← MES Jr. Grade
Past Questions — 2025
Which one of the following types of cams has either a convex or a concave surface?
A)
Conjugate cam
B)
Spherical cam
C)
Globoidal cam
D)
Spiral cam
In the study of Theory of Machines, cams are classified based on their shape and the motion of the follower.
1. **Spherical Cam**: A spherical cam is a cam whose surface is a part of a sphere. Depending on the design, the working surface can be either convex (bulging outward) or concave (curving inward). The follower typically moves in a spherical path.
2. **Conjugate Cam**: These are a pair of cams designed to work together to eliminate backlash or provide a precise return motion. They are defined by their relationship to each other rather than a specific convex/concave geometry.
3. **Globoidal Cam**: A globoidal cam is a 3D cam where the cam surface is developed on a sphere or a cylinder, but it is specifically characterized by its 'globular' shape used to translate rotary motion into a reciprocating motion of a follower that is not necessarily aligned with the axis of rotation. While it is curved, the specific definition of having 'either a convex or concave surface' as a primary classification trait refers to the Spherical cam.
4. **Spiral Cam**: A spiral cam is a type of cylindrical cam where the groove is cut in a spiral shape on the surface of a cylinder. Its primary characteristic is the spiral path, not a convex/concave spherical surface.
Therefore, the Spherical cam is the correct answer as it is explicitly defined by its spherical (convex or concave) geometry.
The shock absorbing capacity of a bolt may be increased by:
A)
increasing its shank diameter
B)
decreasing its shank diameter
C)
tightening the bolt properly
D)
making the shank diameter equal to the core diameter of the thread.
Shock absorbing capacity in a bolt refers to its ability to absorb energy through elastic deformation when subjected to sudden loads or impacts.
1. **Energy Absorption Principle**: The energy absorbed by a material during elastic deformation is given by the strain energy formula: U = (σ²V) / (2E), where σ is the stress, V is the volume of the material, and E is the Young's modulus.
2. **Effect of Diameter**: For a given load, the stress (σ) is inversely proportional to the cross-sectional area (A = πd²/4). If the shank diameter (d) is decreased, the stress increases. Since the energy absorption depends on the square of the stress (σ²), a smaller diameter allows the bolt to undergo greater elastic elongation (strain) for the same load, thereby absorbing more energy before reaching its yield point.
3. **Comparison**:
- Increasing the shank diameter (Option a) makes the bolt stiffer, reducing its ability to stretch and absorb shock.
- Tightening the bolt (Option c) increases the initial tension (preload), which may prevent loosening but does not increase the inherent shock-absorbing capacity of the material itself.
- Making the shank diameter equal to the core diameter (Option d) is a specific design choice but does not inherently 'increase' capacity compared to further reducing the diameter within safe limits.
Therefore, decreasing the shank diameter increases the flexibility and the elastic strain energy capacity of the bolt, enhancing its shock-absorbing ability.
The factor which affects the critical speed of a shaft is:
A)
diameter of the disc
B)
span of the shaft
C)
eccentricity
D)
all of the above
Critical speed (or whirling speed) of a shaft is the speed at which the shaft becomes unstable and vibrates violently. Mathematically, the critical speed (ωc) is equivalent to the natural frequency of transverse vibration of the shaft. For a simple shaft with a central load, the formula is ωc = √(g / δ), where δ is the static deflection. Static deflection is given by δ = (W L^3) / (48 E I), where L is the span of the shaft, E is Young's modulus, and I is the moment of inertia. Therefore, the critical speed is directly dependent on the span of the shaft (L) and the stiffness of the shaft.
Regarding the other options:
- Diameter of the disc (a): While the mass of the disc affects the deflection, the diameter of the disc itself is not a primary parameter in the critical speed formula unless it changes the mass or the distribution of mass significantly.
