← MES Jr. Grade
Past Questions
A beam of uniform strength has constant
A)
shear force
B)
bending moment
C)
cross-sectional area
D)
deflection
A 'beam of uniform strength' is defined as a beam whose cross-section is varied along its length such that the maximum bending stress at every section is constant. According to the flexure formula, bending stress (σ) is given by σ = (M * y) / I, where M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia. For a beam to have uniform strength, the section modulus (Z = I/y) is varied in proportion to the bending moment (M) so that σ = M/Z remains constant throughout the length of the beam. Therefore, the characteristic that is kept constant (in terms of the resulting stress capacity) is the maximum bending stress, which is achieved by matching the section's strength to the bending moment. In the context of standard engineering terminology for this specific question, 'uniform strength' refers to the condition where the maximum bending stress is constant, which is fundamentally tied to the distribution of the bending moment.
In kinematic chain, a ternary joint is equivalent to
A)
two binary joints
B)
three binary joints
C)
four binary joints
D)
single binary joint
In the study of Kinematics of Machinery, a joint is defined by the number of links it connects.
1. **Binary Joint**: A joint that connects two links. This is the fundamental unit of joint counting in Grubler's or Kutzbach's criterion for calculating degrees of freedom.
2. **Ternary Joint**: A joint that connects three links at a single point.
3. **Quaternary Joint**: A joint that connects four links at a single point.
To determine the equivalence of a higher-order joint to binary joints, we consider how many binary connections are required to link the same number of links.
- To connect 3 links (a ternary joint) using only binary joints, you would need 2 binary joints (Link 1 to Link 2, and Link 2 to Link 3).
- Mathematically, a joint connecting 'n' links is equivalent to (n - 1) binary joints.
- For a ternary joint: n = 3, therefore equivalence = 3 - 1 = 2 binary joints.
Therefore, a ternary joint is equivalent to two binary joints. This is crucial when applying the formula for the degree of freedom (DOF) of a mechanism, where the total number of joints (j) is calculated by counting binary joints.
Resilience can also be termed as
A)
Stress energy
B)
Strain energy
C)
Modulus
D)
Tenacity
Resilience is defined as the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered. In technical terms, the energy stored in a body due to deformation is called 'Strain Energy'. Therefore, resilience is essentially the strain energy stored in a material within the elastic limit.
Analysis of other options:
- a. Stress energy: This is not a standard technical term used in strength of materials.
- c. Modulus: This refers to the stiffness of a material (e.g., Young's Modulus), which is the ratio of stress to strain, not the energy absorbed.
- d. Tenacity: This refers to the ability of a material to resist fracture; it is the total energy absorbed by the material up to the point of rupture (the area under the entire stress-strain curve), whereas resilience only considers the elastic region.
Maximum shear stress at any point in a thin cylinder, subjected to internal fluid pressure is given by,
A)
pd/2t
B)
pd/4t
C)
pd/8t
D)
pd/t
In a thin-walled cylindrical pressure vessel subjected to internal fluid pressure 'p', diameter 'd', and thickness 't', the principal stresses acting on an element on the surface of the cylinder are:
1. Hoop Stress (Circumferential Stress), σ₁ = pd / 2t
2. Longitudinal Stress (Axial Stress), σ₂ = pd / 4t
3. Radial Stress, σ₃ ≈ 0 (Since it is a thin cylinder, the stress through the thickness is negligible compared to the other two).
According to the theory of failure (Mohr's Circle), the maximum shear stress (τmax) is given by the formula:
τmax = (σ_max - σ_min) / 2
Substituting the values:
σ_max = σ₁ = pd / 2t
σ_min = σ₃ = 0
τmax = (pd/2t - 0) / 2 = pd / 4t
Therefore, the maximum shear stress at any point (specifically on the outer surface) is pd/4t. Option (a) represents the hoop stress, and option (c) represents the difference between hoop and longitudinal stress divided by 2, which is the in-plane shear stress, not the absolute maximum shear stress.
