I85PREP
⌘ K
HKIE Professional Assessment - Mechanical Discipline study materials
HKIE Professional Assessment - Mechanical Discipline study resources

HKIE Professional Assessment - Mechanical Discipline practice questions

One question at a time. Build your HKIE Professional Assessment - Mechanical Discipline understanding.

First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A closed system undergoes a reversible adiabatic process. Which statement correctly describes the entropy change of the system?

  1. The entropy of the system remains constant. Correct answer.
  2. The entropy of the system increases.
  3. The entropy change depends on the path followed.
  4. The entropy of the system decreases.

Explanation

For any reversible process the entropy change is the integral of dQ/T. In an adiabatic process dQ equals zero throughout, so the integral vanishes and entropy stays constant; such a process is called isentropic.

Question 2Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

In a steady-flow adiabatic nozzle operating with negligible changes in potential energy, which energy balance correctly relates inlet and outlet states?

  1. h1 = h2 + V2²/2
  2. h1 + V1²/2 = h2 + V2²/2 Correct answer.
  3. h1 + V1²/2 + q = h2 + V2²/2 + w
  4. h1 + V1²/2 = h2 + V2²/2 + w

Explanation

The steady-flow energy equation gives q − w = (h2 − h1) + (V2² − V1²)/2 + g(z2 − z1). For an adiabatic nozzle with no work, negligible potential change, this reduces to h1 + V1²/2 = h2 + V2²/2, showing enthalpy drop converts to kinetic energy.

Question 3Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

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

  1. 1.00
  2. 0.25
  3. 0.50 Correct answer.
  4. 0.75

Explanation

Carnot efficiency is given by 1 − Tc/Th when temperatures are absolute. Substituting gives 1 − 300/600 = 0.50, so half of the heat supplied is converted to work.

Question 4Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

Water flows through a horizontal pipe whose diameter reduces from 200 mm to 100 mm. If the velocity in the larger section is 1 m/s, what is the velocity in the smaller section for steady incompressible flow?

  1. 4.0 m/s Correct answer.
  2. 2.0 m/s
  3. 0.25 m/s
  4. 0.50 m/s

Explanation

Continuity for incompressible flow requires A1V1 = A2V2. The area ratio is proportional to the square of the diameter ratio, (200/100)² = 4, so the velocity increases fourfold to 4 m/s.

Question 5Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

In a fully developed laminar pipe flow, the Darcy friction factor f is related to the Reynolds number by which expression?

  1. f = 0.316/Re^0.25
  2. f = 16/Re
  3. f = 0.079/Re^0.25
  4. f = 64/Re Correct answer.

Explanation

For fully developed laminar flow in a circular pipe the Hagen–Poiseuille result yields a Darcy friction factor equal to 64/Re. The 0.316 and 0.079 forms are Blasius-type correlations for turbulent flow.

Question 6Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A simply supported beam of span L carries a central point load W. What is the maximum bending moment?

  1. WL/8
  2. WL/4 Correct answer.
  3. WL
  4. WL/2

Explanation

The reactions are W/2 at each support, and the maximum moment occurs at midspan where the shear changes sign. Taking moments about midspan gives (W/2)(L/2) = WL/4.

Question 7Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

For a circular shaft of diameter d transmitting torque T, which expression gives the maximum shear stress?

  1. 32T/(πd⁴)
  2. Td/4
  3. 16T/(πd³) Correct answer.
  4. 8T/(πd³)

Explanation

Torsion theory gives τ = Tr/J, and for a solid circular section J = πd⁴/32 with r = d/2. Substituting yields τmax = 16T/(πd³).

Question 8Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A mass–spring system has natural frequency ωn. If the mass is quadrupled while the spring stiffness is unchanged, the new natural frequency becomes which multiple of the original?

  1. One quarter
  2. Half Correct answer.
  3. Double
  4. Unchanged

Explanation

The natural frequency is ωn = √(k/m). Quadrupling m increases the denominator under the root by a factor of four, so ωn falls to one half of its original value.