- Eccentricity (c): Eccentricity affects the magnitude of the vibration (the amplitude of the whirl) and the severity of the instability, but it does NOT change the value of the critical speed itself. The critical speed is a property of the system's mass and stiffness, regardless of whether the mass is perfectly centered or eccentric.
Thus, among the given options, the span of the shaft is the factor that fundamentally determines the critical speed.
What do you understand by the instantaneous centre of rotation (centro) in kinematic of machines? Answer briefly.
Distinguish Tresca failure theory and Von Mises yield theory with five important points.
The effect of increasing the stiffness of springs of centrifugal clutch is:
A)
The decrease of engagement speed
B)
The increase of engagement speed
C)
The increase of frictional force at maximum speed
D)
There is no effect on the engagement speed
In a centrifugal clutch, engagement occurs when the centrifugal force acting on the clutch shoes overcomes the compressive force exerted by the engagement springs.
1. The centrifugal force (F_c) is given by the formula: F_c = m * ω² * r, where 'm' is the mass of the shoe, 'ω' is the angular velocity, and 'r' is the radius of the center of gravity of the shoe.
2. The spring force (F_s) is given by: F_s = k * x, where 'k' is the stiffness (spring constant) and 'x' is the deflection.
3. Engagement begins at the 'engagement speed' (ω_e) when the centrifugal force equals the spring force: m * ω_e² * r = k * x.
4. Rearranging for engagement speed: ω_e = √( (k * x) / (m * r) ).
From this relationship, it is clear that the engagement speed (ω_e) is directly proportional to the square root of the spring stiffness (k). Therefore, if the stiffness of the springs is increased, a higher angular velocity (speed) is required to generate enough centrifugal force to compress the springs and engage the clutch.
Regarding other options:
- Option (a) is incorrect because increasing stiffness increases the speed required for engagement, not decreases it.
- Option (c) is incorrect because the frictional force at maximum speed depends on the total centrifugal force minus the spring force; while stiffness affects the net force, the primary and most direct effect of increasing stiffness is the shift in the engagement threshold.
- Option (d) is incorrect as the spring constant is a primary variable in the engagement equation.
Show that the expression for Mohr’s circle for a stress element subjected at any state of stress is (σx + σy)/2 + τxy^2 = τs^2 + ((σx - σy)/2)^2.
What is the difference in the analysis of thick tubes compared to that for thin tubes? State the basic equations describing stress distribution in a thick tube.
Interference can be avoided in involute gears with 20° pressure angle by:
A)
cutting involute correctly
B)
using as small number of teeth as possible
C)
using more than 20 teeth
D)
using more than 8 teeth
Interference in involute gears occurs when the teeth of the pinion are too few, causing the tip of the gear tooth to contact the non-involute portion (the flank) of the pinion tooth. To avoid interference, there is a minimum number of teeth required on the pinion, which depends on the pressure angle (φ) and the gear ratio.
For a standard gear pair where the gear is significantly larger than the pinion (or for a rack and pinion), the minimum number of teeth to avoid interference is given by the formula:
Minimum teeth (z_min) = (2 / sin²φ)
Given the pressure angle φ = 20°:
1. sin(20°) ≈ 0.342
2. sin²(20°) ≈ 0.117
3. z_min = 2 / 0.117 ≈ 17.09
Since the number of teeth must be an integer, the minimum number of teeth required to completely avoid interference for a 20° pressure angle is 18.
Evaluating the options:
- Option (a) is incorrect because correct cutting of the involute profile does not prevent interference if the geometry (number of teeth) is insufficient.
- Option (b) is incorrect because reducing the number of teeth actually increases the likelihood of interference.
- Option (c) 'using more than 20 teeth' is correct because it exceeds the minimum threshold of 18 teeth, ensuring no interference occurs.
- Option (d) 'using more than 8 teeth' is incorrect because 8 teeth is well below the minimum requirement of 18, meaning interference would still occur.
