Practice city guilds model questions vol1 engineering 2020 Past Questions

Question 1 View Details

A 12 V battery is connected to three resistors. Resistor R₁=4 Ω and R₂=6 Ω are connected in parallel, and this combination is in series with R₃=12 Ω. Determine the voltage across R₂.

A. 4 V

Correct B. 2 V

C. 3 V

D. 6 V

Correct Answer: B

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Question 2 View Details

A steel rod is measured with a meter rule that reads 1 % longer than the true length. The observed reading is 150.0 cm and the rule's precision is ±0.2 cm. Find the best estimate of the rod's true length and the maximum possible absolute error in that estimate.

Correct A. 148.5 cm ±0.21 cm

B. 148.0 cm ±0.22 cm

C. 149.5 cm ±0.20 cm

D. 150.0 cm ±0.21 cm

Correct Answer: A

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Question 3 View Details

In a hydraulic press, the small piston has an area of 2 cm² and the large piston an area of 200 cm². If a 50 N weight is placed on the small piston, what upward force does the large piston exert?

A. 2500 N

B. 5500 N

C. 500 N

Correct D. 5000 N

Correct Answer: D

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Question 4 View Details

A steel rod 2.0 m long and 10 mm in diameter is subjected to a tensile load of 20 kN, causing an elongation of 1.2 mm. (a) Determine the Young's modulus of the material in GPa. (b) If the material's yield stress is 250 MPa, does the rod remain within the elastic limit?

A. (a) 210 GPa; (b) Yes, within elastic limit

B. (a) 500 GPa; (b) No, it yields

C. (a) 424 GPa; (b) Yes, within elastic limit

Correct D. (a) 424 GPa; (b) No, it yields

Correct Answer: D

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Question 5 View Details

In orthographic projection, a line segment AB lies on a plane inclined 30° to the horizontal. The front view shows a projection of AB of 40 mm and the top view shows a projection of AB of 55 mm. Determine the true length of AB.

A. 73.5 mm

B. 50.0 mm

C. 62.0 mm

Correct D. 68.0 mm

Correct Answer: D

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Question 6 View Details

A pump delivers water at a rate of \(1200\) L/min. How many cubic metres of water are delivered in \(2.5\) hours?

A. 165

B. 150

Correct C. 180

D. 200

Correct Answer: C

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Question 7 View Details

A lever of total length \(1.2\) m is used to lift a load of \(800\) N. The effort is applied \(0.3\) m from the fulcrum, while the load acts at the opposite end. The fulcrum introduces a \(10\%\) loss of effort due to friction. Determine the minimum effort force required to lift the load.

A. 2400

Correct B. 2666.67

C. 2000

D. 3000

Correct Answer: B

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Question 8 View Details

A steel rod of diameter \(20\) mm is subjected simultaneously to a tensile load of \(30\) kN and a bending moment of \(0.05\) kN·m. The material has a yield strength of \(250\) MPa. Assuming axial and bending stresses superpose, determine the factor of safety against yielding.

A. 3.92

Correct B. 1.57

C. 2.62

D. 1.96

Correct Answer: B

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Question 9 View Details

A series AC circuit contains a resistor \(R\), an inductor with inductive reactance \(X_{L}=40\) \(\Omega\), and a capacitor with capacitive reactance \(X_{C}=30\) \(\Omega\). The source supplies \(120\) V rms and the rms current measured is \(2\) A. Determine the resistance \(R\).

Correct A. 59.2

B. 60.0

C. 60.8

D. 50.0

Correct Answer: A

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Question 10 View Details

A steel rod \(2.0\) m long at \(20^{\circ}\)C is fitted into a steel tube whose inner length at the same temperature is \(2.001\) m. The coefficient of linear expansion for steel is \(12 \times 10^{-6}\ \text{°C}^{-1}\). Assuming uniform expansion and neglecting any clearance beyond the initial \(1\) mm, determine the maximum temperature increase (in \(^{\circ}\)C) the assembly can tolerate before the rod no longer fits.

A. 30

B. 60

C. 50

Correct D. 42

Correct Answer: D

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Question 11 View Details

A workshop must produce 5,000 identical steel shafts (each 150 mm long, 20 mm diameter). Two possible manufacturing processes are considered: **Process T (turning)** - tool life follows \( V T^{0.25}=200 \) (V in m min\(^{-1}\), T in min). Cutting speed V may be chosen between 30 and 80 m min\(^{-1}\). Machining time per shaft is \( t=\frac{0.2}{V}\) min. Tool cost is ₦1,500 per carbide insert. Machine hourly cost is ₦2,500. Setup time per batch is 30 min and a batch can contain at most 200 shafts before a tool change. **Process M (milling)** - tool life follows \( V T^{0.20}=120 \). Cutting speed V may be chosen between 20 and 60 m min\(^{-1}\). Machining time per shaft is \( t=\frac{0.12}{V}\) min. Tool cost is ₦800 per end‑mill. Setup time per batch is 20 min and a batch can contain at most 150 shafts before a tool change. Machine cost is the same as above. Both processes must complete the whole order within 1,200 min (including all setups and tool changes). Determine which process can meet the time requirement and give the minimum total cost (tool cost plus machine operating cost) for that process. State the process name and the total cost in naira.

