Practice city guilds model questions vol1 engineering 2018 Past Questions

Question 1 View Details

A horizontal force of 120 N pulls a 5‑kg block up a smooth incline that makes an angle of $20^{\circ}$ with the horizontal. The block moves a distance of 8 m along the incline. Find the work done by the horizontal force (in joules, to the nearest joule).

A. 840

Correct B. 902

C. 960

D. 720

Correct Answer: B

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Question 2 View Details

A circuit is powered by a 120 V source. The total resistance of the circuit is 30 $\Omega$. The circuit consists of a resistor $R_{1}$ in series with a parallel combination of resistors $R_{2}$ and $R_{3}$. The value of $R_{2}$ is 20 $\Omega$ and the power dissipated in $R_{3}$ is 80 W. Determine the resistance $R_{1}$ (in ohms).

A. 15

Correct B. 20

C. 30

D. 25

Correct Answer: B

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Question 3 View Details

A machine consists of three components in series. Their exponential failure rates are $\lambda_{1}=0.01\ \text{h}^{-1}$, $\lambda_{2}=0.02\ \text{h}^{-1}$ and $\lambda_{3}=0.015\ \text{h}^{-1}$. When a component fails it is repaired immediately; the repair times are $\tau_{1}=2\ \text{h}$, $\tau_{2}=1\ \text{h}$ and $\tau_{3}=1.5\ \text{h}$ respectively. Assuming negligible time between successive failures, calculate the steady‑state availability of the machine (as a percentage, to one decimal place).

A. 92.3

B. 90.8

Correct C. 94.1

D. 95.6

Correct Answer: C

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Question 4 View Details

In a turning operation the cutting time per part is given by $t = \dfrac{K}{V}$ where $K = 0.5\ \text{min·(m/min)}$ and $V$ is the cutting speed in $\text{m/min}$. The tool‑life relationship is $V T^{0.25} = 200$. The cost of a new tool is $50, the machine operating cost is $0.10 per minute, and the material cost per part is $30. Determine the cutting speed $V$ (in $\text{m/min}$, to the nearest whole number) that minimises the total cost per part.

A. 40

B. 35

Correct C. 32

D. 28

Correct Answer: C

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Question 5 View Details

A simply supported rectangular steel beam has a width of 200 mm and an unknown height $h$ (mm). The beam spans $L = 3\ \text{m}$ and carries a central point load $P$. The steel has a yield stress of 250 MPa and a factor of safety of 1.5. If the beam height is 300 mm, calculate the maximum load $P$ (in kN, to the nearest kilonewton) that can be applied without exceeding the allowable bending stress.

Correct A. 667

B. 600

C. 800

D. 720

Correct Answer: A

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Question 6 View Details

A (30\text{ V}\) source supplies a circuit consisting of a resistor $R_{1}=5\ \Omega$ in series with a parallel combination of two resistors $R_{2}$ and $R_{3}$. The total current drawn from the source is $3\ \text{A}$. The current through $R_{2}$ exceeds the current through $R_{3}$ by $0.5\ \text{A}$. Determine the resistance values of $R_{2}$ and $R_{3}$ (in ohms).

A. R2 = 12 Ω, R3 = 60/7 Ω (≈8.57 Ω)

B. R2 = 15 Ω, R3 = 10 Ω

Correct C. R2 = 60/7 Ω (≈8.57 Ω), R3 = 12 Ω

D. R2 = 30/5 Ω (≈6 Ω), R3 = 9 Ω

Correct Answer: C

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Question 7 View Details

In a workshop, three tasks have the following probability (scale 1-5) and severity (scale 1-5) of potential injury: $\text{Task A}:$ probability 3, severity 4; $\text{Task B}:$ probability 2, severity 5; $\text{Task C}:$ probability 4, severity 2. The risk rating is defined as $\text{rating}=\text{probability}\times\text{severity}$. According to safety policy, a rating $\ge 12$ requires an engineering control, a rating of 8-11 requires an administrative control, and a rating $\le 7$ is acceptable with PPE only. If the manager can implement at most one engineering control and one administrative control, and an engineering control reduces a task's rating by 40 % (rounded down to the nearest integer) while an administrative control reduces it by 25 % (rounded down), which tasks should receive each type of control to minimise the total final risk rating? State the final rating for each task after the controls are applied.