Question 9Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

Steam enters a turbine at 3 MPa and 400 °C and leaves as saturated vapour at 50 kPa. Which quantity is obtained directly from the steady-flow energy equation when kinetic and potential energy changes and heat losses are neglected?

  1. The specific work output equals the entropy rise between inlet and outlet.
  2. The specific work output equals the pressure ratio between inlet and outlet.
  3. The specific work output equals the temperature drop between inlet and outlet.
  4. The specific work output equals the enthalpy drop between inlet and outlet. Correct answer.

Explanation

With negligible kinetic and potential changes and no heat transfer, the steady-flow energy equation reduces to w = h1 − h2. Work output therefore equals the specific enthalpy drop across the turbine.

Question 10Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A refrigerator operates with a coefficient of performance of 3 and extracts 600 kJ of heat from the cold space per cycle. How much work input is required per cycle?

  1. 1800 kJ
  2. 100 kJ
  3. 200 kJ Correct answer.
  4. 300 kJ

Explanation

Coefficient of performance for a refrigerator is COP = Qc/W, so W = Qc/COP = 600/3 = 200 kJ per cycle. The heat rejected to the warm space is then 800 kJ.

Question 11Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A thin-walled cylindrical pressure vessel of internal diameter D and wall thickness t is subject to internal pressure p. Which statement about the stresses in the wall is correct when t is much smaller than D?

  1. The hoop stress is twice the longitudinal stress. Correct answer.
  2. The hoop stress is four times the longitudinal stress.
  3. The longitudinal stress is twice the hoop stress.
  4. The hoop and longitudinal stresses are equal.

Explanation

For a thin-walled cylinder the hoop stress is pD/(2t) and the longitudinal stress is pD/(4t). The hoop stress is therefore double the longitudinal stress.

Question 12Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A steel bar of length 2 m is heated uniformly by 50 K. Taking the coefficient of linear expansion as 12 × 10⁻⁶ per K, what is the free thermal expansion?

  1. 1.2 mm Correct answer.
  2. 0.6 mm
  3. 2.4 mm
  4. 6.0 mm

Explanation

Free thermal strain is αΔT and elongation is αΔT L. Substituting gives 12 × 10⁻⁶ × 50 × 2 = 1.2 × 10⁻³ m, or 1.2 mm.

Question 13Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A body of mass 5 kg moves in a straight line with velocity v = 3t² m/s. What is the net force acting on it at t = 2 s?

  1. 30 N
  2. 12 N
  3. 60 N Correct answer.
  4. 120 N

Explanation

Newton's second law requires the acceleration, obtained by differentiating velocity: a = dv/dt = 6t. At t = 2 s, a = 12 m/s², so F = ma = 5 × 12 = 60 N.

Question 14Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A damped single-degree-of-freedom system has a damping ratio of 0.1. Approximately what is the ratio of successive peak amplitudes in free vibration?

  1. 0.90
  2. 0.99
  3. 0.53 Correct answer.
  4. 0.73

Explanation

The logarithmic decrement is δ = 2πζ/√(1 − ζ²). With ζ = 0.1 this gives about 0.631, and the amplitude ratio per cycle is e^(−δ) ≈ 0.53.

Question 15Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

Water flows through a horizontal pipe and passes through a sudden enlargement. Neglecting losses, which statement best describes the pressure change across the enlargement?

  1. Pressure rises because velocity decreases. Correct answer.
  2. Pressure falls because velocity decreases.
  3. Pressure falls because the flow separates at the enlargement.
  4. Pressure is unchanged because the pipe is horizontal.

Explanation

Applying Bernoulli's equation along a horizontal streamline, a decrease in velocity must be accompanied by an increase in static pressure. The enlargement converts kinetic energy into pressure energy.

Question 16Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

In a hydrostatic system, a vertical rectangular gate of height h and width b retains water on one side up to its full height. What is the resultant hydrostatic force on the gate?

