttles the refrigerant from condenser pressure to evaporator pressure, causing a temperature drop so it can absorb heat in the evaporator. Compression occurs in the compressor, and pressure rise occurs in the compressor, not the valve.

Question 20Mechanical Engineering

A steel bar of length 1 m and cross-section 200 mm² is subjected to a tensile load of 40 kN. Given E = 200 GPa, what is the elastic elongation?

  1. 1.0 mm Correct answer.
  2. 0.1 mm
  3. 0.01 mm
  4. 10 mm

Explanation

Stress is 40 000 / 200 = 200 MPa, and strain is 200/200 000 = 0.001. Multiplying by the 1000 mm length gives an elongation of 1.0 mm.

Question 21Mechanical Engineering

Which failure mode is specifically addressed by designing a pressure vessel to the 'leak-before-break' criterion?

  1. Catastrophic fast fracture from a through-thickness crack Correct answer.
  2. General yielding of the shell
  3. Creep rupture at low temperature
  4. Local buckling of the wall

Explanation

Leak-before-break ensures that a growing crack penetrates the wall and causes a detectable leak before it reaches a critical size for fast fracture. It does not address general yielding, buckling, or creep.

Question 22Mechanical Engineering

A flat belt drive has a coefficient of friction of 0.3 and a contact angle of 2.5 rad. Using the belt friction relation, what is the ratio of tight-side to slack-side tension at the point of slip?

  1. 1.35
  2. 7.39
  3. 4.48
  4. 2.12 Correct answer.

Explanation

The limiting tension ratio is e^(μθ) = e^(0.3 × 2.5) = e^0.75 ≈ 2.12. The other values correspond to incorrect exponent arithmetic.

Question 23Mechanical Engineering

In a shell-and-tube heat exchanger, adding baffles on the shell side primarily serves to:

  1. Reduce the tube-side pressure drop
  2. Prevent thermal expansion of the tubes
  3. Increase the shell-side heat transfer coefficient by promoting cross-flow Correct answer.
  4. Increase the overall length of the exchanger

Explanation

Baffles direct the shell-side fluid across the tube bundle, raising velocity and turbulence and thus the shell-side heat transfer coefficient. They increase shell-side pressure drop rather than reduce it, and they do not control thermal expansion.

Question 24Mechanical Engineering

A simply supported beam of rectangular cross-section has depth doubled while the width is halved. How does the maximum bending stress change for the same bending moment?

  1. It quadruples
  2. It remains unchanged
  3. It halves Correct answer.
  4. It doubles

Explanation

Section modulus is bh²/6. Halving b and doubling h multiplies the modulus by (1/2) × 4 = 2, so the stress σ = M/Z is halved. The depth term dominates because it is squared.

Question 25Mechanical Engineering

A pump is required to deliver water against a static head of 20 m with a friction loss of 5 m at the design flow. If the pump efficiency is 70 %, what approximate shaft power is needed for 0.01 m³/s of water? (ρ = 1000 kg/m³, g = 9.81 m/s²)

  1. 3.50 kW Correct answer.
  2. 5.00 kW
  3. 2.45 kW
  4. 4.20 kW

Explanation

Total head is 25 m, so hydraulic power is ρgQH = 1000 × 9.81 × 0.01 × 25 ≈ 2453 W. Dividing by the 0.70 efficiency gives about 3.50 kW of shaft power.

Question 26Mechanical Engineering

A single-acting reciprocating pump has a cylinder bore of 150 mm and a stroke of 300 mm and runs at 60 strokes per minute. Taking π as 3.142, what is the theoretical discharge in m³/s?

  1. 0.01060 m³/s
  2. 0.00265 m³/s
  3. 0.00530 m³/s Correct answer.
  4. 0.03180 m³/s

Explanation

The swept volume per stroke is the bore area times the stroke: (π/4)(0.150)² × 0.300 = 0.00530 m³. A single-acting pump delivers this volume once per revolution, so at 60 strokes per minute (1 stroke per second) the theoretical discharge equals 0.00530 m³/s.

Question 27Mechanical Engineering

Which material property is the most direct measure of a component's resistance to the initiation of a fatigue crack under repeated stress cycles?

  1. Endurance limit Correct answer.
  2. Thermal conductivity
  3. Modulus of resilience
  4. Poisson's ratio

Explanation

The endurance limit is the stress amplitude below which a material survives a very large number of cycles without fatigue failure, so it directly expresses resistance to crack initiation under cyclic loading. Properties such as resilience, Poisson's ratio and conductivity describe elastic energy storage, lateral strain and heat transfer respectively, none of which govern fatigue initiation.

