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AMIE Section B Mechanical study materials
AMIE Section B Mechanical study resources

AMIE Section B Mechanical practice questions

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Question 1Engineering Mathematics and Applied Sciences

The SI unit of the universal gravitational constant G in Newton's law of gravitation is:

  1. N·kg⁻²
  2. N·m²·kg⁻² Correct answer.
  3. N·m·kg⁻²
  4. N·m²·kg⁻¹

Explanation

From F = Gm₁m₂/r², solving for G gives G = Fr²/(m₁m₂), so the units are N·m²/kg², i.e. N·m²·kg⁻². Substituting the base units confirms this combination is dimensionally consistent with the force equation.

Question 2Engineering Mathematics and Applied Sciences

The value of the definite integral ∫₀¹ x² dx is:

  1. 2/3
  2. 1/2
  3. 1/3 Correct answer.
  4. 1/4

Explanation

The antiderivative of x² is x³/3. Evaluating from 0 to 1 gives 1/3 − 0 = 1/3. The result follows directly from the power rule for integration.

Question 3Engineering Mathematics and Applied Sciences

A body moves in a straight line with constant acceleration. Its velocity–time graph is:

  1. A parabola opening upward
  2. A straight line with non-zero slope Correct answer.
  3. A curve of increasing slope
  4. A horizontal straight line

Explanation

With constant acceleration a, velocity obeys v = u + at, which is linear in time. The slope of the velocity–time graph equals the acceleration and is therefore constant and non-zero.

Question 4Engineering Mathematics and Applied Sciences

The moment of inertia of a uniform thin rod of mass M and length L about an axis through its centre perpendicular to its length is:

  1. ML²/2
  2. ML²/12 Correct answer.
  3. ML²/6
  4. ML²/3

Explanation

Integrating r² dm along the rod about the centre gives ML²/12. The parallel-axis theorem then yields ML²/3 for an axis through one end.

Question 5Engineering Mathematics and Applied Sciences

In a simple harmonic oscillator, the acceleration of the mass is:

  1. Proportional to the square of the velocity
  2. Constant in magnitude and direction
  3. Directed toward equilibrium and proportional to displacement Correct answer.
  4. Directed away from equilibrium and proportional to displacement

Explanation

For SHM, a = −ω²x, so acceleration is proportional to displacement and always points toward the equilibrium position. The minus sign expresses the restoring nature of the force.

Question 6Engineering Mathematics and Applied Sciences

The Laplace transform of the constant function f(t) = 1 for t ≥ 0 is:

  1. 1/s²
  2. 1/s Correct answer.
  3. s
  4. e^(−s)

Explanation

By definition, L{1} = ∫₀^∞ e^(−st) dt = 1/s for s > 0. The integral converges only when the real part of s is positive.

Question 7Engineering Mathematics and Applied Sciences

For an ideal gas undergoing an isothermal process, which quantity remains constant?

  1. Pressure
  2. Internal energy Correct answer.
  3. Entropy
  4. Volume

Explanation

For an ideal gas, internal energy depends only on temperature. Since temperature is constant in an isothermal process, internal energy stays constant, and the heat absorbed equals the work done.

Question 8Engineering Mathematics and Applied Sciences

A simply supported beam of span L carries a central point load W. The maximum bending moment is:

  1. WL/4 Correct answer.
  2. WL²/8
  3. WL/2
  4. WL/8

Explanation

Each reaction equals W/2 by symmetry, and the maximum moment occurs under the load at midspan. The moment there is (W/2)(L/2) = WL/4.

Question 9Engineering Mathematics and Applied Sciences

The eigenvalues of the matrix [[2, 1], [1, 2]] are:

  1. −1 and 5
  2. 2 and 2
  3. 0 and 4
  4. 1 and 3 Correct answer.

Explanation

The characteristic equation is (2−λ)² − 1 = 0, giving λ = 2 ± 1. Hence the eigenvalues are 1 and 3, which also sum to the trace 4.