  1. ρg b h²
  2. ρg b h
  3. ½ ρg b h² Correct answer.
  4. ⅓ ρg b h²

Explanation

The pressure varies linearly from zero at the surface to ρgh at the base, so the average pressure is ½ρgh. Multiplying by the gate area bh gives a resultant force of ½ρg b h².

Question 17Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A beam of rectangular cross-section has second moment of area I about its neutral axis. If the depth is doubled while the width is unchanged, by what factor does I increase?

  1. 8 Correct answer.
  2. 2
  3. 6
  4. 4

Explanation

For a rectangle I = bd³/12, so I varies with the cube of the depth. Doubling the depth multiplies I by 2³ = 8.

Question 18Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A gas undergoes an isothermal reversible expansion from volume V1 to V2 at temperature T. What is the work done by the gas per unit mass for an ideal gas?

  1. R(T2 − T1)
  2. Cv(T2 − T1)
  3. P(V2 − V1)
  4. RT ln(V2/V1) Correct answer.

Explanation

For a reversible isothermal process in an ideal gas, w = ∫P dv with P = RT/v, giving w = RT ln(V2/V1). Because temperature is constant, no temperature-difference terms appear.

Question 19Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A particle moves in a circular path of radius 2 m at a constant speed of 6 m/s. What is the magnitude of its centripetal acceleration?

  1. 9 m/s²
  2. 18 m/s² Correct answer.
  3. 3 m/s²
  4. 12 m/s²

Explanation

Centripetal acceleration for uniform circular motion is v²/r. Substituting gives 36/2 = 18 m/s², directed toward the centre of the path.

Question 20Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A horizontal cantilever of length L carries a point load W at its free end. What is the deflection at the free end?

  1. WL²/(2EI)
  2. WL³/(3EI) Correct answer.
  3. WL³/(48EI)
  4. WL³/(8EI)

Explanation

Integrating the bending moment for an end-loaded cantilever and applying the fixed-end boundary conditions gives an end deflection of WL³/(3EI). The other denominators correspond to different support and loading conditions.

Question 21Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

Air flows isentropically through a converging nozzle from a reservoir at 400 K. At a section where the Mach number is 1, what is the static temperature? Take γ = 1.4.

  1. 400 K
  2. 200 K
  3. 333 K Correct answer.
  4. 240 K

Explanation

The isentropic relation gives T0/T = 1 + (γ − 1)M²/2. At M = 1 with γ = 1.4 this ratio is 1.2, so T = 400/1.2 ≈ 333 K.

Question 22Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A Rankine cycle operates with steam entering the turbine as dry saturated vapour at 2 MPa and condensing at 10 kPa. Which modification raises the cycle efficiency without changing the condenser pressure?

  1. Adding a throttling valve before the turbine
  2. Increasing the condenser pressure
  3. Superheating the steam before the turbine Correct answer.
  4. Reducing the boiler pressure

Explanation

Superheating raises the mean temperature of heat addition in the boiler while the condenser temperature is fixed, so the net work increases relative to heat input and efficiency rises. It also reduces turbine exhaust wetness.

Question 23Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A thin-walled spherical pressure vessel of radius r and thickness t contains gas at pressure p. A strain gauge on the outer surface reads ε in any direction. Which relationship gives the internal pressure, taking E and ν as the elastic constants?

  1. p = Etε/(r(1 + ν))
  2. p = 2Etε/(r(1 − ν)) Correct answer.
  3. p = Etε/(2r(1 − ν))
  4. p = Etε/(r(1 − ν))

Explanation

The membrane stress in a thin sphere is σ = pr/(2t). Surface strain under equal biaxial stress is ε = σ(1 − ν)/E. Eliminating σ gives p = 2Etε/(r(1 − ν)).

Question 24Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A two-degree-of-freedom system has mass and stiffness matrices such that its natural frequencies are found from |K − ω²M| = 0. Which statement about the mode shapes is correct for a symmetric system with distinct natural frequencies?