A. Task A: engineering control, final rating 8; Task B: administrative control, final rating 6; Task C: PPE only, final rating 8

B. Task A: PPE only, final rating 12; Task B: engineering control, final rating 5; Task C: administrative control, final rating 5

C. Task A: administrative control, final rating 6; Task B: engineering control, final rating 6; Task C: PPE only, final rating 8

Correct D. Task A: engineering control, final rating 7; Task B: administrative control, final rating 7; Task C: PPE only, final rating 8

Correct Answer: D

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Question 8 View Details

A rectangular workshop floor measures $25\ \text{m}$ by $10\ \text{m}$ (area $250\ \text{m}^2$). The fire‑hazard class is B (flammable liquids). Regulations state that a class‑B fire extinguisher of $6\ \text{kg}$ capacity can protect up to $75\ \text{m}^2$, and that no point in the workshop may be farther than $15\ \text{m}$ from an extinguisher. What is the minimum number of extinguishers required, and how should they be positioned to satisfy both the area‑coverage and distance requirements?

A. Five extinguishers; place them at (5 m,5 m), (5 m,15 m), (15 m,5 m), (15 m,15 m) and (12.5 m,5 m) - more than the minimum required.

B. Four extinguishers; place them at the corners of the workshop (0 m,0 m), (0 m,10 m), (25 m,0 m) and (25 m,10 m) - this exceeds the 15 m distance limit for the centre of the floor.

C. Three extinguishers; place them at the centres of three equal zones (e.g., at (5 m,5 m), (5 m,15 m), and (15 m,10 m)) - this fails the 15 m distance requirement for some corners.

Correct D. Four extinguishers; place them at the centres of the four 50 m² zones (e.g., at (5 m,5 m), (5 m,15 m), (15 m,5 m) and (15 m,15 m)) so that every point is within 15 m.

Correct Answer: D

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Question 9 View Details

In an orthographic projection of a three‑dimensional object, a line segment $AB$ has the following projected lengths: - Front view (xy‑plane): $5\ \text{cm}$ - Top view (xz‑plane): $7\ \text{cm}$ - Side view (yz‑plane): $8\ \text{cm}$ Assuming the projections represent the true lengths of the respective component vectors, determine the actual length of $AB$ in centimeters (give the answer to two decimal places).

Correct A. 8.31 cm

B. 9.12 cm

C. 8.00 cm

D. 7.85 cm

Correct Answer: A

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Question 10 View Details

A metal rod is measured with two instruments. - A steel rule has a systematic error of $+0.2\ \text{mm}$ per $100\ \text{mm}$ (it reads longer). A single measurement with the rule gives $150.6\ \text{mm}$. - A Vernier caliper has a zero error of $-0.03\ \text{mm}$ (reads low) and a random error with standard deviation $0.05\ \text{mm}$. Three readings are obtained: $150.32\ \text{mm},\ 150.28\ \text{mm},\ 150.35\ \text{mm}$. Assuming the steel rule's random error is negligible, determine the best estimate of the rod's true length using a weighted average that accounts for the systematic and random errors. Also compute the combined standard uncertainty of the estimate. Express the length to the nearest $0.01\ \text{mm}$ and the uncertainty to the nearest $0.01\ \text{mm}$.

Correct A. 150.34 mm ± 0.03 mm

B. 150.36 mm ± 0.02 mm

C. 150.31 mm ± 0.04 mm

D. 150.28 mm ± 0.05 mm

Correct Answer: A

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Question 11 View Details

The workshop is divided into three zones: Zone A (12 m × 8 m × 3 m) storing only electrical equipment, Zone B (10 m × 6 m × 3 m) where oil‑based lubricants are used, and Zone C (8 m × 5 m × 3 m) used for general carpentry. A 20 m³ fire‑resistant storage room is located within Zone A and does not need protection. ABC fire extinguishers can protect up to 200 m³ of space, but for zones containing oil‑based materials a safety factor of 1.25 must be applied to the coverage. Determine the minimum total number of ABC extinguishers required to adequately protect the workshop.