During tensile-testing of a specimen using a Universal Testing Machine, the parameters actually measured include:
A)
True stress and true strain
B)
Poisson’s ratio and Young’s modulus
C)
Engineering stress and engineering strain
D)
Load and elongation
In a tensile test conducted using a Universal Testing Machine (UTM), the machine is equipped with two primary sensors: a load cell (to measure the applied force or load) and an extensometer or crosshead displacement sensor (to measure the change in length or elongation).
1. **Load (P):** This is the direct force applied by the machine's crosshead.
2. **Elongation (ΔL):** This is the direct measurement of how much the specimen has stretched.
All other parameters mentioned in the options are 'calculated' or 'derived' values, not 'measured' values:
- **Engineering Stress (σ):** Calculated as Load / Original Area (P/A₀).
- **Engineering Strain (ε):** Calculated as Elongation / Original Length (ΔL/L₀).
- **True Stress and True Strain:** Calculated using the instantaneous area and length during the test.
- **Young's Modulus (E) and Poisson's Ratio (ν):** These are material properties derived from the slope of the stress-strain curve and the ratio of lateral to longitudinal strain, respectively.
In designing a plate clutch, assumption of uniform wear conditions is made because:
A)
It is closer to real life situation
B)
it leads to a safer design
C)
It leads to cost effective design
D)
no other assumption is possible
In the design of plate clutches, two primary theories are used to calculate torque transmission: Uniform Pressure Theory (UPT) and Uniform Wear Theory (UWT).
1. **Uniform Pressure Theory**: Assumes the pressure is constant across the entire contact surface. This is typically applicable to new clutches. The torque calculated using this theory is higher than that calculated using UWT.
2. **Uniform Wear Theory**: Assumes that the product of pressure (p) and radius (r) is constant (p × r = C). This accounts for the fact that as the clutch wears, the pressure distribution changes. Because the pressure is assumed to be lower at the outer radius compared to the inner radius (relative to UPT), the resulting torque capacity calculated is lower.
**Why it leads to a safer design:** In engineering, designing for the 'worst-case scenario' is the standard for safety. Since the Uniform Wear Theory predicts a lower torque transmission capacity than the Uniform Pressure Theory, designing a clutch based on UWT ensures that the clutch will still perform its required function even after it has undergone significant wear. If a designer used UPT, the clutch might fail to transmit the required torque once the surfaces are no longer perfectly new. Therefore, UWT is considered the conservative and safer approach for design.
The rigid body is replaced by two concentrated masses rigidly connected together. The system will be kinetically equivalent of the body if:
A)
the mass of two masses is equal to the mass of rigid body
B)
the centre of gravity of two mass system coincides with the centre of gravity of rigid body
C)
the mass moment of inertia of the two mass system and the rigid body about centre of gravity are equal
D)
all of the above
In the Theory of Machines, specifically in the study of balancing and dynamics, a rigid body can be replaced by a simplified system of concentrated masses. Depending on the requirements of the analysis, we use different types of equivalence:
1. **Statically Equivalent System**: A system is statically equivalent if it has the same total mass and the same center of gravity (CG) as the original body. This ensures that the translational forces (like gravity) are represented correctly. This corresponds to options (a) and (b).
2. **Kinetically Equivalent System**: A system is kinetically equivalent if it is statically equivalent AND has the same mass moment of inertia about the center of gravity as the original body. This ensures that the rotational dynamics (torque and angular acceleration) are represented correctly. This corresponds to option (c).
Therefore, for a system of two concentrated masses to be 'kinetically equivalent' to a rigid body, it must satisfy all three conditions:
- The sum of the masses must equal the total mass of the body (Option a).
- The center of gravity of the two masses must coincide with the center of gravity of the body (Option b).
- The mass moment of inertia about the center of gravity must be identical (Option c).
Since all three conditions are necessary for kinetic equivalence, the correct answer is 'all of the above'.