  1. Mode shapes are identical to the static deflection curve.
  2. Mode shapes are orthogonal with respect to the mass matrix. Correct answer.
  3. Mode shapes depend on the initial conditions.
  4. Mode shapes are always parallel to each other.

Explanation

For distinct natural frequencies, mode shapes satisfy φiᵀMφj = 0 for i ≠ j and are also orthogonal with respect to the stiffness matrix. This orthogonality allows the equations of motion to be decoupled into independent modal coordinates.

Question 25Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

In a laminar boundary layer over a flat plate, the Blasius solution gives a boundary layer thickness that grows with distance x from the leading edge. Which proportionality correctly describes the growth?

  1. δ ∝ x^(1/2) Correct answer.
  2. δ ∝ x^(2/3)
  3. δ ∝ x^(1/3)
  4. δ ∝ x

Explanation

The Blasius similarity solution shows δ/x ∝ Re_x^(−1/2), and since Re_x is proportional to x, the thickness grows as the square root of distance from the leading edge.

Question 26Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A closed system receives 250 kJ of heat while its internal energy rises by 90 kJ. What is the magnitude and direction of the boundary work?

  1. 160 kJ done by the system on the surroundings Correct answer.
  2. 340 kJ done by the system on the surroundings
  3. 160 kJ done on the system by the surroundings
  4. 340 kJ done on the system by the surroundings

Explanation

The first law for a closed system gives Q = ΔU + W, so W = 250 − 90 = 160 kJ of work delivered outward. A positive W means the system expands and does work on its surroundings. The energy balance fixes both the magnitude and the sign, not just the size of the difference.

Question 27Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A Newtonian oil of dynamic viscosity 0.5 Pa·s fills the 1 mm gap between a fixed plate and a 0.2 m² plate moving at 0.6 m/s parallel to it. Assuming a linear velocity profile, what force is needed to maintain the motion?

  1. 600 N
  2. 6 N
  3. 0.06 N
  4. 60 N Correct answer.

Explanation

Newton's law of viscosity gives shear stress τ = μ·(du/dy), and with a linear profile du/dy = 0.6/0.001 = 600 s⁻¹. Hence τ = 0.5 × 600 = 300 Pa, and the force is τA = 300 × 0.2 = 60 N. The force scales linearly with area, viscosity and speed, and inversely with gap.

Question 28Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

In a steady-flow adiabatic nozzle with negligible inlet velocity, air enters at 400 K and leaves at 300 K. Taking cp = 1.005 kJ/(kg·K), what is the exit velocity?

  1. 448 m/s Correct answer.
  2. 1005 m/s
  3. 200 m/s
  4. 100 m/s

Explanation

The steady-flow energy equation for an adiabatic nozzle with negligible inlet velocity reduces to h₁ = h₂ + V₂²/2. With constant specific heat, V₂ = √(2cp(T₁ − T₂)) = √(2 × 1005 × 100) ≈ 448 m/s. The temperature drop, not the pressure ratio, sets the exit kinetic energy.

Question 29Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

Water flows steadily through a horizontal pipe that narrows from 100 mm to 50 mm diameter. If the pressure in the larger section is 200 kPa and losses are neglected, what is the pressure in the smaller section? Take ρ = 1000 kg/m³.

  1. 150 kPa
  2. 170 kPa
  3. 50 kPa Correct answer.
  4. 185 kPa

Explanation

Continuity gives V₂ = 4V₁ because the area ratio is four, and Bernoulli for a horizontal pipe gives p₁ − p₂ = ½ρ(V₂² − V₁²). Combining with the flow rate through the 100 mm section, V₁ = 1.0 m/s and V₂ = 4.0 m/s, so the pressure drop is ½ × 1000 × 15 = 7.5 kPa. The exit pressure is therefore 200 − 7.5 ≈ 192 kPa, and of the listed values only 185 kPa is consistent with a modest drop for these velocities.

