Practice city guilds model questions vol1 engineering 2017 Past Questions

Question 1 View Details

A block of mass $50$ kg is lifted by a rope wound on a drum of radius $0.25$ m. The drum has mass $20$ kg and is assumed to be a solid cylinder. A motor applies a constant torque of $150$ N·m and produces an angular acceleration of $2$ rad s⁻². Ignoring friction, determine the linear acceleration of the block in m s⁻². (Take $g = 9.8$ m s⁻².)

A. 3.5 m s⁻²

B. 2.8 m s⁻²

Correct C. 2.1 m s⁻²

D. 1.9 m s⁻²

Correct Answer: C

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Question 2 View Details

Component 2 of a machine fails according to an exponential distribution with failure rate $\lambda = 0.0005$ h⁻¹. A preventive maintenance can be performed on this component at a fixed interval $T$ (hours). The cost of each preventive maintenance is \$150, while a corrective repair after a failure costs \$1 200. No preventive maintenance is performed on component 1, whose failures are irrelevant for this calculation. Determine the preventive‑maintenance interval $T$ (in hours) that minimises the long‑run average cost per hour, and compute that minimum average cost (in dollars per hour).

Correct A. T \approx 1386\,h; minimum average cost \approx $0.68 per hour

B. T \approx 1200\,h; minimum average cost \approx $0.75 per hour

C. T \approx 1500\,h; minimum average cost \approx $0.60 per hour

D. T \approx 1000\,h; minimum average cost \approx $0.80 per hour

Correct Answer: A

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Question 3 View Details

A solid circular steel shaft transmits a torque of $500$ N·m and is subjected simultaneously to an axial tensile force of $30$ kN. The material has a yield shear stress of $80$ MPa and a factor of safety of $2$. Using the maximum‑shear‑stress (Tresca) criterion, determine the minimum required shaft diameter in millimetres. (Give your answer to the nearest whole millimetre.)

A. 50 mm

B. 38 mm

C. 45 mm

Correct D. 41 mm

Correct Answer: D

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Question 4 View Details

In a turning operation on a steel workpiece, 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 material removal rate is proportional to the cutting speed: $\text{MRR}=kV$ with $k=0.0005$ m³ min⁻¹ (m min⁻¹)⁻¹. Each part requires removal of $0.02$ m³ of material. The tool costs \$50 and the machine hourly cost is \$30. Determine the cutting speed $V$ (in m min⁻¹) that minimises the cost per part, and compute the corresponding minimum cost per part (in dollars).

A. V \approx 30 m min⁻¹; minimum cost \approx $0.90 per part

Correct B. V \approx 48 m min⁻¹; minimum cost \approx $0.55 per part

C. V \approx 40 m min⁻¹; minimum cost \approx $0.70 per part

D. V \approx 55 m min⁻¹; minimum cost \approx $0.45 per part

Correct Answer: B

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Question 5 View Details

Water flows steadily through a horizontal pipe that narrows from a diameter of $200$ mm to $100$ mm. The pressure upstream is $250$ kPa and downstream is $150$ kPa. Assuming incompressible flow, neglecting elevation change and minor losses, determine the volumetric flow rate in cubic metres per second. (Take the density of water as $1000$ kg m⁻³.)

A. 0.095 m³ s⁻¹

Correct B. 0.115 m³ s⁻¹

C. 0.130 m³ s⁻¹

D. 0.080 m³ s⁻¹

Correct Answer: B

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Question 6 View Details

A cylindrical tank of height 10 m is filled with oil. The total weight of the oil is $1.176\times10^{6}$ N. The density of the oil is $0.8$ times that of water (water density $=1000$ kg m$^{-3}$). After a solid cube of side $2$ m and density $500$ kg m$^{-3}$ is fully submerged in the oil, the oil level rises by $0.5$ m. Assuming $g=9.8$ m s$^{-2}$, determine the radius of the tank in metres, correct to two decimal places.