A. 4

B. 8

C. 6

Correct D. 5

Correct Answer: D

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Question 12 View Details

In a set of orthographic drawings at a scale of 1:2 (1 cm on paper = 2 cm actual), a rod AB is shown. Its projection on the front view measures 9 cm and its projection on the top view measures 40 cm. The rod is not parallel to either plane. Determine the true length of AB in centimetres.

A. 78 cm

Correct B. 82 cm

C. 90 cm

D. 84 cm

Correct Answer: B

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Question 13 View Details

A motor runs at $1500$ rpm and delivers a torque of $12$ N·m. It drives a gear train as follows: the driver gear (20 teeth) meshes with an intermediate gear (40 teeth) on the same shaft; this intermediate gear (30 teeth) meshes with a driven gear (60 teeth) attached to a conveyor. Each mesh operates at $95$% efficiency. Find the speed (rpm) and the torque (N·m) delivered to the conveyor shaft.

A. Speed = 750 rpm, Torque ≈ 22.8 N·m

B. Speed = 375 rpm, Torque ≈ 48 N·m

Correct C. Speed = 375 rpm, Torque ≈ 43.3 N·m

D. Speed = 1500 rpm, Torque ≈ 12 N·m

Correct Answer: C

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Question 14 View Details

A hydraulic press has a small piston of diameter $50$ mm and a large piston of diameter $200$ mm. If a force of $500$ N is applied to the small piston, (a) determine the force exerted by the large piston, assuming an incompressible fluid and neglecting losses; (b) if the large piston moves down $5$ cm, calculate how far the small piston moves up.

A. Force = 8000 N; Small piston rise = 20 cm

B. Force = 2000 N; Small piston rise = 80 cm

Correct C. Force = 8000 N; Small piston rise = 80 cm

D. Force = 2000 N; Small piston rise = 20 cm

Correct Answer: C

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Question 15 View Details

A metal rod is measured twice: with a steel rule (uncertainty $\pm0.5$ mm) giving $250.3$ mm and with a digital caliper (uncertainty $\pm0.1$ mm) giving $250.8$ mm. Using inverse‑variance weighting, (a) find the best estimate of the true length and its combined standard uncertainty; (b) if a piece is to be cut to $150.0$ mm using this best estimate as the reference, compute the percentage error associated with the measurement uncertainty.

A. Best estimate = 250.55 mm ± 0.12 mm; Percentage error ≈ 0.075 %

Correct B. Best estimate = 250.78 mm ± 0.10 mm; Percentage error ≈ 0.067 %

C. Best estimate = 251.10 mm ± 0.15 mm; Percentage error ≈ 0.090 %

D. Best estimate = 250.90 mm ± 0.08 mm; Percentage error ≈ 0.058 %

Correct Answer: B

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Question 16 View Details

A composite rod consists of two materials joined in series. Material A has Young's modulus (200\ \text{GPa}\), length (0.5\ \text{m}\) and cross‑sectional area (10\ \text{mm}^2\). Material B has Young's modulus (100\ \text{GPa}\), length (0.3\ \text{m}\) and area (20\ \text{mm}^2\). A tensile force of (5\ \text{kN}\) is applied to the free ends. Assuming elastic behaviour, calculate the total elongation of the composite rod in millimetres.

A. 2.5 mm

B. 3.0 mm

Correct C. 2.0 mm

D. 1.5 mm

Correct Answer: C

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Question 17 View Details

A rod is made by welding a steel section to an aluminium section. The steel part has length (1.2\ \text{m}\) and coefficient of linear expansion (12\times10^{-6}\ \text{°C}^{-1}\). The aluminium part has length (0.8\ \text{m}\) and coefficient (22\times10^{-6}\ \text{°C}^{-1}\). When the assembly is heated, its total length increases by (3.6\ \text{mm}\). Determine the temperature rise $\Delta T$ in degrees Celsius.

Correct A. 112.5 °C

B. 150.0 °C

C. 90.0 °C

D. 75.0 °C

Correct Answer: A

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Question 18 View Details

A surveyor measures the height of a building using a clinometer placed $50.0\ \text{m}$ from the base. The instrument reads an angle of elevation of $30.0^{\circ}$. The clinometer has a known systematic error of +$0.5^{\circ}$ (it reads too high) and a random error of $\pm0.2^{\circ}$. The distance measurement has an uncertainty of $\pm0.1\ \text{m}$. Using the corrected angle, estimate the building height and give the maximum possible absolute error (express the result as "height $\pm$ error" in metres, rounded to two decimal places).

