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MPPSC SES Mechanical study materials
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MPPSC SES Mechanical practice questions

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Question 1Engineering Mathematics and Basic Engineering Sciences

For a simply supported beam of span L carrying a central point load W, the maximum bending moment occurs at mid-span and equals:

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

Explanation

For a simply supported beam with a central point load, the reactions at each support are W/2. The bending moment at mid-span is therefore (W/2)(L/2) = WL/4, which is the maximum value along the span.

Question 2Engineering Mathematics and Basic Engineering Sciences

The Poisson's ratio of a perfectly incompressible isotropic material is:

  1. 0.0
  2. 0.5 Correct answer.
  3. 0.25
  4. 1.0

Explanation

For an isotropic material, bulk modulus K = E/[3(1−2ν)]. A perfectly incompressible material has infinite bulk modulus, which requires 1−2ν = 0, giving ν = 0.5.

Question 3Engineering Mathematics and Basic Engineering Sciences

In a steady-flow constant-pressure process, the heat transferred per unit mass is given by:

  1. change in entropy
  2. change in enthalpy Correct answer.
  3. change in internal energy
  4. change in Gibbs function

Explanation

For a constant-pressure process in a closed system, Q = ΔU + PΔV = ΔH. Hence the heat transferred per unit mass equals the change in specific enthalpy.

Question 4Engineering Mathematics and Basic Engineering Sciences

The efficiency of a Carnot engine operating between a source at 600 K and a sink at 300 K is:

  1. 33%
  2. 25%
  3. 75%
  4. 50% Correct answer.

Explanation

Carnot efficiency is η = 1 − T_sink/T_source. With absolute temperatures 300 K and 600 K, η = 1 − 300/600 = 0.5, that is 50%.

Question 5Engineering Mathematics and Basic Engineering Sciences

In a four-stroke single-cylinder engine running at N rpm, the number of power strokes per minute is:

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

Explanation

In a four-stroke cycle the working stroke occurs once every two revolutions of the crankshaft. Therefore the number of power strokes per minute equals N/2.

Question 6Engineering Mathematics and Basic Engineering Sciences

The main purpose of providing a differential in an automobile is to:

  1. absorb torsional vibrations of the propeller shaft
  2. increase the engine torque at the wheels
  3. allow the two driven wheels to rotate at different speeds during a turn Correct answer.
  4. reduce the unsprung mass of the rear axle

Explanation

When a vehicle turns, the outer wheel travels a longer path than the inner wheel and must rotate faster. The differential transmits power to both wheels while permitting this speed difference.

Question 7Engineering Mathematics and Basic Engineering Sciences

A simply supported rectangular beam of width b and depth d carries a bending moment M. The maximum bending stress developed is:

  1. 12M/(bd³)
  2. M/(bd²)
  3. 3M/(bd²)
  4. 6M/(bd²) Correct answer.

Explanation

The section modulus for a rectangle is Z = bd²/6. The maximum bending stress is σ = M/Z = 6M/(bd²), occurring at the extreme fibres.

Question 8Engineering Mathematics and Basic Engineering Sciences

The ratio of the maximum shear stress to the average shear stress for a solid circular shaft in torsion is:

  1. 1.5
  2. 1.0
  3. 2.0
  4. 1.33 Correct answer.

Explanation

For a solid circular section, the shear stress varies linearly from zero at the centre to a maximum at the surface. The maximum value is 4/3 times the average shear stress.

Question 9Engineering Mathematics and Basic Engineering Sciences

In a vapour-compression refrigeration cycle, the function of the expansion valve is to:

  1. remove heat from the refrigerant
  2. separate liquid from vapour before the compressor
  3. compress the refrigerant isentropically
  4. reduce pressure and control refrigerant flow to the evaporator Correct answer.

Explanation

The expansion valve throttles the refrigerant from condenser pressure to evaporator pressure, controlling the flow rate and causing partial flashing. This prepares the refrigerant for evaporation.