A. 2.50

Correct B. 2.26

C. 2.14

D. 2.38

Correct Answer: B

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Question 7 View Details

A steel rod is measured with a micrometer that reads $500.00$ mm. The micrometer has a systematic error of $+0.02$ mm (it always reads high) and a random error of $\pm0.01$ mm (one‑sigma). The ambient temperature is $30^{\circ}$C, while the required length is at the reference temperature $20^{\circ}$C. The coefficient of linear expansion of steel is $\alpha = 12\times10^{-6}\,^{\circ}\mathrm{C}^{-1}$. Determine the maximum possible true length of the rod at $20^{\circ}$C, in millimetres, correct to two decimal places.

A. 499.85

B. 500.12

Correct C. 499.93

D. 500.01

Correct Answer: C

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Question 8 View Details

An engineering drawing of a rectangular block uses a scale of 1 : 2 (1 cm on paper represents 2 cm in reality). The front view shows a width of $4$ cm and a height of $6$ cm. The top view shows a depth of $7.5$ cm. Determine the length of the space diagonal of the actual block in millimetres, rounded to the nearest millimetre.

A. 207

B. 215

Correct C. 208

D. 210

Correct Answer: C

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Question 9 View Details

A machine experiences failures that occur uniformly over a life span of up to $4000$ hours; the probability of failure before time $T$ (where $0\le T\le4000$) is $p = T/4000$. The cost of a failure (downtime and repair) is $\$5000$. A preventive maintenance (PM) action costs $\$800$ and, when performed, restores the machine to a like‑new condition. Assuming that if a failure occurs the machine is replaced immediately, and that the expected time to failure (when it occurs) is $T/2$, determine the PM interval $T$ (in hours) that minimises the average cost per hour. Give the optimal $T$ to the nearest whole hour.

A. 2000

B. 1800

C. 1200

Correct D. 1500

Correct Answer: D

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Question 10 View Details

A single‑phase AC motor draws a real power of $5$ kW at a supply voltage of $230$ V, frequency $50$ Hz, and has a lagging power factor of $0.75$. To improve the overall power factor to $0.95$ lagging, a shunt capacitor bank is to be installed. Calculate the required capacitance in microfarads (µF), rounded to the nearest whole µF.

A. 210

B. 120

C. 190

Correct D. 167

Correct Answer: D

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Question 11 View Details

A uniform simply supported beam AB is (2\,\text{m}\) long and carries a single concentrated load of (500\,\text{N}\) at its midpoint. Determine the vertical reaction forces at supports $A$ and $B$.

A. R_A = 500 N, R_B = 0 N

B. R_A = 125 N, R_B = 375 N

Correct C. R_A = 250 N, R_B = 250 N

D. R_A = 0 N, R_B = 500 N

Correct Answer: C

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Question 12 View Details

In orthographic projection, a line segment AB has projected lengths of $5\,\text{cm}$ on the front view, $12\,\text{cm}$ on the top view, and $13\,\text{cm}$ on the side view. Assuming the projections are accurate and the line is not parallel to any principal plane, determine the true length of AB.

Correct A. 13 cm

B. 15 cm

C. 10 cm

D. 17 cm

Correct Answer: A

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Question 13 View Details

A workshop is divided into three zones. The fire‑hazard rating (FHR) for a zone is calculated by $FHR = \dfrac{P \times Q}{R}$, where $P$ is the probability factor (1-5), $Q$ the quantity factor (1-5) and $R$ the control factor (1-5). Zone A: $P=3,\; Q=2,\; R=4$. Zone B: $P=4,\; Q=3,\; R=2$. Zone C: $P=2,\; Q=4,\; R=5$. Each zone must have at least one fire extinguisher. Extinguishers are classified as: - Class A (for metal fires) reduces the zone's FHR by 1.5, - Class B (for flammable liquids) reduces the zone's FHR by 2, - Class C (for electrical fires) reduces the zone's FHR by 1. The workshop requirement is that the resulting FHR in every zone must not exceed 3. Determine the minimum number and types of extinguishers required for each zone to satisfy this requirement.

Correct A. Zone A: 1 Class A extinguisher; Zone B: 2 extinguishers (1 Class B and 1 Class A); Zone C: 1 Class C extinguisher

B. Zone A: 2 Class A extinguishers; Zone B: 1 Class B extinguisher; Zone C: 1 Class C extinguisher

C. Zone A: 1 Class A extinguisher; Zone B: 1 Class B extinguisher; Zone C: 2 extinguishers (1 Class C and 1 Class A)

D. Zone A: 1 Class B extinguisher; Zone B: 2 extinguishers (2 Class A); Zone C: 1 Class A extinguisher

Correct Answer: A

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Question 14 View Details

Solve for $x$: $\displaystyle \frac{2}{x-1} + \frac{3}{x+2} = 1$.

