Practice city guilds model questions vol1 engineering 2025 Past Questions

Question 1 View Details

A composite rod consists of two sections in series. Section A is steel, length \(1.2\ \text{m}\), coefficient of thermal expansion \(\alpha_1 = 12\times10^{-6}\ \text{°C}^{-1}\) and Young's modulus \(E_1 = 200\ \text{GPa}\). Section B is aluminium, length \(0.8\ \text{m}\), coefficient \(\alpha_2 = 23\times10^{-6}\ \text{°C}^{-1}\) and Young's modulus \(E_2 = 70\ \text{GPa}\). Both sections have the same circular cross‑section of area \(20\ \text{mm}^2\). The left end of the rod is fixed, and a linear spring of stiffness \(k = 5.0\times10^{5}\ \text{N\,m}^{-1}\) is attached to the free right end, resisting extension. The whole assembly is uniformly heated by \(\Delta T = 60\ \text{°C}\). Determine the compressive force in the spring after heating (assume static equilibrium).

A. 820 N

Correct B. 685 N

C. 750 N

D. 620 N

Correct Answer: B

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Question 2 View Details

A steel rod of length \(2.00\ \text{m}\) and circular cross‑section area \(25\ \text{mm}^2\) has Young's modulus \(E = 200\ \text{GPa}\) and coefficient of linear expansion \(\alpha = 12\times10^{-6}\ \text{°C}^{-1}\). The rod is subjected to a tensile force of \(12\ \text{kN}\) and is uniformly heated by \(40\ \text{°C}\). Find the total change in length of the rod.

A. 4.80 mm

B. 6.24 mm

Correct C. 5.76 mm

D. 7.20 mm

Correct Answer: C

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Question 3 View Details

A solid flywheel has a moment of inertia \(I = 0.50\ \text{kg·m}^2\). It is driven by a motor that supplies a constant power of \(150\ \text{W}\) for \(10\ \text{s}\) starting from rest. Assuming no losses, determine the angular speed of the flywheel at the end of the \(10\ \text{s}\) interval.

A. 70 rad/s

B. 85 rad/s

Correct C. 77.5 rad/s

D. 65 rad/s

Correct Answer: C

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Question 4 View Details

In a series circuit a \(12\ \text{V}\) battery supplies three resistors: \(R_1 = 4\ \Omega\), \(R_2 = 6\ \Omega\) and \(R_3 = 8\ \Omega\). Find (a) the voltage across the \(6\ \Omega\) resistor and (b) the power dissipated in that resistor.

Correct A. Voltage = 4 V; Power = 2.67 W

B. Voltage = 3 V; Power = 2.00 W

C. Voltage = 5 V; Power = 3.33 W

D. Voltage = 6 V; Power = 4.00 W

Correct Answer: A

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Question 5 View Details

A piston has a circular face of diameter \(100\ \text{mm}\). A force of \(5.0\ \text{kN}\) acts on the piston. Calculate the pressure exerted on the piston surface in kilopascals (kPa).

A. 720 kPa

B. 580 kPa

Correct C. 637 kPa

D. 500 kPa

Correct Answer: C

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Question 6 View Details

A cylindrical steel shaft of length 200 mm and diameter 50 mm is to be turned on a CNC lathe. The machine can deliver a maximum power of 7.5 kW. The cutting force can be approximated by \(F_c = K_c \times A\) where \(K_c = 1800 \text{ N/mm}^2\) for the steel and the cross‑sectional area of cut is \(A = d_{\text{cut}} \times a\) with depth of cut \(d_{\text{cut}} = 2 \text{ mm}\) and feed per revolution \(a\) (mm). The cutting speed is \(V = \pi D N / 1000\) (m min\(^{-1}\)) where \(D = 50 \text{ mm}\) and spindle speed \(N\) is limited to 1200 rpm. Determine the maximum allowable feed per revolution \(a\) so that the power does not exceed 7.5 kW. Then compute the material removal rate \(\text{MRR} = \pi D a d_{\text{cut}} N\) (mm\(^3\) min\(^{-1}\)) and state whether it meets a required production rate of \(1.5 \times 10^{6}\) mm\(^3\) min\(^{-1}\).

Correct A. Maximum feed ≈ 0.011 mm/rev; MRR ≈ 4.2 × 10³ mm³/min; required production rate not met.

