WORKED SAMPLES
One worked question for each of the 8 official subject areas of Mechanical Engineering, from a bank built on ETEC’s academic standards. Work them here, then practise the full set — with spaced review and timed mocks — in the app, free.
Area 01 · Mechanics & vibrations
A beam fixed at both ends with a central load W in the middle will have zero bending moment at
For a fixed–fixed beam with central load, the moment is hogging at supports and sagging under the load. Sign reversal occurs at two points at L/4 and 3L/4 from the ends — two contraflexure points where M = 0.
Sample — the full set, with spaced review and mocks, is in the app.
Area 02 · Mechanics of materials
A composite bar consists of a steel core and an aluminum sleeve bonded together, both of the same length, loaded axially in tension by a total force P. The cross-sectional areas are A_steel and A_aluminum, and the moduli are E_steel and E_aluminum. The bond ensures both materials undergo the same elongation. Which expression gives the fraction of the total load carried by the steel core?
Compatibility (equal strains): ε = σₛ/Eₛ = σₐ/Eₐ. Equilibrium: P = σₛ Aₛ + σₐ Aₐ = ε(Eₛ Aₛ + Eₐ Aₐ). The steel force fraction is Fₛ/P = (σₛ Aₛ)/(σₛ Aₛ + σₐ Aₐ) = (Eₛ Aₛ)/(Eₛ Aₛ + Eₐ Aₐ), which is option A.
Sample — the full set, with spaced review and mocks, is in the app.
Area 03 · Materials & manufacturing
Hard steels and non-ferrous metal do not exhibit a definite yield point when pulled in the testing machine and for such cases a better measure of their elastic properties is defined by
When no distinct yield point exists, proof stress (e.g., 0.2% offset) is used as the measure of elastic yield behaviour.
Sample — the full set, with spaced review and mocks, is in the app.
Area 04 · Fluid mechanics
Water flows through a horizontal pipe with a sudden contraction. The pressure drop across the contraction is measured to be 15 kPa. Assuming the flow is steady, incompressible, and frictionless, and neglecting changes in kinetic energy, what is the head loss due to the contraction? (Take density of water = 1000 kg/m³, g = 9.81 m/s²)
h_L = Δp/(ρg) = 15,000/(1000 × 9.81) ≈ 1.53 m. Option A is correct. (Note: the stem calls it 'head loss due to a contraction' while neglecting kinetic energy changes; the numerical result is the given pressure-head conversion regardless.)
Sample — the full set, with spaced review and mocks, is in the app.
Area 05 · Thermodynamics
The same volume of all gases at same temperatureand pressure would represent their
By Avogadro's law, equal volumes of gases at the same temperature and pressure contain equal numbers of molecules, so the molecular weights represent the relative masses; hence the answer is molecular weights.
Sample — the full set, with spaced review and mocks, is in the app.
Area 06 · Heat transfer
In a chemical plant, a hot process stream at 90°C is used to preheat a cold stream from 25°C to 65°C in a counter-flow heat exchanger. An engineer remarks that the heat duty of this exchanger is simply the product of the cold stream's mass flow rate, its specific heat, and the cold stream's temperature rise. Why is this statement valid for the cold stream?
For the cold stream with no phase change, an energy balance gives Q = ṁ·cₚ·ΔT. That is exactly the product stated in the stem, so option A is correct.
Sample — the full set, with spaced review and mocks, is in the app.
Area 07 · Measurements & controls
A thermocouple with a Seebeck coefficient of 40 µV per °C is connected to an amplifier with a gain of 500. The amplifier output is read by a 12-bit ADC with a full-scale range of 0 to 5 V. The thermocouple reference junction is at 0 °C. If the amplifier output saturates at 5 V, what is the highest temperature that can be measured without saturation, and what is the temperature resolution of the system?
Amplified sensitivity = 40 µV/°C × 500 = 20 mV/°C = 0.02 V/°C. Maximum temperature = 5 V / 0.02 V/°C = 250 °C. ADC resolution = 5 V / 4096 = 1.2207 mV. Temperature resolution = 1.2207 mV / 0.02 V/°C = 0.061035 °C ≈ 0.061 °C. Thus, option C is correct.
Sample — the full set, with spaced review and mocks, is in the app.
Area 08 · Mechanical design
Find parametric equation for X-coordinates of hermite cubic spline curve having end points P0[4,4]; P1[8,5]
For a Hermite cubic spline the X coordinate takes the form x(u)=a u³+b u²+c u+d, where the coefficients follow from the two end points and their tangent vectors. Substituting the end points P0[4,4] and P1[8,5] into that form gives the cubic coefficient -5 and quadratic coefficient 8, so x(u) = -5u³+8u²+u+1.
Sample — the full set, with spaced review and mocks, is in the app.
Every question explains why each option is right or wrong, and brings back what you miss.
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