Question 28Mechanical Engineering

A shaft transmits 15 kW at 300 rev/min. Taking π as 3.142, what torque is carried by the shaft?

  1. 50 N·m
  2. 477 N·m Correct answer.
  3. 159 N·m
  4. 2865 N·m

Explanation

Power equals torque times angular velocity, with ω = 2πN/60 = 2 × 3.142 × 300/60 = 31.42 rad/s. Torque is therefore 15 000/31.42 = 477 N·m.

Question 29Mechanical Engineering

In a four-stroke internal combustion engine, which valve event is deliberately timed to occur before bottom dead centre during the power stroke?

  1. Injection in a petrol engine
  2. Exhaust valve opening Correct answer.
  3. Ignition in a diesel engine
  4. Inlet valve opening

Explanation

The exhaust valve opens before bottom dead centre so that the burnt gases can blow down while cylinder pressure is still above exhaust pressure, reducing the work needed to push out the remaining gas. Inlet opening, ignition and injection all occur around top dead centre regions rather than before bottom dead centre of the power stroke.

Question 30Mechanical Engineering

Which type of steel is specified for a large gear rim that must combine a hard, wear-resistant tooth surface with a tough, shock-resistant core?

  1. Free-cutting mild steel
  2. Grey cast iron
  3. Case-hardening steel Correct answer.
  4. Austenitic stainless steel

Explanation

Case-hardening steel is a low-carbon steel that can be carburised and hardened so the surface becomes hard and wear resistant while the low-carbon core stays tough. Free-cutting mild steel and austenitic stainless steel cannot be surface hardened to a comparable degree, and grey cast iron is brittle and not a steel grade.

Question 31Mechanical Engineering

A beam is loaded by a concentrated force applied at a point. Which internal quantity changes abruptly at that point along the beam?

  1. Bending moment
  2. Shear force Correct answer.
  3. Slope
  4. Deflection

Explanation

A concentrated point load produces a step change in the shear force diagram at the load position, because the shear must jump by the magnitude of the applied load. Bending moment, deflection and slope remain continuous at that point, although the moment diagram shows a change of gradient.

Question 32Mechanical Engineering

A hydraulic cylinder with a piston diameter of 80 mm is to produce an extending force of 20 kN. What oil pressure is required?

  1. 15.9 MPa
  2. 0.40 MPa
  3. 1.59 MPa
  4. 3.98 MPa Correct answer.

Explanation

Piston area is (π/4)(0.080)² = 5.027 × 10⁻³ m². Pressure equals force divided by area, giving 20 000/5.027 × 10⁻³ = 3.98 × 10⁶ Pa, or 3.98 MPa.

Question 33Mechanical Engineering

Which heat-treatment process involves holding steel at a suitable temperature and then cooling it in still air to relieve internal stresses and improve machinability?

  1. Normalising Correct answer.
  2. Austempering
  3. Quenching
  4. Tempering

Explanation

Normalising heats steel above its critical range and cools it in still air, producing a finer, more uniform ferrite-pearlite structure with reduced internal stress and better machinability. Quenching uses a rapid quench to form martensite, tempering reheats hardened steel, and austempering holds at a bainite transformation temperature.

Question 34Mechanical Engineering

A rectangular key of width 12 mm and length 40 mm connects a shaft to a hub and transmits a torque of 200 N·m at a shaft radius of 25 mm. What is the average shear stress on the key?

  1. 33.3 MPa
  2. 8.3 MPa
  3. 4.2 MPa
  4. 16.7 MPa Correct answer.

Explanation

The tangential force at the shaft surface is torque divided by radius: 200/0.025 = 8000 N. The shear area resisting this force is the key width times its length, 0.012 × 0.040 = 4.8 × 10⁻⁴ m², giving a shear stress of 8000/4.8 × 10⁻⁴ = 16.7 MPa.

Question 35Mechanical Engineering

In a centrifugal pump installation, cavitation is most likely to occur when:

  1. The available net positive suction head falls below the value required by the pump Correct answer.
  2. The discharge valve is throttled while the suction valve is fully open
  3. The pump runs at a speed below its design value
  4. The delivery pipe is oversized relative to the suction pipe

Explanation

Cavitation occurs when the local static pressure at the impeller eye drops to the vapour pressure of the liquid, which happens when the net positive suction head available is less than that required by the pump. Throttling the discharge, reducing speed or oversizing the delivery line either reduces flow demand or has no direct bearing on suction pressure at the impeller eye.

Question 36Mechanical Engineering

A steel rod of length 500 mm is fixed between two rigid supports at 20 °C. If the temperature rises to 80 °C, what compressive stress develops? Take E = 200 GPa and α = 12 × 10⁻⁶ per °C.