Question 10Engineering Mathematics and Applied Sciences

A projectile is launched at 20 m/s at 30° above the horizontal. Taking g = 10 m/s², the horizontal range on level ground is approximately:

  1. 40 m
  2. 35 m Correct answer.
  3. 17 m
  4. 20 m

Explanation

Range R = u² sin2θ / g = 400 × sin60° / 10 ≈ 400 × 0.866 / 10 ≈ 34.6 m. Rounding gives about 35 m.

Question 11Engineering Mathematics and Applied Sciences

A steel bar of length 2 m is heated through 50 °C. If the coefficient of linear expansion is 12 × 10⁻⁶ /°C, the increase in length is:

  1. 0.12 mm
  2. 1.2 mm Correct answer.
  3. 2.4 mm
  4. 0.6 mm

Explanation

ΔL = αLΔT = 12 × 10⁻⁶ × 2 × 50 = 1.2 × 10⁻³ m, which is 1.2 mm.

Question 12Engineering Mathematics and Applied Sciences

For fully developed laminar flow in a circular pipe, the velocity profile across a diameter is:

  1. Uniform
  2. Linear from wall to centre
  3. Parabolic Correct answer.
  4. Logarithmic

Explanation

Hagen–Poiseuille flow gives u(r) proportional to (R² − r²), a parabolic profile with zero velocity at the wall and maximum at the axis.

Question 13Engineering Mathematics and Applied Sciences

The Fourier series of an odd function defined on [−L, L] contains:

  1. Both sine and cosine terms
  2. Only cosine terms
  3. Only constant terms
  4. Only sine terms Correct answer.

Explanation

For an odd function, the product with cosine is odd and integrates to zero, so all cosine coefficients vanish. The sine coefficients generally survive, so the series contains only sine terms.

Question 14Engineering Mathematics and Applied Sciences

In a tensile test, a material shows a linear elastic region up to 200 MPa and then yields. If Young's modulus is 100 GPa, the strain at the yield point is:

  1. 0.0002
  2. 0.002 Correct answer.
  3. 0.02
  4. 0.2

Explanation

Strain at yield equals stress divided by Young's modulus: 200 × 10⁶ / 100 × 10⁹ = 0.002. This is 0.2 % strain.

Question 15Engineering Mathematics and Applied Sciences

A flywheel of moment of inertia 5 kg·m² is accelerated uniformly from rest to 20 rad/s in 4 s. The torque required is:

  1. 80 N·m
  2. 100 N·m
  3. 5 N·m
  4. 25 N·m Correct answer.

Explanation

Angular acceleration is 20/4 = 5 rad/s². Torque is Iα = 5 × 5 = 25 N·m.

Question 16Engineering Mathematics and Applied Sciences

The solution of dy/dx = ky with y(0) = y₀ is:

  1. y = y₀ e^(kx) Correct answer.
  2. y = y₀ e^(−kx)
  3. y = y₀ sin(kx)
  4. y = y₀ + kx

Explanation

Separating variables gives dy/y = k dx, so ln y = kx + C. Applying y(0) = y₀ gives C = ln y₀, hence y = y₀e^(kx).

Question 17Engineering Mathematics and Applied Sciences

In a heat engine operating on the Carnot cycle between 600 K and 300 K, the maximum theoretical efficiency is:

  1. 0.75
  2. 0.25
  3. 1.00
  4. 0.50 Correct answer.

Explanation

Carnot efficiency is 1 − T_cold/T_hot = 1 − 300/600 = 0.5. No engine operating between these reservoirs can exceed this value.

Question 18Engineering Mathematics and Applied Sciences

A particle's position is given by x = 3t² − 2t (SI units). Its acceleration at t = 2 s is:

  1. 10 m/s²
  2. 6 m/s² Correct answer.
  3. 4 m/s²
  4. 12 m/s²

Explanation

Differentiating twice: v = 6t − 2 and a = 6 m/s², which is constant. The acceleration is therefore 6 m/s² at any time, including t = 2 s.