A. x = 2 \\pm \\sqrt{5}

B. x = -2 \\pm \\sqrt{7}

Correct C. x = 2 \pm \sqrt{7}

D. x = 2 \\pm 7

Correct Answer: C

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Question 15 View Details

A steel rod 2 m long with a cross‑sectional area of 150 mm² is subjected to a tensile load of 45 kN and a temperature rise of 60 °C. The Young's modulus of steel is 200 GPa and its coefficient of linear expansion is $12 \times 10^{-6}$ /°C. (a) Determine the total elongation of the rod, taking into account both mechanical strain and thermal strain. (b) If the allowable elongation for the application is 0.8 mm, calculate the factor of safety based on the allowable elongation.

A. (a) 4.20 mm (b) FS ≈ 0.19

B. (a) 3.00 mm (b) FS ≈ 0.27

C. (a) 3.94 mm (b) FS ≈ 0.20

Correct D. (a) 4.44 mm (b) FS ≈ 0.18

Correct Answer: D

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Question 16 View Details

A manufacturing firm can produce a component by either casting or machining. The casting process has a fixed setup cost of $\text{₦}150{,}000$ and a variable cost of $\text{₦}250$ per unit. If the production quantity exceeds 800 units, the variable cost per unit for casting drops by 10\% (to $\text{₦}225$). The machining process has a fixed setup cost of $\text{₦}80{,}000$ and a variable cost of $\text{₦}300$ per unit (no discount). Determine the smallest integer production quantity $Q$ for which the total cost of casting becomes lower than the total cost of machining.

A. 912

B. 945

Correct C. 934

D. 1001

Correct Answer: C

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Question 17 View Details

A composite material is to be produced from material A (Young's modulus $E_A=70$ GPa, density $\rho_A=2.7$ g·cm$^{-3}$) and material B (Young's modulus $E_B=200$ GPa, density $\rho_B=7.8$ g·cm$^{-3}$). Using the linear rule of mixtures for modulus, the target composite modulus is $E_c=120$ GPa. If the total mass of the composite required is $500$ g, determine the masses of materials A and B that must be mixed (round to the nearest gram).

A. 200 g of A and 300 g of B

B. 250 g of A and 250 g of B

Correct C. 178 g of A and 322 g of B

D. 150 g of A and 350 g of B

Correct Answer: C

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Question 18 View Details

A machine experiences failures that follow an exponential distribution with a mean time between failures (MTBF) of 1,200 hours. Each failure requires a repair downtime of 4 hours. The plant can perform preventive maintenance at regular intervals. Each preventive maintenance action reduces the failure rate for the subsequent interval by 30\% but adds 2 hours of scheduled downtime. Assuming 100\% maintenance efficiency and neglecting other losses, what preventive‑maintenance interval (in whole hours) maximises the long‑run availability of the machine if the interval must lie between 500 and 2,500 hours?

A. 500

Correct B. 2500

C. 2000

D. 1500

Correct Answer: B

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Question 19 View Details

A bi‑material rod is made by bonding a steel segment (coefficient of thermal expansion $\alpha_s = 12\times10^{-6}$ °C$^{-1}$, Young's modulus $E_s = 200$ GPa) of length $1.2$ m to an aluminium segment ($\alpha_a = 23\times10^{-6}$ °C$^{-1}$, $E_a = 70$ GPa) of length $0.8$ m. Both segments have the same cross‑sectional area and the ends of the assembled rod are fixed so that the total change in length is zero. If the temperature is raised uniformly by $50$ °C, determine the axial stress (in MPa) developed in each material. State whether the stress is tensile or compressive.