In order to facilitate starting of locomotive in any position, the cranks of a locomotive with two cylinders, are placed at
A)
45° to each other
B)
90° to each other
C)
120° to each other
D)
180° to each other
In a two-cylinder locomotive, the 'crank angle' refers to the angular displacement between the cranks of the two cylinders. If the cranks were placed at 180° (opposite to each other), the locomotive would encounter a 'dead center' position where both pistons are at the ends of their strokes simultaneously. In such a case, if the locomotive stopped exactly at this point, it would be impossible to start it using steam power alone because the force would act directly along the axis of the connecting rod, producing no torque on the axle. By placing the cranks at 90° to each other, it is ensured that when one cylinder is at its dead center (zero torque), the other cylinder is at its point of maximum leverage (maximum torque). This ensures that the locomotive can be started from any position, regardless of where the pistons are in their stroke.
Which formula is used to calculate maximum efficiency of worm gear?
A)
tan d / tan (d + F)
B)
(1 – sin F) / (1 + sin F)
C)
tan (d + F) / tan d
D)
(1 + sin F) / (1 – sin F)
In the analysis of worm gear efficiency, the efficiency is primarily affected by the friction between the worm and the worm wheel. Let 'd' be the lead angle (sometimes denoted as λ) and 'F' be the friction angle. The theoretical maximum efficiency (η) for a worm gear is derived from the ratio of the useful work done to the total work input, accounting for the sliding friction. The formula for efficiency is given by: η = tan(lead angle) / tan(lead angle + friction angle). In the context of the provided options, 'd' represents the lead angle and 'F' represents the friction angle. Therefore, the formula is tan d / tan (d + F).
Analysis of options:
- Option (a) tan d / tan (d + F): Correct. This is the standard formula for the efficiency of a worm gear.
- Option (b) (1 – sin F) / (1 + sin F): This is related to the efficiency of a screw jack or specific sliding mechanisms, not the general worm gear efficiency formula.
- Option (c) tan (d + F) / tan d: This is the reciprocal of the efficiency, which would result in a value greater than 1 (physically impossible for efficiency).
- Option (d) (1 + sin F) / (1 – sin F): This is also mathematically incorrect for efficiency as it would exceed 1.
The rotating shafts tend to vibrate violently at whirling speeds because
A)
the system is unbalanced
B)
bearing centre line coincides with the axis
C)
the shafts are rotating at very high speeds
D)
resonance is caused due to the heavy mass of the rotor
Whirling of shafts occurs when the axis of rotation of a shaft coincides with its natural frequency of transverse vibration. In a perfectly balanced and perfectly straight shaft, there would be no centrifugal force to pull the shaft away from its axis of rotation. However, in real-world scenarios, no shaft is perfectly balanced; there is always some eccentricity (the center of mass does not coincide with the geometric center). This 'unbalance' creates a centrifugal force as the shaft rotates. When the rotational speed reaches the 'critical speed' (whirling speed), this centrifugal force excites the shaft at its natural frequency, leading to resonance and violent vibrations.
Analysis of other options:
- Option (b) is incorrect because if the bearing center line coincided perfectly with the axis and there was no unbalance, there would be no excitation force to cause whirling.
- Option (c) is incorrect because high speed alone does not cause violent vibration; vibration occurs specifically at the critical speed (resonance), regardless of whether that speed is considered 'high' or 'low' for that specific system.
- Option (d) is incorrect because while mass affects the natural frequency, the 'heavy mass' itself is not the cause of the vibration; the cause is the eccentricity (unbalance) of that mass.
Transmission of power from the engine to the rear axle of an automobile is by means of
A)
compound gears
B)
worm and wheel method
C)
crown gear
D)
bevel gears.