Question 19Engineering Mathematics and Applied Sciences

A simply supported beam of rectangular cross-section has depth doubled while breadth is unchanged. Its second moment of area about the neutral axis becomes:

  1. 8 times Correct answer.
  2. 2 times
  3. 4 times
  4. 16 times

Explanation

For a rectangle, I = bd³/12, so I scales with the cube of depth. Doubling depth multiplies I by 2³ = 8.

Question 20Engineering Mathematics and Applied Sciences

The curl of the vector field F = (y, −x, 0) is:

  1. (0, 0, 2)
  2. (2, 0, 0)
  3. (0, 0, −2) Correct answer.
  4. (0, 0, 0)

Explanation

The z-component of curl F is ∂F_y/∂x − ∂F_x/∂y = −1 − 1 = −2, and the other components vanish. Hence curl F = (0, 0, −2).

Question 21Engineering Mathematics and Applied Sciences

A uniform rod of mass M and length L is pivoted at one end and released from horizontal. Its angular speed when it reaches the vertical position is:

  1. √(3g/L) Correct answer.
  2. √(3g/2L)
  3. √(2g/L)
  4. √(g/L)

Explanation

Energy conservation gives MgL/2 = ½Iω² with I = ML²/3. Solving, ω² = 3g/L, so ω = √(3g/L).

Question 22Engineering Mathematics and Applied Sciences

The Fourier transform of a Gaussian pulse is also Gaussian. This property is most directly responsible for which feature of signal analysis?

  1. A narrow pulse has a broad spectrum Correct answer.
  2. Phase information is lost
  3. Sampling rates are irrelevant
  4. Energy is always conserved

Explanation

Because the Gaussian maps to a Gaussian with reciprocal width, compressing the pulse in time widens its spectrum. This is the basis of the time–bandwidth uncertainty relation in signal processing.

Question 23Engineering Mathematics and Applied Sciences

A cantilever of length L carries a point load W at its free end. The maximum deflection is:

  1. WL³/(3EI) Correct answer.
  2. WL²/(2EI)
  3. WL³/(8EI)
  4. WL³/(48EI)

Explanation

Integrating the bending moment twice with the fixed-end boundary conditions gives δ = WL³/(3EI) at the free end. This is the standard end-loaded cantilever result.

Question 24Engineering Mathematics and Applied Sciences

A mixture of 1 mol of an ideal monatomic gas and 1 mol of an ideal diatomic gas (with no vibrational modes active) is treated as ideal. The molar heat capacity at constant volume of the mixture is approximately:

  1. 2.0 R Correct answer.
  2. 2.5 R
  3. 1.5 R
  4. 3.0 R

Explanation

Monatomic Cv = 3R/2 and diatomic Cv = 5R/2, so the average over equal mole fractions is (3R/2 + 5R/2)/2 = 2R.

Question 25Engineering Drawing and Graphics

In a first-angle orthographic projection, where is the top view placed relative to the front view?

  1. To the right of the front view
  2. Above the front view
  3. Below the front view Correct answer.
  4. To the left of the front view

Explanation

First-angle projection places the object between the observer and the plane, so the view seen from above is projected onto a plane below the object. The resulting top view is therefore drawn below the front view. Second-angle and third-angle arrangements differ, with third-angle placing the top view above the front view.

Question 26Engineering Drawing and Graphics

Which line type is conventionally used to represent hidden edges and outlines in an engineering drawing?

  1. Chain line with long and short dashes
  2. Continuous thick line
  3. Continuous thin line
  4. Dashed line of short strokes Correct answer.

Explanation

Hidden features are shown with dashed lines made of short evenly spaced strokes, so the viewer knows an edge exists but is not directly visible. Continuous thick lines are reserved for visible outlines, and chain lines mark centre lines or cutting planes.

Question 27Engineering Drawing and Graphics

A drawing is stated to be at a scale of 1:5. A feature measures 24 mm on the drawing. What is its actual length?