B. Maximum feed ≈ 0.012 mm/rev; MRR ≈ 4.8 × 10³ mm³/min; required production rate not met.

C. Maximum feed ≈ 0.009 mm/rev; MRR ≈ 3.8 × 10³ mm³/min; required production rate met.

D. Maximum feed ≈ 0.015 mm/rev; MRR ≈ 5.6 × 10³ mm³/min; required production rate not met.

Correct Answer: A

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Question 7 View Details

In the orthographic projection of a part, line AB is inclined in space. In the front view its projection appears as a line of length 100 mm making an angle of \(30^{\circ}\) with the horizontal (z‑axis) of that view. In the top view the projection of AB has a length of 120 mm. Determine (a) the true length of AB, and (b) the angle that AB makes with the horizontal plane.

A. True length = 125 mm; angle with horizontal plane ≈ 20.0°.

B. True length = 140 mm; angle with horizontal plane ≈ 30.0°.

C. True length = 135 mm; angle with horizontal plane ≈ 25.4°.

Correct D. True length = 130 mm; angle with horizontal plane ≈ 22.6°.

Correct Answer: D

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Question 8 View Details

A three‑phase balanced Y‑connected load is supplied from a 400 V line‑to‑line source. The total real power consumed is 30 kW and the power factor is 0.8 lagging. Determine the per‑phase impedance magnitude and angle, and then find the resistance and inductive reactance of each phase.

A. Per‑phase impedance Z = 4.27 Ω ∠ 45.0°; resistance R = 3.42 Ω; inductive reactance X_L = 3.00 Ω.

B. Per‑phase impedance Z = 3.85 Ω ∠ 45.0°; resistance R = 2.70 Ω; inductive reactance X_L = 2.70 Ω.

Correct C. Per‑phase impedance Z = 4.27 Ω ∠ 36.9°; resistance R = 3.42 Ω; inductive reactance X_L = 2.56 Ω.

D. Per‑phase impedance Z = 5.12 Ω ∠ 30.0°; resistance R = 4.42 Ω; inductive reactance X_L = 3.00 Ω.

Correct Answer: C

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Question 9 View Details

Find the sum of the first 10 terms of the arithmetic series whose first term is 5 and common difference is 3.

Correct A. 185

B. 190

C. 150

D. 200

Correct Answer: A

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Question 10 View Details

A series RLC circuit contains a resistor \(R = 10\;\Omega\), an inductor \(L = 0.2\;\text{H}\) and is connected to a 50 Hz AC source. (a) Determine the capacitance \(C\) required for the circuit to be at resonance. (b) At resonance, compute the total impedance and the rms current drawn from the source if the source voltage is 120 V rms.

Correct A. C ≈ 5.1 × 10⁻⁵ F (≈ 51 µF); impedance = 10 Ω; rms current = 12 A.

B. C ≈ 1.0 × 10⁻⁴ F (≈ 100 µF); impedance = 10 Ω; rms current = 12 A.

C. C ≈ 5.1 × 10⁻⁵ F (≈ 51 µF); impedance = 20 Ω; rms current = 6 A.

D. C ≈ 2.5 × 10⁻⁵ F (≈ 25 µF); impedance = 10 Ω; rms current = 12 A.

Correct Answer: A

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Question 11 View Details

A steel rod 2.0 m long with a cross‑sectional area of 20 mm² is subjected to a tensile load of 50 kN and a uniform temperature rise of 30 °C. The Young's modulus of steel is \(200\text{ GPa}\) and its coefficient of linear expansion is \(12\times10^{-6}\,^{\circ}\text{C}^{-1}\). Assuming the load and temperature change act simultaneously, calculate the total change in length of the rod. Give your answer in millimetres to two decimal places.

Correct A. 25.72 mm

B. 30.12 mm

C. 27.80 mm

D. 23.45 mm

Correct Answer: A

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Question 12 View Details

Find the value of \(k\) for which the quadratic equation \(x^{2}-(k-3)x+(2k+1)=0\) has \(x=1\) as a root.

A. 0

B. 5

C. -3

Correct D. -5

Correct Answer: D

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Question 13 View Details

A rectangular solid has a volume of \(2400\ \text{cm}^{3}\). The area of its base (faces with dimensions \(a\) and \(b\)) is \(300\ \text{cm}^{2}\) and the area of one vertical face (dimensions \(b\) and \(c\)) is \(400\ \text{cm}^{2}\). Determine the length of the space diagonal of the solid. Give your answer in centimetres, exact form.