A. 28.00 m ± 0.25 m

B. 27.85 m ± 0.22 m

Correct C. 28.29 m ± 0.24 m

D. 29.10 m ± 0.30 m

Correct Answer: C

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Question 19 View Details

A simple gear train drives a conveyor. Gear A (driver) has 20 teeth and rotates at 1500 rpm. It meshes with gear B (40 teeth) which is fixed on the same shaft as gear C (30 teeth). Gear C meshes with gear D (60 teeth) that is attached to the conveyor shaft. Determine the conveyor speed in revolutions per minute.

A. 300 rpm

Correct B. 375 rpm

C. 450 rpm

D. 500 rpm

Correct Answer: B

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Question 20 View Details

A solid steel rod of circular cross‑section has a diameter of $12\ \text{mm}$ and a yield strength of $250\ \text{MPa}$. The design requires a factor of safety of 2.5. What is the maximum permissible axial load that can be applied to the rod (express your answer in kilonewtons, rounded to one decimal place)?

A. 13.1 kN

B. 7.9 kN

Correct C. 11.3 kN

D. 9.8 kN

Correct Answer: C

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Question 21 View Details

A workshop must produce 5,000 good aluminium components that require a dimensional tolerance of ±0.02 mm. Two manufacturing routes are available: - Process A (CNC milling): setup time 2 h, cycle time 0.8 min per part, machine cost ₦150 per hour, scrap rate 2 %. - Process B (investment casting followed by drilling): setup time 5 h, casting cycle time 1.5 min per part, machine cost ₦120 per hour, scrap rate 0.5 %; after casting each good part requires an additional drilling operation of 0.3 min at the same machine cost. Assuming both processes meet the tolerance, which process yields the lower total production cost and what is that cost (in naira, rounded to the nearest naira)?

Correct A. Process A, total cost ₦10,504

B. Process B, total cost ₦10,504

C. Process B, total cost ₦11,210

D. Process A, total cost ₦9,872

Correct Answer: A

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Question 22 View Details

A steel gear is to be hardened by the following heat‑treatment sequence: austenitising at 850 °C for a time (a) minutes, immediate oil quench (time negligible), then tempering at 200 °C for (t) minutes. The final Rockwell hardness (H) (in HRC) after tempering is approximated by (H = 65 - 0.05,t). The austenitising time must be at least 30 min, and for every additional 10 min beyond 30 min the required tempering time decreases by 5 min. To obtain at least 55 HRC, determine the minimum total heat‑treatment time ((a + t) minutes).

A. 250 minutes

Correct B. 230 minutes

C. 240 minutes

D. 210 minutes

Correct Answer: B

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Question 23 View Details

Solve for (x): ( \log_{3}(x^{2} - 4x + 4) = 2\). State all real solutions.

Correct A. x = 5 or x = -1

B. x = 4 or x = -2

C. x = 6 or x = -2

D. x = 3 or x = 0

Correct Answer: A

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Question 24 View Details

Water (density $ \rho = 1000 \;\text{kg/m}^{3}$) flows in a horizontal pipe of diameter 100 mm at a speed of 2 m s$^{-1}$. The pipe then rises vertically by 5 m. Assuming negligible friction losses, calculate the increase in pressure (in kPa) required at the inlet to maintain the flow, using $g = 9.81 \;\text{m s}^{-2}$.

Correct A. 49.1 kPa

B. 39.2 kPa

C. 45.0 kPa

D. 52.3 kPa

Correct Answer: A

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Question 25 View Details

A steel rod is subjected to a tensile stress of $ \sigma = 200 \;\text{MPa}$. The Young's modulus of the steel is $E = 200 \;\text{GPa}$. Determine the strain‑energy density (energy stored per unit volume) in joules per cubic metre.

Correct A. 1.0×10^5 J/m³

B. 5.0×10^4 J/m³

C. 2.0×10^5 J/m³

D. 1.0×10^6 J/m³

Correct Answer: A

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