  1. 240 mm
  2. 4.8 mm
  3. 120 mm Correct answer.
  4. 29 mm

Explanation

A scale of 1:5 means one unit on the drawing represents five units on the real object, so the drawing is a reduction. Multiplying the drawn length by the scale factor gives 24 mm times 5, equal to 120 mm. Dividing instead of multiplying would wrongly shrink the object.

Question 28Engineering Drawing and Graphics

Which statement correctly describes the title block of a technical drawing?

  1. It lists every dimension used in the drawing
  2. It records drawing number, title, scale and approval details Correct answer.
  3. It contains the bill of materials only
  4. It shows the isometric view of the part

Explanation

The title block is a reserved panel, usually at the bottom right, that identifies the drawing and controls its issue. It typically carries the drawing number, part name, scale, projection symbol, dates and signatures of those who drew and checked it. It does not carry the geometry or the full dimension set.

Question 29Engineering Drawing and Graphics

A rectangular block is 60 mm long, 30 mm wide and 20 mm high. In an isometric drawing, how is the height usually represented along the vertical axis?

  1. At half length, drawn vertically
  2. At true length, drawn at 30 degrees to the horizontal
  3. At true length, drawn vertically Correct answer.
  4. At 0.816 of true length, drawn at 30 degrees

Explanation

In standard isometric drawing the three axes are set 120 degrees apart, with one axis vertical and the other two at 30 degrees to the horizontal. All three axes are drawn to full scale, so the height is laid off at true length along the vertical axis even though the pictorial is not a true projection.

Question 30Engineering Drawing and Graphics

Which statement about a sectional view is correct?

  1. Section lines are drawn only where the cutting plane passes through solid material Correct answer.
  2. Hatching lines are drawn parallel to the outline of the section
  3. Hidden lines must always be shown inside the sectioned area
  4. The cutting plane is always shown as a continuous thick line

Explanation

A section reveals the interior by imagining the object cut and the near portion removed. Hatching is applied only to the areas where the cutting plane actually passes through solid material, so voids and holes remain unhatched. This convention makes the solid section immediately readable.

Question 31Engineering Drawing and Graphics

A line in a drawing is required to indicate the centre of a circular hole. Which line type and pattern is appropriate?

  1. A continuous thick line
  2. A dashed line of equal short strokes
  3. A chain line of long and short dashes Correct answer.
  4. A wavy continuous thin line

Explanation

Centre lines are drawn as chain lines consisting of long dashes alternating with short dashes, extending slightly beyond the feature. This distinguishes them from hidden lines, which use equal short dashes, and from visible outlines, which are thick and continuous.

Question 32Engineering Drawing and Graphics

A drawing of a long shaft is shortened by omitting a middle portion, with the break indicated by freehand wavy lines. What is this technique called?

  1. A removed detail view
  2. An auxiliary view
  3. A broken or interrupted view Correct answer.
  4. A revolved section

Explanation

When a long uniform part would waste drawing space, a broken view omits the unchanged middle and joins the ends with break lines. The break lines signal that material has been left out, while the overall dimension still states the true full length. This keeps the drawing compact without misrepresenting the part.

Question 33Engineering Drawing and Graphics

A flat plate has an inclined face that appears foreshortened in both the front and top views. Which view would show that face in true shape?

  1. An auxiliary view projected perpendicular to the inclined face Correct answer.
  2. A second front view rotated by 90 degrees
  3. A section view taken through the plate centre
  4. An isometric pictorial of the plate

Explanation

A surface appears in true shape only when the line of sight is perpendicular to it. An auxiliary view is set up on a plane parallel to the inclined face, so the foreshortening present in the principal views is removed. The auxiliary view is projected from the edge view of the inclined face.

Question 34Engineering Drawing and Graphics

A dimension is given as 42 +0.05/-0.02 mm. What is the permissible size range of the feature?