Correct A. 10\sqrt{26} cm

B. 8\sqrt{26} cm

C. 10\sqrt{25} cm

D. 10\sqrt{24} cm

Correct Answer: A

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Question 14 View Details

In a workshop three hazards have been identified with the following probability (P) and severity (S) ratings (on a scale of 1 to 5):\n\n- Hazard A: \(P=3,\; S=4\)\n- Hazard B: \(P=2,\; S=5\)\n- Hazard C: \(P=4,\; S=3\)\n\nThe risk rating is calculated as \(R = P \times S\).\n\n(a) Compute the risk rating for each hazard.\n(b) Identify the hazard(s) with a risk rating of 12 or higher.\n(c) For the hazard with the highest rating, state the most appropriate level of control from the hierarchy: Eliminate, Substitute, Engineering control, Administrative control, Personal protective equipment.

Correct A. Hazard A and Hazard C have risk rating 12; recommended control: Eliminate

B. Hazard B has risk rating 12; recommended control: Engineering control

C. Hazard A and Hazard B have risk rating 12; recommended control: Substitute

D. Hazard A and Hazard C have risk rating 12; recommended control: Personal protective equipment

Correct Answer: A

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Question 15 View Details

The diameter of a shaft varies along its length according to a quadratic function \(d(x)=ax^{2}+bx+c\) (in millimetres), where \(x\) is the distance in millimetres measured from the start of the transition. The shaft has a diameter of \(20\ \text{mm}\) at \(x=0\), a diameter of \(27\ \text{mm}\) at the midpoint \(x=20\ \text{mm}\), and a diameter of \(30\ \text{mm}\) at the end of the transition \(x=40\ \text{mm}\). Determine the diameter of the shaft at \(x=10\ \text{mm}\). Give your answer in millimetres to one decimal place.

A. 25.5 mm

B. 23.0 mm

Correct C. 24.0 mm

D. 22.5 mm

Correct Answer: C

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Question 16 View Details

A steel rod has a nominal length of \(2.500\) m. Two independent measurements are taken: Instrument A reads \(2.4987\) m with a stated uncertainty of \(\pm0.2\) mm, and Instrument B reads \(2.5003\) m with an uncertainty of \(\pm0.15\) mm. Using inverse‑variance weighting, determine the combined best estimate of the length and its combined uncertainty. Then state whether the rod satisfies the tolerance of \(\pm0.3\) mm about the nominal length.

Correct A. Yes, the rod meets the tolerance; weighted average length = 2.4997 m (±0.12 mm).

B. Yes, the rod meets the tolerance; weighted average length = 2.4985 m (±0.10 mm).

C. No, the rod does not meet the tolerance; weighted average length = 2.5010 m (±0.20 mm).

D. No, the rod does not meet the tolerance; weighted average length = 2.5002 m (±0.15 mm).

Correct Answer: A

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Question 17 View Details

A machine has a constant failure rate of \(\lambda = 0.02\) h\(^{-1}\) (exponential distribution). A preventive maintenance (PM) action costs \(\text{₦}500\) and requires 1 h of downtime. An unexpected failure costs \(\text{₦}3000\) and results in an average downtime of 4 h. If a preventive maintenance interval of \(T\) hours is adopted, the expected cost per hour is given by \[\frac{C_{\text{PM}} + C_{\text{F}}\,P_f}{e^{-\lambda T}(T+1) + P_f\bigl(E[t\mid t<T]+4\bigr)}\] where \(P_f = 1-e^{-\lambda T}\) and \(E[t\mid t<T]=\frac{1}{\lambda}-\frac{T e^{-\lambda T}}{P_f}\). Determine the value of \(T\) that minimises the expected cost per hour and give the minimum cost (to the nearest naira).

Correct A. Run‑to‑failure (no preventive maintenance); minimum expected cost ≈ ₦65 per hour.

B. Preventive maintenance every 20 h; minimum expected cost ≈ ₦80 per hour.

C. Run‑to‑failure; minimum expected cost ≈ ₦75 per hour.

D. Preventive maintenance every 10 h; minimum expected cost ≈ ₦70 per hour.

Correct Answer: A

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Question 18 View Details

A mixing tank receives 150 kg of water at \(80^{\circ}\)C and 100 kg of water at \(20^{\circ}\)C. The specific heat capacity of water is \(4.186\) kJ kg\(^{-1}\) K\(^{-1}\). During mixing, 5 % of the total heat released by the hot water is lost to the surroundings. Assuming no heat loss from the cold water, determine the final equilibrium temperature of the mixture (to one decimal place).