Question 10Engineering Mathematics and Basic Engineering Sciences

The Laplace transform of the unit step function u(t) is:

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

Explanation

The Laplace transform of a unit step is the integral of e^(−st) from zero to infinity, which evaluates to 1/s. This is a standard transform pair.

Question 11Engineering Mathematics and Basic Engineering Sciences

If A is a square matrix and its determinant is zero, then the system Ax = b has:

  1. either no solution or infinitely many solutions Correct answer.
  2. no solution for any b
  3. a unique solution for every b
  4. exactly two solutions

Explanation

A zero determinant means the matrix is singular, so its columns are linearly dependent. The system is either inconsistent or has infinitely many solutions, but never a unique solution.

Question 12Engineering Mathematics and Basic Engineering Sciences

The value of the definite integral of x² over the interval from 0 to 1 is:

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

Explanation

The antiderivative of x² is x³/3. Evaluating from 0 to 1 gives 1/3 − 0 = 1/3.

Question 13Engineering Mathematics and Basic Engineering Sciences

For a steady, incompressible, one-dimensional flow through a pipe of varying cross-section, the continuity equation states that:

  1. velocity divided by area is constant
  2. velocity times area is constant Correct answer.
  3. density times velocity is constant
  4. pressure times area is constant

Explanation

Conservation of mass for incompressible flow gives A₁V₁ = A₂V₂, so the product of area and velocity is constant along the pipe.

Question 14Engineering Mathematics and Basic Engineering Sciences

The Reynolds number of flow through a pipe is 1500. The flow is:

  1. transitional
  2. turbulent
  3. fully rough turbulent
  4. laminar Correct answer.

Explanation

For pipe flow, the critical Reynolds number is about 2000. A value of 1500 is below this threshold, so the flow is laminar.

Question 15Engineering Mathematics and Basic Engineering Sciences

In a first-law analysis of a steady-flow adiabatic nozzle with negligible inlet velocity, the exit velocity is obtained from:

  1. √(2(h₁ − h₂)) Correct answer.
  2. √(h₁ − h₂)
  3. h₁ − h₂
  4. (h₁ − h₂)/2

Explanation

For an adiabatic nozzle with negligible inlet kinetic energy and no work, the energy balance gives V₂²/2 = h₁ − h₂. Hence V₂ = √(2(h₁ − h₂)).

Question 16Engineering Mathematics and Basic Engineering Sciences

In a simple gear train with two external gears, the driver has 20 teeth and the driven gear has 60 teeth. The speed ratio (driver speed to driven speed) is:

  1. 1:3
  2. 3:1 Correct answer.
  3. 2:1
  4. 1:2

Explanation

The speed ratio is inversely proportional to the tooth ratio: N_driver/N_driven = T_driven/T_driver = 60/20 = 3. So the ratio is 3:1.

Question 17Engineering Mathematics and Basic Engineering Sciences

A body of mass 2 kg is moving with a velocity of 3 m/s. Its kinetic energy is:

  1. 18 J
  2. 9 J Correct answer.
  3. 6 J
  4. 3 J

Explanation

Kinetic energy is ½mv². Substituting m = 2 kg and v = 3 m/s gives ½ × 2 × 9 = 9 J.

Question 18Engineering Mathematics and Basic Engineering Sciences

A simply supported beam carries a uniformly distributed load of intensity w over its entire span L. The maximum shear force occurs at the supports and equals:

  1. wL²/2
  2. wL
  3. wL/2 Correct answer.
  4. wL/4

Explanation

For a uniformly distributed load, each support carries half the total load wL. The shear force is maximum at the supports and equals wL/2.

Question 19Engineering Mathematics and Basic Engineering Sciences

In a Pelton wheel, the maximum hydraulic efficiency is obtained when the bucket speed is:

  1. one-fourth the jet velocity
  2. equal to the jet velocity
  3. twice the jet velocity
  4. half the jet velocity Correct answer.