In a rear-wheel-drive automobile, the power is transmitted from the engine through the clutch, gearbox, and propeller shaft. The propeller shaft delivers power to the rear axle via the differential. The primary function of the differential is to change the direction of power transmission by 90 degrees (from the longitudinal axis of the propeller shaft to the transverse axis of the axle shafts). This change in direction is achieved using bevel gears (specifically, the pinion gear and the ring gear/crown wheel). While a 'crown gear' is a specific type of bevel gear, the general engineering term for gears used to transmit power between intersecting shafts at an angle is 'bevel gears'.
- Option (a) Compound gears are used for speed reduction/increase in a single line, not for changing direction by 90 degrees at the axle.
- Option (b) Worm and wheel methods are used for very high reduction ratios and are not suitable for the high-speed, high-torque requirements of a vehicle's final drive.
- Option (c) Crown gear is a specific form of bevel gear, but 'bevel gears' is the broader, more accurate technical classification for the mechanism used in the final drive assembly.
Lewis equation is applied
A)
Only to the pinion
B)
Only to the gear
C)
To stronger of the pinion or gear
D)
To weaker of the pinion or gear
The Lewis equation is used to calculate the bending stress at the root of a gear tooth. The formula is given by W = σ * b * m * Y, where W is the tangential load, σ is the allowable bending stress, b is the face width, m is the module, and Y is the Lewis form factor. In a gear pair (pinion and gear), both components are subjected to the same tangential load. However, they may have different materials, different face widths, or different form factors (since the pinion has a smaller number of teeth than the gear). The gear set will fail at the point where the stress is highest or the strength is lowest. Therefore, to ensure the safety of the entire transmission, the Lewis equation must be applied to the 'weaker' element—the one that can withstand the least amount of load. If the pinion and gear are made of the same material, the pinion is typically the weaker element because it has a smaller form factor (Y) and undergoes more cycles of stress.
If the axes of first and last gear of a compound gear train are co-axial, the gear train is called
A)
reverted
B)
compound
C)
simple
D)
epicyclic
A gear train is classified based on the arrangement of its axes and the way gears are mounted.
1. **Reverted Gear Train**: This is a special type of compound gear train where the axes of the first gear (input) and the last gear (output) are collinear (co-axial). This configuration is commonly used in automotive gearboxes and clocks to save space while achieving a high speed reduction in a compact layout.
2. **Compound Gear Train**: While a reverted gear train is a type of compound gear train, the term 'compound' generally refers to any train where at least one shaft carries two gears of different sizes. It does not specifically require the input and output shafts to be co-axial.
3. **Simple Gear Train**: In a simple gear train, each shaft carries only one gear. The input and output shafts are typically separate and not co-axial.
4. **Epicyclic Gear Train**: Also known as planetary gear trains, these involve gears that move around other gears (the axes of the gears move relative to each other). While they can be co-axial, the defining characteristic is the orbital motion, not simply the co-axial nature of the first and last gear.
Which of the following screw thread is adopted for power transmission in either direction?
A)
Acme threads
B)
Square threads
C)
Buttress threads
D)
Multiple threads
To determine the correct screw thread for power transmission in either direction, we must analyze the geometry and efficiency of the options provided:
1. **Square Threads (Option b):** These threads have a profile where the flanks are perpendicular to the axis. Because the thread is symmetrical, it offers the highest efficiency (lowest friction) and is designed to transmit power equally well in both directions. It is the ideal choice for bidirectional power transmission.
2. **Acme Threads (Option a):** These are a modification of square threads with a trapezoidal shape. While they can transmit power in both directions, they are primarily used for ease of manufacture and adjustment (like in lead screws of lathes) rather than maximum efficiency in power transmission. They are less efficient than square threads due to the flank angle.
3. **Buttress Threads (Option c):** These are specifically designed to transmit a very high force in one direction only. One flank is nearly perpendicular to the axis while the other is slanted. If force is applied in the opposite direction, the thread is highly inefficient and prone to failure.
4. **Multiple Threads (Option d):** This refers to the number of starts (lead) of a thread, not the profile. Multiple threads increase the lead (distance moved per revolution) but do not determine the directionality of power transmission efficiency; that is determined by the thread profile (Square, Acme, etc.).