Correct A. 55.3 °C

B. 58.7 °C

C. 51.2 °C

D. 60.0 °C

Correct Answer: A

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Question 19 View Details

In a turning operation the tool‑life relationship is given by \(V T^{0.25}=200\), where \(V\) is the cutting speed in m·min\(^{-1}\) and \(T\) is the tool life in minutes. The machine can operate at cutting speeds between 30 m·min\(^{-1}\) and 80 m·min\(^{-1}\). The machining time for each part is inversely proportional to the cutting speed and is described by \(t_{\text{part}} = \dfrac{8}{V}\) minutes. A batch of 500 parts must be produced. Each tool change takes 10 minutes. Determine the cutting speed that minimises the total production time and give that minimum time (to the nearest minute).

A. Cutting speed = 70 m·min⁻¹; minimum total time ≈ 57 minutes.

B. Cutting speed = 80 m·min⁻¹; minimum total time ≈ 58 minutes.

Correct C. Cutting speed = 73 m·min⁻¹; minimum total time ≈ 55 minutes.

D. Cutting speed = 68 m·min⁻¹; minimum total time ≈ 60 minutes.

Correct Answer: C

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Question 20 View Details

A projectile is launched from level ground with an initial speed \(v_0\) at an angle of \(30^{\circ}\) to the horizontal. If its horizontal range is \(80\) m and the acceleration due to gravity is \(9.8\) m·s\(^{-2}\), calculate the required initial speed \(v_0\) (to one decimal place).

A. 28.4 m·s⁻¹

B. 36.7 m·s⁻¹

Correct C. 30.1 m·s⁻¹

D. 33.2 m·s⁻¹

Correct Answer: C

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Question 21 View Details

A workshop records three independent hazards with annual incident probabilities of \(0.02\) (electrical), \(0.03\) (chemical) and \(0.04\) (mechanical). A safety training programme reduces each of these probabilities by 30 % of their original values, but introduces a new minor hazard whose probability is \(0.005\). After the programme, does the total expected number of incidents per year exceed \(0.1\)? State "Yes" or "No" and give the total expected number of incidents (to three decimal places).

A. No; 0.075

Correct B. No; 0.068

C. Yes; 0.068

D. No; 0.058

Correct Answer: B

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Question 22 View Details

Material A has a tensile strength of \(250\) MPa and a density of \(2.7\) g cm\(^{-3}\). Material B has a tensile strength of \(150\) MPa and a density of \(7.8\) g cm\(^{-3}\). A component must have a tensile strength of at least \(200\) MPa and an overall density not exceeding \(4.0\) g cm\(^{-3}\). Using the rule of mixtures for both strength and density, determine the minimum volume fraction of Material A required. Give your answer as a decimal rounded to two decimal places.

A. 0.65

B. 0.55

Correct C. 0.75

D. 0.80

Correct Answer: C

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Question 23 View Details

A bearing has an inner radius of \(50\) mm at \(20^{\circ}\)C and expands radially with a coefficient of linear expansion \(10\times10^{-6}\) °C\(^{-1}\). A shaft that fits into this bearing is initially given a radial clearance of \(c\) mm at \(20^{\circ}\)C. The shaft itself does not expand radially. The operating temperature may rise to \(80^{\circ}\)C, and the design requires that after this temperature increase the clearance be at least \(0.1\) mm. Determine the minimum initial clearance \(c\) (in mm) that satisfies this condition. Give your answer to two decimal places.

A. 0.10

Correct B. 0.13

C. 0.12

D. 0.15

Correct Answer: B

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Question 24 View Details

The Brinell hardness number (BHN) of a steel after quenching is empirically related to its carbon content \(C\) (in weight %) by the equation \(\text{BHN}=500-2000C+3000C^{2}\). The component must attain a BHN of at least \(250\). Determine the range of carbon content \(C\) (to three decimal places) that satisfies this requirement.

Correct A. C ≤ 0.167% or C ≥ 0.500%

B. C ≤ 0.150% or C ≥ 0.480%

C. C ≤ 0.160% or C ≥ 0.520%

D. C ≤ 0.180% or C ≥ 0.460%

Correct Answer: A

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Question 25 View Details

A motor runs at \(1500\) rpm and drives Gear A with \(20\) teeth. Gear A meshes with Gear B (\(40\) teeth) that is fixed on the same shaft as Gear C (\(30\) teeth). Gear C drives Gear D (\(60\) teeth) which is attached to a conveyor.\ (a) Determine the angular speed of the conveyor in rpm.\ (b) If the conveyor must not exceed \(500\) rpm, what is the maximum permissible motor speed (in rpm)?

A. (a) 600 rpm; (b) 2400 rpm

B. (a) 750 rpm; (b) 1000 rpm

Correct C. (a) 375 rpm; (b) 2000 rpm

D. (a) 500 rpm; (b) 1500 rpm

Correct Answer: C

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