What are true stress and true strain? Why is true strain a better measure of strain and true stress a better representation of stress?
Derive the expression for thermal stress when expansion of a body is fully restrained.
A pulley and belt in a belt drive form a:
A)
Cylindrical pair
B)
turning pair
C)
rolling pair
D)
sliding pair
In the Theory of Machines, a kinematic pair is defined by the type of relative motion between two links.
1. **Analysis of the Pulley and Belt**: A pulley is essentially a cylinder. When a belt wraps around a pulley, the contact surface is the curved surface of the cylinder. The relative motion allowed is the rotation of the pulley and the linear translation of the belt along the circumference.
2. **Cylindrical Pair**: A cylindrical pair is formed when one link is a cylinder and the other is a hole/surface that allows both rotation and translation along the axis or surface. In the context of a belt drive, the interaction between the belt and the pulley surface is categorized as a cylindrical pair because the belt 'wraps' around the cylindrical geometry of the pulley.
3. **Why other options are incorrect**:
- **Turning Pair (Revolute Pair)**: This involves a pin joint where one link rotates about a fixed axis relative to another (e.g., a hinge). The belt does not rotate 'about' the pulley in a pin-joint fashion.
- **Rolling Pair**: This occurs when two surfaces roll over each other without slipping (e.g., a ball bearing). While there is friction, a belt drive is designed to prevent rolling; it relies on grip/friction to transmit power.
- **Sliding Pair**: This occurs when two flat surfaces slide over each other (e.g., a piston in a cylinder). The geometry here is curved, not flat.
Twenty-degree full depth involute profiled 19-tooth pinion and 37-tooth gear are in mesh. If the module is 5 mm, the centre distance between the gear pair will be:
A)
140 mm
B)
150 mm
C)
280 mm
D)
300 mm
To find the center distance between a pinion and a gear, we use the standard formula for spur gears.
1. **Given Data:**
- Number of teeth on pinion ($z_p$) = 19
- Number of teeth on gear ($z_g$) = 37
- Module ($m$) = 5 mm
- Pressure angle = 20° (Note: The pressure angle is provided but is not required for calculating the center distance of standard gears).
2. **Formula for Pitch Circle Diameter (D):**
The diameter of a gear is the product of the module and the number of teeth.
- Diameter of pinion ($D_p$) = $m \times z_p = 5 \text{ mm} \times 19 = 95 \text{ mm}$
- Diameter of gear ($D_g$) = $m \times z_g = 5 \text{ mm} \times 37 = 185 \text{ mm}$
3. **Formula for Center Distance (C):**
The center distance is the sum of the radii of the pinion and the gear, or half the sum of their pitch circle diameters.
- $C = \frac{D_p + D_g}{2}$
- $C = \frac{95 + 185}{2}$
- $C = \frac{280}{2}$
- $C = 140 \text{ mm}$
Alternatively, the formula can be written as: $C = \frac{m(z_p + z_g)}{2} = \frac{5(19 + 37)}{2} = \frac{5 \times 56}{2} = 5 \times 28 = 140 \text{ mm}$.
Comparing this result to the options:
- Option (a) 140 mm is correct.
- Option (b) 150 mm is incorrect.
- Option (c) 280 mm is the sum of the diameters, not the center distance.
- Option (d) 300 mm is incorrect.
For a point inside a rod subjected to pure torsion with shear stress , which of the following correctly describes Mohr’s circle?
A)
Centre at (0,0) with a radius equal to the normal stress
B)
Centre at (0,0) with a radius equal to the shear stress ()
C)
Centre at (,0) with a radius equal to the shear stress ()
D)
A point along the normal stress axis
Step-by-step reasoning:
1. **State of Stress**: A rod subjected to pure torsion experiences a state of 'pure shear'. For a point inside the rod, the normal stresses in the longitudinal and transverse directions are zero (σx = 0, σy = 0), and the only non-zero stress is the shear stress (τxy = τ).