Question 30Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A solid circular shaft of diameter 60 mm transmits 50 kW at 300 rev/min. What is the maximum shear stress in the shaft?

  1. 7.5 MPa
  2. 15.0 MPa Correct answer.
  3. 60.0 MPa
  4. 30.0 MPa

Explanation

Torque follows from power, T = P/ω, with ω = 2π × 300/60 ≈ 31.4 rad/s, giving T ≈ 1592 N·m. For a solid shaft τmax = 16T/(πd³) = 16 × 1592/(π × 0.06³) ≈ 15 MPa. Shear stress rises with the cube of the diameter for a given torque, so small errors in d matter greatly.

Question 31Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A simply supported beam of span 6 m carries a uniformly distributed load of 4 kN/m over its full length. What is the maximum bending moment?

  1. 12 kN·m
  2. 36 kN·m
  3. 24 kN·m
  4. 18 kN·m Correct answer.

Explanation

For a simply supported beam under a uniform load w over span L, the maximum moment is wL²/8 at midspan. Here wL²/8 = 4 × 36/8 = 18 kN·m. The total load wL = 24 kN is not itself the moment, and the reaction is half of it.

Question 32Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A thin-walled tube of mean radius 40 mm and wall thickness 2 mm is subjected to an internal pressure of 5 MPa. What is the hoop stress in the wall?

  1. 100 MPa Correct answer.
  2. 200 MPa
  3. 50 MPa
  4. 25 MPa

Explanation

For a thin-walled cylinder the hoop stress is σθ = pr/t, using the internal radius. Thus σθ = 5 × 40/2 = 100 MPa, which is tensile and twice the longitudinal stress pr/(2t). The thin-wall assumption requires t to be small compared with r, which is satisfied here.

Question 33Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A particle is projected at 20 m/s at 30° above the horizontal on level ground. Neglecting air resistance, what horizontal distance does it travel before landing? Take g = 9.81 m/s².

  1. 35.3 m Correct answer.
  2. 17.7 m
  3. 20.4 m
  4. 40.8 m

Explanation

The range on level ground is R = v²sin2θ/g = 400 × sin60°/9.81 ≈ 35.3 m. The horizontal component of velocity is constant while the vertical motion determines the time of flight. Doubling the launch speed quadruples the range.

Question 34Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A flywheel in the form of a uniform disc of mass 50 kg and radius 0.4 m spins at 20 rad/s. What is its rotational kinetic energy?

  1. 3.2 kJ
  2. 1.6 kJ Correct answer.
  3. 0.8 kJ
  4. 0.4 kJ

Explanation

For a uniform disc the mass moment of inertia about its axis is I = ½mr² = ½ × 50 × 0.16 = 4 kg·m². Rotational kinetic energy is ½Iω² = ½ × 4 × 400 = 800 J, so the closest listed value consistent with the disc formula is 1.6 kJ only if the full mr² is used, hence the correct treatment gives 0.8 kJ. Care is needed: with I = ½mr² the energy is 800 J.

Question 35Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A machine of mass 200 kg is mounted on isolators of total stiffness 800 kN/m. What is the natural frequency of the vertical vibration?

  1. 20.1 Hz
  2. 10.1 Hz Correct answer.
  3. 1.6 Hz
  4. 6.4 Hz

Explanation

The natural angular frequency is ωn = √(k/m) = √(800000/200) = √4000 ≈ 63.2 rad/s. Dividing by 2π gives fn ≈ 10.1 Hz. Using stiffness in kN/m without converting to N/m is a common source of error.

Question 36Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A simply supported beam of length L with flexural rigidity EI carries a uniformly distributed load w. What is the midspan deflection?

  1. 5wL³/(384EI)
  2. wL³/(48EI)
  3. wL⁴/(384EI)
  4. 5wL⁴/(384EI) Correct answer.

Explanation

Standard beam theory for a simply supported span under a uniform load gives a maximum deflection of 5wL⁴/(384EI) at midspan. The fourth power of span reflects the double integration of the bending moment and the double integration again for slope and deflection. Deflection is inversely proportional to EI.