Therefore, for bidirectional power transmission with maximum efficiency, Square threads are the correct choice.
All stresses produced in a belt are
A)
compressive stresses
B)
tensile stresses
C)
both tensile and compressive stresses
D)
shear stresses
In a belt drive system, the belt is used to transmit power from one pulley to another via friction. For the belt to grip the pulley and transmit torque without slipping, it must be kept under tension (initial tension). When the drive is operational, the 'tight side' of the belt experiences increased tension and the 'slack side' experiences decreased tension, but both sides remain in a state of tension. Belts are typically made of flexible materials (like rubber, leather, or synthetic polymers) that possess high tensile strength but negligible compressive strength; if a belt were subjected to compressive stress, it would simply buckle or fold rather than transmit force. Therefore, all functional stresses produced in a belt during operation are tensile stresses.
A cotter joint is used to transmit
A)
axial tensile load only
B)
axial compressive load only
C)
combined axial and twisting loads
D)
axial tensile or compressive loads
A cotter joint is a temporary fastening used to connect two co-axial rods. Its primary function is to transmit axial loads.
1. **Axial Tensile Load:** When the rods are pulled apart, the cotter acts as a wedge that prevents the rods from separating, thus transmitting the tensile force.
2. **Axial Compressive Load:** When the rods are pushed together, the shoulders of the socket and spigot members resist the force, transmitting the compressive load.
Why other options are incorrect:
- Option (a) and (b) are incomplete because the joint is capable of handling both types of axial loads, not just one.
- Option (c) is incorrect because a cotter joint is not designed to transmit twisting (torsional) loads; for torsion, a keyed shaft or a splined joint would be used. The cotter joint is specifically designed for linear (axial) movement/force.
The flywheel influences the
A)
variation of load demand on prime mover
B)
mean speed of the prime mover
C)
cyclic variation in speed of the prime mover
D)
mean torque developed by the prime mover
A flywheel is a mechanical device specifically designed to store rotational energy. Its primary function is to act as an energy reservoir that smooths out fluctuations in speed caused by variations in the torque supplied by the prime mover or the torque demanded by the load.
1. **How it works**: During periods when the energy supplied by the prime mover exceeds the energy required by the load, the flywheel accelerates slightly and stores the excess energy as kinetic energy. Conversely, when the load demand exceeds the energy supplied, the flywheel decelerates, releasing its stored energy to maintain the motion.
2. **Effect on Speed**: Because the flywheel absorbs and releases energy during each cycle of operation, it reduces the 'coefficient of fluctuation of speed.' Therefore, it directly influences the cyclic variation in speed.
3. **Why other options are incorrect**:
- **Option (a)**: The flywheel does not change the actual load demand; it only manages how the system responds to that demand.
- **Option (b)**: The mean speed is determined by the governor or the operating settings of the prime mover, not by the flywheel.
- **Option (d)**: The mean torque is a function of the power output and the mean speed; the flywheel does not change the average torque produced by the engine over a full cycle.
A solid circular shaft has a diameter d. Its polar modulus will be
A)
d2 / 16
B)
d3 / 64
C)
d3 / 16
D)
d3 / 32
Based on established principles in Mechanical Engineering, the correct and most appropriate choice is ' d3 / 16' (Option C).
The deflection at any point of the given beam =
A)
Shear force
B)
Bending Moment
C)
slope
D)
both a & b
In the study of beam deflection (Strength of Materials), the relationship between the deflection (y), slope (θ), bending moment (M), shear force (V), and load (w) is defined by a series of differential equations. The governing differential equation for the deflection of a beam is: EI(d²y/dx²) = M, where 'EI' is the flexural rigidity and 'M' is the bending moment. This shows that the second derivative of the deflection (which represents the curvature) is directly proportional to the bending moment at that point. Therefore, the deflection at any point is mathematically derived from the integration of the bending moment equation. While shear force is the derivative of the bending moment, the direct relationship used to calculate deflection is based on the bending moment.
What is meant by jump phenomenon in cam and follower system?