A. Turning, 54000

Correct B. Milling, 55950

C. Turning, 56200

D. Milling, 60000

Correct Answer: B

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Question 12 View Details

In a workshop a hydraulic press presents a crushing hazard. The estimated probability of an accident occurring in a year is 0.02 and the severity rating (on a scale of 1-10) is 8. The risk rating is calculated as \( R = P \times S \). A risk rating above 0.2 requires additional control measures. Two possible single‑control options are considered: *Engineering control* - reduces the probability by 60 % while leaving severity unchanged. *Administrative control* - reduces the severity by 30 % while leaving probability unchanged. The management wishes to bring the risk rating below 0.1. Which single control should be implemented? Provide the chosen control type.

A. No control needed

Correct B. Engineering control

C. Both controls

D. Administrative control

Correct Answer: B

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Question 13 View Details

A 240 V supply feeds a circuit consisting of a 12 Ω resistor \(R_{1}\) in series with a parallel network of an unknown resistor \(R_{2}\) and a known 20 Ω resistor \(R_{3}\). The total current drawn from the supply is 8 A. Determine the resistance value of \(R_{2}\) (in ohms).

A. 90

B. 150

C. 200

Correct D. 180

Correct Answer: D

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Question 14 View Details

In an orthographic drawing of a line segment AB, the front view shows a projected length of 40 mm and the top view shows a projected length of 30 mm. The drawing scale is 1 : 2 (1 mm on the drawing equals 2 mm in reality). Find the true length of AB in millimetres.

A. 120

B. 110

Correct C. 100

D. 80

Correct Answer: C

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Question 15 View Details

A workshop is divided into two zones. Zone A (120 m²) stores flammable liquids (fire class B). Zone B (80 m²) contains electrical equipment (fire class C). Regulations require a minimum extinguishing capacity of 0.1 L per m² for class B and 0.05 L per m² for class C. Available extinguishers are: - Type 1 (class B) - 6 L capacity, - Type 2 (class C) - 4 L capacity. Determine the minimum number of each type of extinguisher that must be provided to satisfy the regulations for both zones.

A. 2 Type 1 extinguishers and 2 Type 2 extinguishers

B. 3 Type 1 extinguishers and 0 Type 2 extinguishers

C. 1 Type 1 extinguishers and 2 Type 2 extinguishers

Correct D. 2 Type 1 extinguishers and 1 Type 2 extinguisher

Correct Answer: D

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Question 16 View Details

In an orthographic projection, a line segment AB is inclined at \(30^{\circ}\) to the horizontal in the front view and its projected length in that view is \(50\) mm. In the top view the projection of AB measures \(60\) mm. Determine the true length of AB in millimetres.

A. 80

B. 70

C. 55

Correct D. 65

Correct Answer: D

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Question 17 View Details

If \(\tan \theta = \dfrac{3}{4}\) and \(0^{\circ}<\theta<90^{\circ}\), find \(\sin \theta\).

Correct A. 3/5

B. 4/5

C. 3/4

D. 5/3

Correct Answer: A

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Question 18 View Details

A steel workpiece of length \(150\) mm and initial diameter \(50\) mm is to be turned to a final diameter of \(48\) mm. Two machines are available:\n\nMachine A: cutting speed \(V=60\) m/min, feed \(f=0.2\) mm/rev, depth of cut \(d=2\) mm.\nMachine B: cutting speed \(V=80\) m/min, feed \(f=0.15\) mm/rev, depth of cut \(d=1.5\) mm.\n\nAssuming a belt efficiency of 95%, calculate for each machine (i) the material removal rate (MRR) in mm³/min, (ii) the machining time for the single pass, and (iii) which machine provides the higher MRR and by what percentage it exceeds the other.

A. Machine A has MRR ≈ 21000 mm³/min, Machine B ≈ 18000 mm³/min; Machine A's MRR is about 16.7% higher. Both machining times ≈ 2.10 min.

B. Machine A has MRR ≈ 24000 mm³/min, Machine B ≈ 18000 mm³/min; Machine B's MRR is about 33.3% higher. Both machining times ≈ 1.96 min.

Correct C. Machine A has MRR ≈ 24000 mm³/min, Machine B ≈ 18000 mm³/min; Machine A's MRR is about 33.3% higher. Both machining times ≈ 1.96 min.

D. Machine A has MRR ≈ 24000 mm³/min, Machine B ≈ 20000 mm³/min; Machine A's MRR is about 20% higher. Both machining times ≈ 1.96 min.