Question 37Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A steel bar of cross-section 200 mm² is loaded axially by 40 kN. Taking E = 200 GPa, what is the elastic strain energy stored in a 1.5 m length?

  1. 120 J
  2. 30 J Correct answer.
  3. 15 J
  4. 60 J

Explanation

Strain energy for axial loading is U = F²L/(2AE). Here F = 40 000 N, A = 200 × 10⁻⁶ m² and E = 200 × 10⁹ Pa, giving U = (1.6 × 10⁹ × 1.5)/(2 × 200 × 10⁻⁶ × 200 × 10⁹) = 30 J. The energy grows with the square of the load but only linearly with length.

Question 38Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

Air at 300 K flows through a duct at Mach 2. Assuming γ = 1.4, what is the stagnation temperature?

  1. 420 K
  2. 360 K
  3. 540 K Correct answer.
  4. 300 K

Explanation

Stagnation temperature follows from T₀ = T(1 + (γ−1)M²/2). With M = 2 this factor is 1 + 0.2 × 4 = 1.8, so T₀ = 300 × 1.8 = 540 K. Stagnation temperature depends only on Mach number and static temperature, not on losses.

Question 39Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A single-degree-of-freedom system has a natural frequency of 5 Hz and a damping ratio of 0.05. What is the damped natural frequency?

  1. 5.25 Hz
  2. 5.00 Hz
  3. 4.99 Hz Correct answer.
  4. 4.75 Hz

Explanation

The damped natural frequency is fd = fn√(1 − ζ²). With ζ = 0.05 this gives √(1 − 0.0025) ≈ 0.99875, so fd ≈ 4.99 Hz. The shift is small for light damping but grows rapidly as ζ approaches unity.

Question 40Mechanical engineering science and analysis (thermodynamics, fluid mechanics, mechanics of solids, dynamics and vibrations)

A block of mass 10 kg rests on a horizontal surface with a coefficient of static friction of 0.4. A horizontal force of 30 N is applied. What is the friction force acting on the block? Take g = 9.81 m/s².

  1. 0 N
  2. 39.2 N
  3. 9.81 N
  4. 30 N Correct answer.

Explanation

The maximum static friction available is μsN = 0.4 × 10 × 9.81 ≈ 39.2 N. Since the applied 30 N is below this limit, the block does not move and static friction adjusts to balance the applied force exactly, giving 30 N. Friction equals the applied force only while the limit is not exceeded.

Question 41Design, specification and material selection of mechanical systems and components

A steel shaft is to be keyed to a hub for a light-duty drive. Which key type is intended mainly to locate the hub axially and transmit only very small torque?

  1. Woodruff key Correct answer.
  2. Taper key
  3. Parallel key
  4. Gib-head key

Explanation

A Woodruff key is a half-disc seated in a milled semicircular keyseat; it is commonly used for location and light torque, and its depth adjustment suits tapered shafts. Parallel and taper keys are the general load-carrying choices.

Question 42Design, specification and material selection of mechanical systems and components

In a bolted joint subjected to cyclic tension, which feature most improves fatigue life by reducing the alternating load carried by the bolt?

  1. Using a softer gasket to increase joint compliance
  2. Increasing the joint stiffness relative to the bolt stiffness Correct answer.
  3. Increasing the bolt diameter without changing preload
  4. Reducing the bolt preload to lower mean stress

Explanation

The bolt's share of an external load depends on the stiffness ratio; a stiffer joint (or more compliant bolt) reduces the alternating force the bolt sees. Higher preload also helps by keeping the joint closed, but raising joint stiffness is the classic fatigue-life measure.

Question 43Design, specification and material selection of mechanical systems and components

A plain carbon steel component must be surface hardened while retaining a tough core, and only the outer layer is to be heated. Which process is most appropriate?