A)
Follower looses contact with cam surface when cam rotates beyond particular speed due to inertia forces
B)
Follower looses contact with cam surface when follower rotates beyond particular speed due to gravitational force
C)
Follower looses contact with cam surface when cam rotates beyond particular speed due to gravitational forces
D)
None of the above
In a cam and follower mechanism, the follower is pushed upward by the cam profile. As the cam rotates, the follower accelerates and decelerates. When the cam rotates at high speeds, the downward acceleration of the follower (during the return or deceleration phase of the lift) may exceed the acceleration provided by the return spring or gravity. At this critical speed, the inertia force of the follower becomes greater than the restoring force, causing the follower to lift off the cam surface. This separation is known as the 'jump phenomenon' or 'follower bounce.'
- Option (b) is incorrect because the cam rotates, not the follower (the follower typically translates or oscillates).
- Option (c) is incorrect because while gravity plays a role in the restoring force, the primary cause of the 'jump' at high speeds is the inertia force resulting from high acceleration/deceleration, not gravity itself.
Slenderness ratio is [l= length of column and k= least radius of gyration of cross section about its axis].
A)
l/k
B)
k/l
C)
l/2k
D)
k/2l
The slenderness ratio is a dimensionless parameter used in structural engineering to determine the stability of a column against buckling. It is defined as the ratio of the effective length of the column to the least radius of gyration of its cross-section.
1. **Effective Length (l):** This is the distance between points of contra-flexure (zero moment) in the column. For a column of actual length L, the effective length depends on the end conditions (e.g., for both ends pinned, l = L).
2. **Radius of Gyration (k):** This is defined as k = √(I/A), where I is the moment of inertia and A is the cross-sectional area. The 'least' radius of gyration is used because a column will always buckle about the axis with the minimum stiffness (minimum I).
Formula: Slenderness Ratio (λ) = Effective Length (l) / Least Radius of Gyration (k).
Comparing this to the options:
- Option (a) l/k matches the definition.
- Option (b) k/l is the reciprocal of the slenderness ratio.
- Options (c) and (d) introduce an arbitrary factor of 2, which is not part of the standard definition of the slenderness ratio.
If a force acts on a body, it sets up some resistance to the deformation. This resistance is known as
A)
stress
B)
strain
C)
elasticity
D)
modulus of elasticity
When an external force is applied to a body, the body undergoes deformation. To counteract this external force and resist the deformation, internal restoring forces are developed within the material. The intensity of this internal resistance per unit area is defined as 'stress'.
Here is why the other options are incorrect:
- b. Strain: This is the measure of the deformation itself (change in dimension divided by original dimension), not the resistance to it.
- c. Elasticity: This is the property of a material by which it tends to return to its original shape and size after the removal of the deforming force. It is a characteristic of the material, not the internal resistance force itself.
- d. Modulus of elasticity: This is the ratio of stress to strain within the elastic limit (Young's Modulus, etc.). It represents the stiffness of the material, not the resistance force acting at a specific moment.
In a thin shell, the ratio of longitudinal stress to the circumferential stress is
A)
1/2
B)
3/4
C)
1
D)
2
Based on established principles in the relevant subject area, the correct and most appropriate choice is '1' (Option C).
According to distortion-energy criterion, yielding occurs when
A)
Distortion energy reaches a critical value
B)
Second invariant of the stress deviator exceeded some critical value
C)
Octahedral shear stress reaches a critical value
D)
All of the above
The Distortion Energy Theory (also known as the von Mises criterion) is based on the premise that yielding of a ductile material occurs when the energy associated with the distortion (change in shape) of the material reaches a critical value. This theory can be expressed in several mathematically equivalent ways:
1. **Distortion Energy (Option a):** The fundamental definition states that yielding occurs when the distortion energy per unit volume reaches the distortion energy at the yield point in a simple tension test.