  1. 24 MPa
  2. 72 MPa
  3. 144 MPa Correct answer.
  4. 288 MPa

Explanation

The restrained thermal strain is αΔT = 12 × 10⁻⁶ × 60 = 7.2 × 10⁻⁴. Because the ends cannot move, the elastic stress is E times this strain: 200 × 10⁹ × 7.2 × 10⁻⁴ = 144 × 10⁶ Pa, or 144 MPa in compression.

Question 37Mechanical Engineering

A vapour-compression refrigeration system using R134a operates with an evaporating temperature of −10 °C and a condensing temperature of 40 °C. Which change would reduce the coefficient of performance of the cycle?

  1. Reducing the pressure drop in the suction line
  2. Lowering the condensing temperature while keeping evaporation unchanged
  3. Raising the condensing temperature while keeping evaporation unchanged Correct answer.
  4. Raising the evaporating temperature while keeping condensation unchanged

Explanation

A higher condensing temperature increases the compressor pressure ratio and the enthalpy of compression, so more work is required for the same refrigeration effect and the coefficient of performance falls. Lowering condensation or raising evaporation reduces the pressure ratio, and reducing suction pressure drop reduces compressor work, all of which improve performance.

Question 38Mechanical Engineering

A spur gear pair has a module of 4 mm, a pinion with 18 teeth and a wheel with 54 teeth. Using the standard addendum of one module, what is the addendum circle diameter of the wheel?

  1. 216 mm
  2. 224 mm Correct answer.
  3. 232 mm
  4. 108 mm

Explanation

The pitch circle diameter of the wheel is module times teeth: 4 × 54 = 216 mm. The addendum circle diameter adds twice the addendum, so 216 + 2 × 4 = 224 mm.

Question 39Mechanical Engineering

A thick-walled cylinder is designed using the Lamé equations. At the bore of a cylinder under internal pressure only, which statement describes the stress state?

  1. The hoop stress is compressive and reaches its maximum at the bore
  2. The radial stress is tensile and reaches its maximum at the bore
  3. The hoop stress is uniform through the wall thickness
  4. The hoop stress is tensile and reaches its maximum value at the bore Correct answer.

Explanation

For internal pressure only, the Lamé solution gives a tensile hoop stress that is greatest at the bore and falls towards the outside, while the radial stress is compressive and equal to the internal pressure at the bore. The stress distribution is therefore not uniform through the wall.

Question 40Mechanical Engineering

A flat plate of area 0.5 m² slides over a stationary surface separated by an oil film 0.5 mm thick. If the oil dynamic viscosity is 0.2 Pa·s and the plate moves at 1.5 m/s, what is the viscous drag force?

  1. 150 N
  2. 30 N
  3. 300 N Correct answer.
  4. 600 N

Explanation

For a thin film with linear velocity gradient, shear stress is μU/h = 0.2 × 1.5/0.0005 = 600 Pa. The drag force is shear stress times area: 600 × 0.5 = 300 N.

Question 41Mechanical Engineering

In a mechanical assembly, a dowel pin is used in addition to bolts to locate two components. What is the primary function of the dowel pin?

  1. To carry transverse shear loads and maintain accurate relative location Correct answer.
  2. To allow controlled thermal expansion between the parts
  3. To prevent the bolt from rotating during tightening
  4. To apply clamping preload to the joint

Explanation

Dowel pins are fitted into reamed holes so they take transverse shear and locate the parts precisely, protecting the bolts from shear and preventing relative slip. Clamping preload is provided by the bolts themselves, and dowels restrain rather than permit thermal movement.

Question 42Mechanical Engineering

A simply supported beam of span 4 m carries a central point load of 12 kN. What is the maximum bending moment?

  1. 24 kN·m
  2. 48 kN·m
  3. 12 kN·m Correct answer.
  4. 6 kN·m

Explanation

For a central point load on a simply supported beam, the maximum moment is PL/4 = 12 × 4/4 = 12 kN·m at mid-span. The reactions are each 6 kN, and the moment at mid-span is 6 × 2 = 12 kN·m.

Question 43Mechanical Engineering

A composite wall consists of two layers in series, the first with thermal resistance 0.02 K/W and the second with 0.06 K/W. If the temperature difference across the whole wall is 80 K, what is the heat transfer rate?

  1. 4000 W
  2. 1000 W Correct answer.
  3. 400 W
  4. 1333 W

Explanation

Resistances in series add, giving a total of 0.08 K/W. The heat transfer rate is the temperature difference divided by the total resistance: 80/0.08 = 1000 W, and the same heat flows through both layers.