Explanation

For a Pelton wheel the optimum bucket speed is half the jet velocity, which maximises the energy transfer from the jet to the buckets.

Question 20Engineering Mathematics and Basic Engineering Sciences

The stress at which a material exhibits a specified limiting permanent set, typically 0.2%, is called:

  1. elastic limit
  2. proof stress Correct answer.
  3. proportional limit
  4. ultimate tensile strength

Explanation

Proof stress is defined as the stress corresponding to a specified permanent strain, commonly 0.2% for materials without a distinct yield point. It is determined by the offset method on the stress-strain curve.

Question 21Engineering Mechanics and Strength of Materials

A simply supported beam of span L carries a central point load W. What is the maximum bending moment?

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

Explanation

For a simply supported beam with a central point load, each reaction equals W/2, so the maximum moment at midspan is (W/2)(L/2) = WL/4. The bending moment diagram is triangular with its peak at the centre.

Question 22Engineering Mechanics and Strength of Materials

The maximum shear stress in a solid circular shaft of diameter d transmitting torque T occurs at the surface and equals:

  1. 8T/(πd³)
  2. 16T/(πd³) Correct answer.
  3. 4T/(πd³)
  4. 32T/(πd³)

Explanation

Torsion theory gives τ = T·r/J with J = πd⁴/32 for a solid circular section. Substituting r = d/2 yields τmax = 16T/(πd³) at the outer fibre, where stress is greatest.

Question 23Engineering Mechanics and Strength of Materials

A body of weight W rests on a rough horizontal plane with coefficient of friction μ. The minimum horizontal force needed to just start sliding is:

  1. W
  2. μW²
  3. W/μ
  4. μW Correct answer.

Explanation

On a horizontal plane the normal reaction equals the weight W, so the limiting friction is F = μN = μW. This is the smallest horizontal force that can initiate motion.

Question 24Engineering Mechanics and Strength of Materials

For a material obeying Hooke's law, the ratio of lateral strain to longitudinal strain within the elastic limit is called:

  1. Young's modulus
  2. Bulk modulus
  3. Poisson's ratio Correct answer.
  4. Modulus of rigidity

Explanation

Poisson's ratio is defined as the negative ratio of lateral strain to longitudinal strain under uniaxial loading. It is a dimensionless elastic constant, typically around 0.3 for metals.

Question 25Engineering Mechanics and Strength of Materials

A particle moves in a straight line with constant acceleration. Its velocity-time graph is a straight line. The area under this graph between two instants represents:

  1. Rate of change of acceleration
  2. Acceleration of the particle
  3. Jerk of the particle
  4. Distance travelled by the particle Correct answer.

Explanation

Velocity is the rate of displacement, so the integral of velocity over time gives displacement, which for straight-line motion without reversal equals distance travelled. Graphically this integral is the area under the v-t curve.

Question 26Engineering Mechanics and Strength of Materials

The point through which the resultant of distributed hydrostatic or gravity forces on a body acts is known as the:

  1. Metacentre
  2. Centre of gravity
  3. Centre of pressure Correct answer.
  4. Centroid of area

Explanation

The centre of pressure is the point where the resultant pressure force on a submerged surface acts. For a plane area it lies below the centroid whenever pressure increases with depth.

Question 27Engineering Mechanics and Strength of Materials

A bar of length L, area A and Young's modulus E is subjected to an axial pull P. The elongation is:

  1. PA/(LE)
  2. PE/(AL)
  3. PL/(AE) Correct answer.
  4. AE/(PL)

Explanation

Axial stress is P/A and axial strain is stress/E = P/(AE). Multiplying strain by the original length gives elongation δ = PL/(AE), which increases with load and length and decreases with stiffness and area.