  1. 41.98 mm to 42.05 mm Correct answer.
  2. 41.98 mm to 42.02 mm
  3. 42.00 mm to 42.05 mm
  4. 41.95 mm to 42.02 mm

Explanation

The stated size is the basic dimension, and the deviations are applied to it to obtain the limits. The upper limit is 42 plus 0.05, giving 42.05 mm, and the lower limit is 42 minus 0.02, giving 41.98 mm. The tolerance is therefore 0.07 mm.

Question 35Engineering Drawing and Graphics

A drawing uses a scale of 2:1 and shows a component 90 mm long. Which statement is correct?

  1. The real component is 22.5 mm long
  2. The real component is 45 mm long Correct answer.
  3. The real component is 90 mm long
  4. The real component is 180 mm long

Explanation

A scale of 2:1 means the drawing is twice the size of the real object, so it is an enlargement. The real length is found by dividing the drawn length by 2, giving 45 mm. Multiplying by 2 would apply the scale in the wrong direction.

Question 36Engineering Drawing and Graphics

A hexagonal prism is drawn in isometric with its axis vertical. Which construction gives the isometric view of the top hexagonal face?

  1. An ellipse constructed in a square or rhombus isometric box Correct answer.
  2. A circle drawn with a compass at true radius
  3. A regular hexagon with all sides at true length and 120-degree angles
  4. A hexagon whose corners lie on a circle of diameter equal to the true diameter

Explanation

In isometric drawing, a horizontal circular face appears as an ellipse, and it is normally obtained by constructing the ellipse inside the isometric square, or rhombus, that represents the circumscribing square. The four-centre method is commonly used for this construction. Drawing a true circle or true hexagon ignores the foreshortening of the pictorial axes.

Question 37Thermodynamics and Heat Transfer

In a steady-flow process at constant pressure with negligible kinetic and potential energy changes, the heat transfer per unit mass is best expressed as which quantity?

  1. Change in specific entropy
  2. Change in specific internal energy
  3. Change in specific enthalpy Correct answer.
  4. Change in specific volume

Explanation

For a steady-flow device with no work other than flow work and negligible kinetic and potential changes, the first law reduces to q = Δh at constant pressure. The flow work term is absorbed into enthalpy, so internal energy alone does not account for it.

Question 38Thermodynamics and Heat Transfer

A gas is compressed slowly in a cylinder while its temperature stays constant. Which description of the process is correct?

  1. Isobaric process
  2. Adiabatic process
  3. Isochoric process
  4. Isothermal process Correct answer.

Explanation

An isothermal process maintains constant temperature throughout. Slow compression with heat removal can keep temperature fixed, distinguishing it from adiabatic, constant-volume, and constant-pressure processes.

Question 39Thermodynamics and Heat Transfer

The Kelvin-Planck statement of the second law forbids which of the following?

  1. A heat engine rejecting some heat to a low-temperature sink
  2. A refrigerator moving heat from cold to hot with work input
  3. A cyclic device converting all heat from one reservoir into work Correct answer.
  4. An irreversible process producing entropy

Explanation

The Kelvin-Planck statement says no cyclic device can convert all heat absorbed from a single reservoir entirely into work. Real engines must reject some heat to a lower-temperature sink.

Question 40Thermodynamics and Heat Transfer

Which mode of heat transfer requires a material medium and involves bulk fluid motion?

  1. Radiation
  2. Convection Correct answer.
  3. Conduction through a solid
  4. Evaporation

Explanation

Convection combines fluid bulk motion with conduction at the surface, so it needs a moving medium. Radiation needs no medium, and solid conduction involves no bulk motion.

Question 41Thermodynamics and Heat Transfer

For an ideal gas, the specific heat at constant pressure cp exceeds cv by which quantity?

  1. The universal gas constant divided by temperature
  2. The gas constant R Correct answer.
  3. The molar mass
  4. The ratio cp/cv

Explanation

For an ideal gas, cp − cv = R, the specific gas constant, because at constant pressure some heat goes into expansion work. The ratio cp/cv is the specific heat ratio, not a difference.

Question 42Thermodynamics and Heat Transfer

In a steady-state heat conduction problem through a plane wall, which quantity is constant through the wall?