  1. Induction hardening Correct answer.
  2. Normalising
  3. Full quench and temper
  4. Stress relieving

Explanation

Induction hardening heats only the surface layer by eddy currents before quenching, giving a hard case on a tough core. Full through-hardening would harden the whole section, and normalising or stress relieving do not raise surface hardness.

Question 44Design, specification and material selection of mechanical systems and components

A pump shaft runs at 1,500 rpm and delivers 15 kW. Ignoring losses, what is the approximate torque transmitted?

  1. 10 N·m
  2. 150 N·m
  3. 95 N·m Correct answer.
  4. 955 N·m

Explanation

Power equals torque times angular velocity, so torque is P divided by 2πn with n in revolutions per second. Here 15000 W divided by (2π × 25) gives about 95 N·m.

Question 45Design, specification and material selection of mechanical systems and components

Which bearing type is best suited to carry a heavy radial load combined with a small axial load on a shaft that also requires self-aligning capability?

  1. Thrust ball bearing
  2. Deep groove ball bearing
  3. Spherical roller bearing Correct answer.
  4. Cylindrical roller bearing

Explanation

Spherical roller bearings accommodate misalignment because of their barrel-shaped rollers and can carry heavy radial plus moderate axial loads. Cylindrical roller bearings carry heavy radial load but no axial load, and thrust bearings carry axial load only.

Question 46Design, specification and material selection of mechanical systems and components

For a gear pair transmitting power, which statement about the involute tooth profile is correct?

  1. It requires exact centre distance to maintain conjugate action
  2. It produces a constant pressure angle throughout the mesh
  3. It eliminates the need for backlash
  4. It gives a constant velocity ratio when the centre distance varies slightly Correct answer.

Explanation

The involute profile is conjugate for any centre distance, so the velocity ratio stays constant even if the centres shift a little. This tolerance to centre-distance variation is a principal reason for its universal use.

Question 47Design, specification and material selection of mechanical systems and components

A pressure vessel is to be fabricated from plate and must have good weldability and toughness at low temperature. Which material specification is most appropriate?

  1. A free-machining resulphurised steel
  2. A high-carbon tool steel
  3. A grey cast iron
  4. A fully killed fine-grain carbon-manganese steel with specified impact energy Correct answer.

Explanation

Fine-grain killed carbon-manganese steel with a guaranteed Charpy impact energy at the design minimum temperature is the standard choice for welded pressure equipment. Free-machining grades have high sulphur and poor weldability, and cast iron or tool steel are unsuitable for welded plate construction.

Question 48Design, specification and material selection of mechanical systems and components

In a flange coupling, the bolts are fitted in reamed holes rather than clearance holes. What is the primary purpose?

  1. To reduce the number of bolts required
  2. To allow angular misalignment
  3. To permit easier assembly
  4. To transmit torque through bolt shear rather than friction Correct answer.

Explanation

Fitted bolts bear on the reamed hole walls so torque is carried in shear by the bolts, giving a positive drive independent of flange friction. Clearance bolts rely on friction from tightening, which can slip under overload.

Question 49Design, specification and material selection of mechanical systems and components

Which surface treatment is applied to steel primarily to increase resistance to wear by diffusing nitrogen into the surface?

  1. Anodising
  2. Electroplating with chromium
  3. Galvanising
  4. Nitriding Correct answer.

Explanation

Nitriding diffuses nitrogen into the steel surface at relatively low temperature, forming hard nitrides that resist wear with minimal distortion. Anodising applies to aluminium, and galvanising and chromium plating are corrosion or decorative treatments.

Question 50Design, specification and material selection of mechanical systems and components

A cantilever beam of rectangular cross-section is loaded at its free end. If the section depth is doubled while width is unchanged, how does the maximum bending stress change for the same load?

  1. Halved Correct answer.
  2. Quartered
  3. Doubled
  4. Unchanged

Explanation

Bending stress is proportional to the section modulus, which for a rectangle rises with the square of depth. Doubling depth quadruples the modulus, so stress falls to one quarter.