Question 28Engineering Mechanics and Strength of Materials

For a beam subjected to pure bending, the bending stress at a distance y from the neutral axis is proportional to:

  1. y Correct answer.
  2. √y
  3. 1/y
  4. y²

Explanation

The flexure formula σ = My/I shows that bending stress varies linearly with distance from the neutral axis. Stress is zero at the neutral axis and maximum at the extreme fibres, so the section modulus governs strength.

Question 29Engineering Mechanics and Strength of Materials

A simply supported beam of span 6 m carries a uniformly distributed load of 10 kN/m over its entire length. The maximum bending moment is:

  1. 90 kN·m
  2. 45 kN·m Correct answer.
  3. 30 kN·m
  4. 60 kN·m

Explanation

For a UDL w over span L, the maximum moment at midspan is wL²/8 = 10 × 36/8 = 45 kN·m. Total load is 60 kN, each reaction 30 kN, and the midspan moment equals 30 × 3 − 10 × 3 × 1.5 = 45 kN·m.

Question 30Engineering Mechanics and Strength of Materials

A hollow circular shaft has outer diameter D and inner diameter d. Its polar moment of inertia about the centroidal axis is:

  1. π(D⁴ + d⁴)/32
  2. π(D² − d²)/32
  3. π(D⁴ − d⁴)/32 Correct answer.
  4. π(D⁴ − d⁴)/64

Explanation

The polar moment of a solid circle is πD⁴/32, so a hollow shaft is the difference π(D⁴ − d⁴)/32. This value enters the torsion formula τ = T·r/J and shows why hollow shafts carry torque efficiently.

Question 31Engineering Mechanics and Strength of Materials

A block of weight 100 N rests on a plane inclined at 30° to the horizontal. The component of weight acting along the plane is:

  1. 86.6 N
  2. 25 N
  3. 50 N Correct answer.
  4. 100 N

Explanation

The component of weight parallel to an incline is W sin θ = 100 × sin 30° = 50 N. The normal component is W cos θ = 86.6 N, which sets the available friction.

Question 32Engineering Mechanics and Strength of Materials

A steel bar of length 2 m, area 500 mm² and E = 200 GPa carries an axial tensile load of 100 kN. Its elongation is closest to:

  1. 4.0 mm
  2. 0.5 mm
  3. 2.0 mm Correct answer.
  4. 1.0 mm

Explanation

Using δ = PL/(AE) with P = 100,000 N, L = 2000 mm, A = 500 mm² and E = 200,000 N/mm², we get δ = (100000 × 2000)/(500 × 200000) = 2.0 mm. Consistent units are essential in this calculation.

Question 33Engineering Mechanics and Strength of Materials

The principal stresses at a point are 80 MPa and −20 MPa. The maximum shear stress at that point is:

  1. 100 MPa
  2. 50 MPa Correct answer.
  3. 60 MPa
  4. 30 MPa

Explanation

The maximum in-plane shear stress equals half the difference of the principal stresses: (80 − (−20))/2 = 50 MPa. The negative sign matters because the stresses are of opposite nature.

Question 34Engineering Mechanics and Strength of Materials

A rectangular section of width b and depth d is used as a beam. Its section modulus about the horizontal centroidal axis is:

  1. bd³/12
  2. bd²/3
  3. bd²/6 Correct answer.
  4. bd/6

Explanation

The second moment of area is I = bd³/12 and the extreme fibre distance is d/2, so Z = I/(d/2) = bd²/6. Section modulus converts bending moment directly into extreme fibre stress.

Question 35Engineering Mechanics and Strength of Materials

A simply supported beam of span L carries a point load W at a distance a from the left support. The deflection under the load is maximum when the load is placed:

  1. At midspan Correct answer.
  2. At the left quarter point
  3. Near the right support
  4. At either support

Explanation

For a moving point load on a simply supported beam, the deflection under the load is greatest when the load acts at midspan. The standard result δ = WL³/(48EI) applies for that central position.