  1. Temperature gradient magnitude
  2. Thermal conductivity
  3. Heat transfer rate Correct answer.
  4. Temperature

Explanation

At steady state with no internal generation, energy conservation requires the same heat rate to cross every section of the wall. Temperature and its gradient vary with position, and conductivity is a material property.

Question 43Thermodynamics and Heat Transfer

Which property of a pure substance is defined as the ratio of its density to the density of water at a specified reference condition?

  1. Specific volume
  2. Specific weight
  3. Specific heat
  4. Specific gravity Correct answer.

Explanation

Specific gravity is a dimensionless ratio comparing a substance's density with a reference density, usually water. Specific volume is the reciprocal of density, specific weight is weight per unit volume, and specific heat relates heat to temperature change.

Question 44Thermodynamics and Heat Transfer

A Carnot engine operates between 600 K and 300 K. What is its thermal efficiency?

  1. 0.75
  2. 0.60
  3. 0.50 Correct answer.
  4. 0.30

Explanation

Carnot efficiency equals 1 − Tc/Th, so 1 − 300/600 = 0.50. The absolute temperatures must be used in kelvin for this ratio.

Question 45Thermodynamics and Heat Transfer

An ideal gas at 300 K is heated at constant volume until its pressure triples. What is the final temperature?

  1. 900 K Correct answer.
  2. 300 K
  3. 1200 K
  4. 600 K

Explanation

At constant volume, Gay-Lussac's law gives p/T constant, so tripling pressure triples absolute temperature. Thus 3 × 300 K = 900 K.

Question 46Thermodynamics and Heat Transfer

A plane wall 0.2 m thick has thermal conductivity 2 W/(m·K) and a temperature difference of 40 K across it. What is the steady heat flux?

  1. 200 W/m²
  2. 400 W/m² Correct answer.
  3. 16 W/m²
  4. 40 W/m²

Explanation

Fourier's law for a plane wall gives q'' = kΔT/L = 2 × 40 / 0.2 = 400 W/m². The flux is proportional to conductivity and temperature difference and inversely proportional to thickness.

Question 47Thermodynamics and Heat Transfer

Water enters a boiler at 50 °C and leaves as saturated vapor at 150 °C. Which term dominates the energy added?

  1. Superheat addition
  2. Latent heat of vaporization Correct answer.
  3. Heat of fusion
  4. Sensible heat of the liquid

Explanation

Most of the energy in boiling goes into the latent heat of vaporization at the saturation temperature. Sensible heating from 50 °C to saturation is comparatively small, and no superheat or fusion occurs here.

Question 48Thermodynamics and Heat Transfer

In natural convection over a vertical plate, which dimensionless group primarily governs the flow regime?

  1. Rayleigh number Correct answer.
  2. Reynolds number
  3. Mach number
  4. Prandtl number alone

Explanation

The Rayleigh number, the product of Grashof and Prandtl numbers, measures buoyancy versus viscous and thermal diffusion and sets the natural convection regime. Reynolds number governs forced flow, and Mach number is compressibility.

Question 49Thermodynamics and Heat Transfer

A heat exchanger operates with hot fluid entering at 120 °C and leaving at 70 °C while cold fluid enters at 20 °C and leaves at 60 °C. Which flow arrangement produces these terminal differences?

  1. Direct mixing
  2. Cross flow with one pass
  3. Counterflow Correct answer.
  4. Parallel flow

Explanation

In counterflow the hot outlet faces the cold inlet, allowing the cold outlet to approach the hot outlet. Here the cold exit at 60 °C exceeds the hot exit at 70 °C proximity typical of parallel flow limits.

Question 50Thermodynamics and Heat Transfer

Which statement correctly describes the entropy change of an isolated system undergoing an irreversible process?

  1. It remains exactly constant
  2. It decreases
  3. It increases Correct answer.
  4. It becomes zero at equilibrium only

Explanation

The second law states that entropy of an isolated system increases for irreversible processes and stays constant only for reversible ones. It can never decrease in an isolated system.