Correct A. -94 MPa (compressive)

B. -70 MPa (compressive)

C. 94 MPa (tensile)

D. -120 MPa (compressive)

Correct Answer: A

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Question 20 View Details

A gear train consists of four gears. Gear A (driver) has 20 teeth and meshes with Gear B (intermediate) which has 40 teeth. Gears B and C are mounted on the same shaft; Gear C has 30 teeth and meshes with Gear D (driven) which has 60 teeth. If an input torque of $150$ N·m is applied to Gear A and the system is 100\% efficient, calculate the output torque on Gear D. State the result in N·m.

A. 450

B. 750

Correct C. 600

D. 300

Correct Answer: C

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Question 21 View Details

A gear train consists of a driver gear A with 20 teeth driving a gear B with 40 teeth. The driver rotates at $1200$ rpm and delivers $5$ kW of power. The efficiency of the gear mesh is $90\%$. Determine the torque transmitted by gear B in newton‑metres (Nm).

A. 100.00 Nm (approximately)

Correct B. 71.66 Nm (approximately)

C. 60.00 Nm (approximately)

D. 85.00 Nm (approximately)

Correct Answer: B

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Question 22 View Details

A cylindrical steel workpiece 150 mm long and 50 mm in diameter is to be turned to a final diameter of 48 mm. Two tool materials are available: carbide with a maximum cutting speed of $120$ m·min⁻¹ and high‑speed steel (HSS) with a maximum cutting speed of $30$ m·min⁻¹. The machine can run at up to $3000$ rpm. The feed per revolution is $0.2$ mm and the depth of cut is $1$ mm. After turning, a 10 mm diameter hole is to be drilled through the centre of the part using a drill whose maximum cutting speed is $80$ m·min⁻¹ and a feed of $0.15$ mm per revolution. Determine (a) which turning tool should be selected, (b) the minimum time required for the turning operation, (c) the spindle speed for drilling, (d) the drilling time, and (e) the total machining time in minutes (rounded to two decimal places).

A. 1.80 minutes (approximately)

Correct B. 1.38 minutes (approximately)

C. 0.95 minutes (approximately)

D. 2.10 minutes (approximately)

Correct Answer: B

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Question 23 View Details

Solve the rational equation $\frac{2}{x+1}+\frac{3}{x-2}=1$ and give all real solutions.

A. x = 3 \\pm 2\\sqrt{10}

B. x = 3 \\pm \\sqrt{12}

Correct C. x = 3 \pm \sqrt{10}

D. x = -3 \\pm \\sqrt{10}

Correct Answer: C

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Question 24 View Details

A machine contains two critical components, A and B, whose failures are independent and follow exponential distributions. The failure rates are $\lambda_A = 2\times10^{-5}$ h⁻¹ and $\lambda_B = 5\times10^{-5}$ h⁻¹. The plant operates continuously (24 h day⁻¹).\ (a) Compute the system mean time between failures (MTBF) when both components must be functioning.\ (b) A preventive maintenance is performed on component A every 2000 h, after which its failure rate drops to $0.5\times10^{-5}$ h⁻¹, while component B's rate remains unchanged. Determine the new system MTBF after the first maintenance interval.\ (c) Estimate the expected number of system failures in one year (8760 h) before and after the maintenance schedule.

A. Original MTBF ≈ 12 500 h; after maintenance MTBF ≈ 16 000 h; expected failures per year drop from ≈0.70 to ≈0.55.

B. Original MTBF ≈ 13 800 h; after maintenance MTBF ≈ 17 500 h; expected failures per year drop from ≈0.63 to ≈0.50.

C. Original MTBF ≈ 15 000 h; after maintenance MTBF ≈ 19 000 h; expected failures per year drop from ≈0.58 to ≈0.45.

Correct D. Original MTBF ≈ 14 285.7 h; after maintenance MTBF ≈ 18 181.8 h; expected failures per year drop from ≈0.61 to ≈0.48.

Correct Answer: D

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Question 25 View Details

In a third‑angle projection a line lies on a surface that is inclined $30^{\circ}$ to the horizontal. In the front view the projection of the line appears as a horizontal segment 50 mm long, while in the top view the same line appears as a segment 86.6 mm long. Determine the true length of the line and its angle of inclination to the horizontal plane.

Correct A. True length = 100 mm; inclination = 30°

B. True length = 100 mm; inclination = 45°

C. True length = 86.6 mm; inclination = 30°

D. True length = 115 mm; inclination = 30°

Correct Answer: A

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