Question 36Engineering Mechanics and Strength of Materials

A thin cylindrical pressure vessel of diameter D and wall thickness t carries internal pressure p. The hoop stress is:

  1. pD/(2t) Correct answer.
  2. pD/(4t)
  3. 2pD/t
  4. pD/t

Explanation

Equilibrium of a longitudinal half-section gives hoop stress σh = pD/(2t). The longitudinal stress is half this value, pD/(4t), and the hoop stress governs design of thin shells.

Question 37Engineering Mechanics and Strength of Materials

A body is in equilibrium under the action of three non-parallel coplanar forces. According to Lami's theorem, each force is proportional to the:

  1. Tangent of the angle between the other two forces
  2. Cosine of the angle between the other two forces
  3. Sum of the other two forces
  4. Sine of the angle between the other two forces Correct answer.

Explanation

Lami's theorem states that P/sin α = Q/sin β = R/sin γ, where each angle is measured between the other two forces. It follows from applying the sine rule to the closed force triangle.

Question 38Engineering Mechanics and Strength of Materials

A cantilever of length L carries a uniformly distributed load w per unit length over its whole length. The maximum deflection at the free end is:

  1. wL⁴/(3EI)
  2. wL⁴/(8EI) Correct answer.
  3. 5wL⁴/(384EI)
  4. wL³/(3EI)

Explanation

For a cantilever with a full UDL, the free-end deflection is wL⁴/(8EI), obtained by integrating the moment twice. The fixed end carries the maximum moment wL²/2.

Question 39Engineering Mechanics and Strength of Materials

A shaft is designed to transmit power P at rotational speed N. If the speed is doubled while the torque remains the same, the power transmitted:

  1. Halves
  2. Doubles Correct answer.
  3. Remains unchanged
  4. Becomes four times

Explanation

Power in a rotating shaft is P = 2πNT/60, so at constant torque power is directly proportional to speed. Doubling N therefore doubles the transmitted power.

Question 40Engineering Mechanics and Strength of Materials

A horizontal beam carries a vertical load and is also subjected to an axial compressive force. The resulting stress at a section is best obtained by:

  1. Superposing axial stress and bending stress algebraically Correct answer.
  2. Using only the flexure formula
  3. Applying the torsion formula
  4. Using only the axial stress formula

Explanation

For small deformations the effects are linear and independent, so the axial stress P/A and the bending stress My/I are superposed algebraically with signs. This gives the combined direct and bending stress distribution across the section.

Question 41Engineering Mechanics and Strength of Materials

A simply supported beam carries a point load at midspan. The bending moment diagram is:

  1. A rectangle
  2. A cubic curve
  3. A triangle with peak at midspan Correct answer.
  4. A parabola with peak at midspan

Explanation

For a central point load, the shear force is constant in each half and the moment varies linearly from zero at each support to WL/4 at midspan. The resulting diagram is two straight lines forming a triangle.

Question 42Engineering Mechanics and Strength of Materials

A solid circular shaft and a hollow shaft of the same material have equal cross-sectional area and equal outer diameter. Compared with the solid shaft, the hollow shaft:

  1. Has lower torsional strength but lower weight
  2. Has higher torsional strength but greater weight
  3. Has identical torsional strength
  4. Has higher torsional strength for the same weight Correct answer.

Explanation

Material near the axis contributes little to torsional resistance, so moving area to the outer radius raises the polar moment for the same mass. Hence a hollow shaft is stronger and stiffer in torsion per unit weight than a solid one.

Question 43Engineering Mechanics and Strength of Materials

A rectangular beam is cut from a circular log of diameter d. For maximum bending strength, the depth-to-width ratio should be:

  1. √2 : 1 Correct answer.
  2. 1 : 1
  3. √3 : 1
  4. 2 : 1

Explanation

Maximising section modulus bd²/6 subject to b² + d² = d² gives d² = 2b², hence d/b = √2. The optimum rectangle inscribed in a circle therefore has depth about 1.414 times its width.