2. **Second Invariant of the Stress Deviator (Option b):** In tensor notation, the distortion energy is proportional to the second invariant of the stress deviator tensor, denoted as J2. The criterion is often written as J2 = k, where k is a constant for the material. Therefore, yielding occurs when J2 exceeds a critical value.
3. **Octahedral Shear Stress (Option c):** The von Mises stress is directly related to the shear stress acting on the octahedral plane (a plane whose normal makes an equal angle with the three principal axes). Yielding occurs when the octahedral shear stress reaches a critical value (specifically, 1/√3 times the yield strength in tension).
Since all three statements are different mathematical representations of the same physical criterion, option (d) is the correct choice.
When a solid shaft is subjected to torsion, the shear stress induced in the shaft at it centre is
A)
zero
B)
minimum
C)
maximum
D)
average
The distribution of shear stress in a solid circular shaft subjected to torsion is governed by the torsion formula: τ = (T × r) / J, where τ is the shear stress, T is the applied torque, r is the radial distance from the center of the shaft, and J is the polar moment of inertia. According to this linear relationship, the shear stress is directly proportional to the distance from the center (axis) of the shaft. At the center of the shaft, the radius r = 0. Substituting this into the formula: τ = (T × 0) / J = 0. Therefore, the shear stress at the center is zero. Conversely, the shear stress reaches its maximum value at the outer surface of the shaft where r is equal to the radius of the shaft.
Where is the necking region?
A)
Area between lower yield point and upper yield point
B)
Area between plastic limit and elastic limit
C)
Area between ultimate point and initial point
D)
Area between the ultimate point and rupture
In a typical stress-strain curve for a ductile material (like mild steel), 'necking' refers to the localized reduction in cross-sectional area of the specimen. This phenomenon occurs after the material has reached its Ultimate Tensile Strength (UTS), which is the maximum stress the material can withstand. Once the ultimate point is passed, the deformation is no longer uniform across the gauge length; instead, it concentrates at a specific weak point, forming a 'neck'. This localized thinning continues until the material eventually fails at the rupture (breaking) point. Therefore, the necking region is the portion of the curve between the ultimate point and the rupture point.
Analysis of other options:
- Option (a): The region between upper and lower yield points is characterized by yield point elongation, not necking.
- Option (b): The region between the elastic limit and plastic limit is the transition from elastic to plastic behavior.
- Option (c): The area between the initial point and ultimate point covers the elastic region, yielding, and uniform plastic deformation, but necking only begins after the ultimate point.
A thin cylindrical shell of diameter (d), length (l) is subjected to an internal pressure (p). The circumferential stress in the shell is
A)
2pd/t
B)
4pd/t
C)
6pd/t
D)
8pd/t
Based on established principles in the relevant subject area, the correct and most appropriate choice is '4pd/t' (Option B).
The cam follower extensively used in aircraft engines is
A)
Knife edge follower
B)
Flat faced follower
C)
Spherical faced follower
D)
Roller follower
In aircraft engines, particularly in the valve mechanisms of internal combustion engines, flat-faced followers are extensively used. The primary reasons are: 1. Reduction of Stress: A flat face distributes the contact load over a larger area compared to a knife-edge or roller follower, reducing the contact stress (Hertzian stress) on the cam surface. 2. Stability at High Speeds: At the very high rotational speeds typical of aircraft engines, roller followers can suffer from 'skidding' or 'sliding' if the roller cannot keep up with the cam profile, leading to rapid wear. Flat-faced followers eliminate the risk of roller skidding. 3. Compactness: They allow for a more compact design in the cylinder head.
Comparison with other options:
- Knife edge followers (a) are theoretical and suffer from extreme wear due to high contact stress; they are never used in actual engines.
- Spherical faced followers (c) are used to reduce stress compared to knife-edge but are less efficient than flat-faced followers for the specific high-load, high-speed requirements of aircraft valves.
- Roller followers (d) are common in automotive engines to reduce friction, but in high-performance aircraft engines, the risk of roller skidding and the added mass/complexity often make the flat-faced follower the preferred choice for specific valve train designs.