Correct Answer: C

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Question 19 View Details

A rectangular steel plate is \(200\) mm long. A circular hole is placed on the plate such that the distance from the left edge of the plate to the nearest edge of the hole is specified as \(30\) mm \(\pm\) \(0.2\) mm. The hole diameter is \(10\) mm \(\pm\) \(0.1\) mm. Determine the maximum possible distance between the right edge of the hole and the right edge of the plate.

A. 160.2

B. 158.9

C. 159.5

Correct D. 159.7

Correct Answer: D

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Question 20 View Details

A motor delivers \(5\) kW at \(1500\) rpm and drives a belt‑pulley system. The driver pulley has a diameter of \(200\) mm and the driven pulley a diameter of \(500\) mm. The belt efficiency is \(95\%\). The load on the driven pulley requires a torque of \(250\) Nm. Determine (i) whether the motor can supply the required torque after the belt, (ii) the maximum torque available at the driven pulley, and (iii) the speed of the driven pulley in rpm.

A. No; maximum torque ≈ 85.2 Nm, driven speed = 600 rpm (required 250 Nm cannot be met).

Correct B. No; maximum torque ≈ 75.6 Nm, driven speed = 600 rpm (required 250 Nm cannot be met).

C. Yes; maximum torque ≈ 75.6 Nm, driven speed = 600 rpm (required 250 Nm can be met).

D. No; maximum torque ≈ 75.6 Nm, driven speed = 500 rpm (required 250 Nm cannot be met).

Correct Answer: B

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Question 21 View Details

A motor supplies \(5\ \text{kW}\) of mechanical power at \(1500\ \text{rpm}\) to a gear train. The train consists of gear A (20 teeth) meshing with gear B (40 teeth) on the same shaft as gear C (30 teeth), which drives gear D (60 teeth). The overall efficiency of the gear train is 85 %. Determine the torque delivered by gear D (in N·m), correct to one decimal place.

A. 63.7

Correct B. 108.2

C. 54.1

D. 127.3

Correct Answer: B

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Question 22 View Details

An alloy is produced by mixing 2 kg of metal A (density \(7.8\ \text{g\,cm}^{-3}\)) with 3 kg of metal B (density \(2.7\ \text{g\,cm}^{-3}\)). Find the density of the resulting alloy in \(\text{g\,cm}^{-3}\), correct to two decimal places.

A. 3.55

B. 4.12

C. 3.80

Correct D. 3.66

Correct Answer: D

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Question 23 View Details

Two independent measurements of a length are obtained. Using a steel rule the length is measured as \(125.4\ \text{mm}\) with an uncertainty of \(\pm0.5\ \text{mm}\). Using a digital caliper the length is measured as \(125.6\ \text{mm}\) with an uncertainty of \(\pm0.1\ \text{mm}\). Determine the best estimate of the length by inverse‑variance weighting and give the combined standard uncertainty, both to two decimal places.

A. 125.70 mm ± 0.08 mm

B. 125.30 mm ± 0.15 mm

Correct C. 125.59 mm ± 0.10 mm

D. 125.45 mm ± 0.12 mm

Correct Answer: C

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Question 24 View Details

A CNC milling operation uses a 6‑tooth end mill (\(z=6\)) with a feed per tooth of \(0.20\ \text{mm}\) at a spindle speed of \(2500\ \text{rpm}\). The width of cut is \(30\ \text{mm}\). The specific cutting force is \(K_c = 3000\ \text{N\,mm}^{-2}\) and the machine's power limit is \(5\ \text{kW}\).\n\n(a) Calculate the maximum allowable depth of cut \(d_{\max}\) (in mm) so that the cutting power does not exceed the limit.\n(b) Using this depth, compute the resulting material removal rate (MRR) in \(\text{mm}^3\text{/min}\). Give answers to two decimal places.

Correct A. a) 2.78 mm, b) 100.00 mm³/min

B. a) 2.78 mm, b) 85.00 mm³/min

C. a) 2.50 mm, b) 90.00 mm³/min

D. a) 3.10 mm, b) 115.00 mm³/min

Correct Answer: A

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Question 25 View Details

A steel rod of length \(2.00\ \text{m}\) and diameter \(20\ \text{mm}\) is subjected to a tensile stress of \(120\ \text{MPa}\). The material has a Young's modulus of \(200\ \text{GPa}\) and a yield strength of \(250\ \text{MPa}\).\n\n(a) Determine the elongation of the rod in millimetres, correct to one decimal place.\n(b) With a required factor of safety of 1.5 based on yield strength, state whether the rod is safe under the given stress.

A. a) 0.9 mm, b) Safe

B. a) 2.0 mm, b) Safe

Correct C. a) 1.2 mm, b) Safe

D. a) 1.5 mm, b) Unsafe

Correct Answer: C

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