Question 44Mechanical Engineering

Which statement best explains why a helical compression spring is usually designed so that the coils do not close solid under the maximum working load?

  1. Solid length would increase the spring rate and reduce the natural frequency
  2. Solid length would eliminate the need for end grinding
  3. Solid length would prevent further deflection and cause a sudden rise in stiffness and stress Correct answer.
  4. Solid length would reverse the direction of the applied load

Explanation

When the coils touch, the spring becomes effectively solid, so additional load is carried by direct compression of the wire rather than by torsion, causing a sharp increase in stiffness and local stress. The spring rate before solid contact depends on wire diameter, coil diameter and active coils, not on the solid length.

Question 45Mechanical Engineering

A pipe of internal diameter 50 mm carries water at a mean velocity of 2 m/s. Taking the density as 1000 kg/m³, what is the mass flow rate?

  1. 1.96 kg/s
  2. 0.157 kg/s
  3. 3.93 kg/s Correct answer.
  4. 7.85 kg/s

Explanation

The cross-sectional area is (π/4)(0.050)² = 1.963 × 10⁻³ m², so the volume flow is 1.963 × 10⁻³ × 2 = 3.93 × 10⁻³ m³/s. Multiplying by density gives a mass flow of 3.93 kg/s.

Question 46Mechanical Engineering

In a bolted flange joint subjected to a fluctuating external load, which measure most improves the fatigue life of the bolt?

  1. Increasing the bolt preload so the joint stays closed and the bolt sees a smaller load fluctuation Correct answer.
  2. Increasing the bolt length without changing the grip length
  3. Using a thinner flange to increase joint flexibility
  4. Reducing the bolt preload so the bolt carries more of the external load

Explanation

A high preload keeps the joint faces closed so that most of the external load is carried by the clamped members rather than the bolt, reducing the alternating stress in the bolt and improving fatigue life. Lower preload or a more flexible joint increases the bolt's share of the fluctuating load.

Question 47Mechanical Engineering

A shaft is supported by two deep-groove ball bearings and rotates at 1500 rev/min. Which bearing arrangement best accommodates thermal expansion of the shaft while locating it axially?

  1. One bearing fixed axially and the other free to float in its housing Correct answer.
  2. Both bearings fixed axially in their housings
  3. Both bearings free to float axially
  4. Both bearings preloaded against each other with no float

Explanation

A fixed-and-floating arrangement locates the shaft axially at one bearing while allowing the other to slide, so thermal growth does not induce large axial loads. Fixing both bearings or preloading them without float would generate damaging thrust when the shaft expands.

Question 48Mechanical Engineering

A closed-loop control system has a forward-path transfer function of 10/(s + 2) and unity negative feedback. What is the steady-state error to a unit step input?

  1. 0
  2. 0.167 Correct answer.
  3. 0.100
  4. 0.833

Explanation

The closed-loop transfer function is 10/(s + 12), so the steady-state output to a unit step is 10/12 = 0.833 and the error is 1 − 0.833 = 0.167. Equivalently, the position error constant is Kp = 10/2 = 5, giving error 1/(1 + Kp) = 1/6.

Question 49Mechanical Engineering

A pressure vessel is to be designed with the 'leak-before-break' criterion. Which combination of conditions is required for the criterion to be satisfied?

  1. A crack that grows only by fatigue and never by stress corrosion
  2. A through-thickness crack that leaks at a length shorter than the critical crack length for unstable fracture Correct answer.
  3. A surface crack that remains stable until the wall yields over its full thickness
  4. A wall thickness that exceeds the critical crack length by a factor of two

Explanation

Leak-before-break requires that a growing crack penetrates the wall and produces a detectable leak before it reaches the critical length for fast fracture. This depends on the fracture toughness, the applied stress and the wall thickness being such that the critical crack length exceeds the wall thickness.

Question 50Mechanical Engineering

A thin-walled tube of mean radius 40 mm and wall thickness 2 mm is subjected to an internal pressure of 3 MPa. What are the approximate hoop and longitudinal stresses?

  1. Hoop 120 MPa, longitudinal 60 MPa
  2. Hoop 60 MPa, longitudinal 15 MPa
  3. Hoop 60 MPa, longitudinal 30 MPa Correct answer.
  4. Hoop 30 MPa, longitudinal 60 MPa

Explanation

For a thin cylinder, hoop stress is pr/t = 3 × 40/2 = 60 MPa and longitudinal stress is pr/(2t) = 30 MPa. The hoop stress is twice the longitudinal stress because the longitudinal stress must balance the pressure load on the end caps over twice the metal area.