Question 44Engineering Mechanics and Strength of Materials

A beam of uniform cross-section is subjected to a pure bending moment. Which statement about the neutral axis is correct?

  1. It coincides with the extreme fibre of the section
  2. It passes through the centroid of the cross-section and carries zero bending stress Correct answer.
  3. It shifts towards the tension side as the moment increases
  4. It lies at one-third of the depth from the top fibre

Explanation

For pure bending of a homogeneous section within the elastic range, the neutral axis passes through the centroid because the net axial force must vanish. Strain and stress are zero on this axis and vary linearly with distance from it.

Question 45Theory of Machines and Mechanical Vibrations

In a simple slider-crank mechanism, the primary unbalanced inertia force due to the reciprocating mass varies with crank rotation at which frequency relative to the crank speed?

  1. Equal to the crank speed Correct answer.
  2. Twice the crank speed
  3. Half the crank speed
  4. Four times the crank speed

Explanation

The primary reciprocating inertia force is proportional to the component of crank acceleration at crank frequency, so it completes one cycle per crank revolution. The secondary force, arising from the obliquity term, oscillates at twice the crank speed. Hence the primary force is at crank speed.

Question 46Theory of Machines and Mechanical Vibrations

The number of degrees of freedom of a four-bar planar linkage with four turning pairs, computed by Grubler's criterion, is:

  1. 0
  2. 2
  3. 1 Correct answer.
  4. 3

Explanation

Grubler's criterion gives F = 3(N-1) - 2j for lower pairs, with N = 4 links and j = 4 joints, so F = 3(3) - 2(4) = 1. A single input is therefore sufficient to define the configuration of a four-bar linkage.

Question 47Theory of Machines and Mechanical Vibrations

In a Hartnell governor, the controlling force is provided primarily by:

  1. Centrifugal force of the flywheel rim
  2. Gravity acting on the sleeve alone
  3. A single dead weight on the spindle
  4. A spring opposing the outward movement of rotating balls Correct answer.

Explanation

A Hartnell governor is a spring-controlled governor in which the centrifugal force of the rotating balls is balanced by a coil spring acting on the sleeve. The spring stiffness determines the sensitiveness and stability of the governor. No dead weight is used as in a Porter governor.

Question 48Theory of Machines and Mechanical Vibrations

The critical damping coefficient of a single-degree-of-freedom system with mass m and stiffness k is given by:

  1. sqrt(k*m)
  2. 2*sqrt(k/m)
  3. k/(2*m)
  4. 2*m*sqrt(k/m) Correct answer.

Explanation

Critical damping is cc = 2*m*omega_n, with natural frequency omega_n = sqrt(k/m), giving cc = 2*m*sqrt(k/m). At this value the system returns to equilibrium without oscillation in the shortest time.

Question 49Theory of Machines and Mechanical Vibrations

A flywheel stores energy mainly to:

  1. Increase the torque of the prime mover
  2. Reduce the mean speed of the shaft
  3. Limit the fluctuation of speed during a cycle Correct answer.
  4. Balance the reciprocating masses completely

Explanation

A flywheel absorbs energy when the driving torque exceeds the load and releases it when the load exceeds the drive, thereby limiting speed fluctuation within a cycle. It does not change the mean speed or the mean torque delivered.

Question 50Theory of Machines and Mechanical Vibrations

The Coriolis component of acceleration exists in a mechanism when:

  1. A crank rotates at constant speed with no sliding pair
  2. A slider moves along a rotating link Correct answer.
  3. A link rotates about a fixed axis only
  4. Two links are connected by a turning pair at rest

Explanation

The Coriolis acceleration 2*omega*v arises when a point slides along a link that is itself rotating, so the velocity direction of the sliding point changes continuously. It is absent when there is no relative sliding along a rotating body.