2. **Mohr's Circle Parameters**: The center of Mohr's circle is located at the average normal stress: Center = ((σx + σy) / 2, 0). Substituting the values: Center = ((0 + 0) / 2, 0) = (0, 0).
3. **Radius Calculation**: The radius (R) of Mohr's circle is given by the formula: R = sqrt(((σx - σy)/2)^2 + τxy^2). Substituting the values: R = sqrt(((0 - 0)/2)^2 + τ^2) = sqrt(τ^2) = τ.
4. **Conclusion**: The circle is centered at the origin (0,0) and has a radius equal to the magnitude of the shear stress τ.
Analysis of other options:
- Option (a) is incorrect because there is no applied normal stress in pure torsion.
- Option (c) is incorrect because the center is at the origin, not at (τ, 0).
- Option (d) is incorrect because pure shear results in a full circle representing various stress states at different planes, not a single point.
Explain the construction and working of Whitworth quick return mechanism.
Define ‘slenderness ratio’. How it is used to define long and short columns?
Write an essay on any one of the following: - Relationship between mental health and modern work culture. - Efficacy of the current educational system in fostering innovation. - The imperative of urban planning in enhancing the quality of life. - The impact of scientific advancements on modern education.
Write the précis of the provided passage regarding free speech, democracy, and the necessity of opposition in about one-third of its original length.
For the mid-point cycloconverter, source voltage is Vm sinvt. Derive an expression for the rms value of output voltage (a) for firing angle a = 0° and (b) for firing angle a = a1.
The universal gates are:
A)
AND, OR, NOT
B)
NAND and NOR
C)
X-OR and X-NOR
D)
All of the above
In digital electronics, a 'universal gate' is a gate that can be used to implement any other Boolean function without the need for any other gate type.
1. **NAND Gate**: By combining NAND gates, one can create NOT, AND, OR, and XOR functions. For example, a NAND gate with tied inputs acts as a NOT gate.
2. **NOR Gate**: Similarly, by combining NOR gates, one can implement all basic logic functions (NOT, OR, AND, etc.).
Evaluating the options:
- Option (a): AND, OR, and NOT are 'Basic Gates'. While they can implement any function together, no single one of them can implement all others on its own.
- Option (b): NAND and NOR are the only two gates that possess the property of universality.
- Option (c): XOR and XNOR are 'Special Purpose Gates' used primarily for parity checking and arithmetic operations; they are not universal.
- Option (d): Incorrect because only option (b) satisfies the definition.
Nyquist rate for a signal with maximum frequency fmax is:
A)
fmax
B)
2 fmax
C)
fmax /2
D)
4 fmax
The Nyquist Sampling Theorem states that to perfectly reconstruct a continuous-time signal from its samples, the sampling frequency (fs) must be at least twice the highest frequency component (fmax) present in the signal.
1. Definition: The minimum sampling rate required to avoid aliasing is called the Nyquist Rate.
2. Mathematical Formula: Nyquist Rate = 2 × fmax.
3. Reasoning: If the sampling rate is less than 2 fmax, overlapping occurs in the frequency domain (aliasing), making it impossible to recover the original signal.
Evaluating the options:
- Option (a) fmax: This is only half the required rate; aliasing will occur.
- Option (b) 2 fmax: This is the correct definition of the Nyquist rate.
- Option (c) fmax / 2: This is significantly below the required rate.
- Option (d) 4 fmax: While sampling at this rate would prevent aliasing (oversampling), it is not the 'Nyquist rate', which specifically refers to the minimum required rate.
Assume that 4 bit counter is holding the count 0101. What will be the count after 27 clock pulse?
A)
0000
B)
0001
C)
0010
D)
0011
A 4-bit counter counts modulo 16, so after every 16 clock pulses it repeats. Starting from 0101 (decimal 5), after 27 pulses the count becomes 5 + 27 = 32. Modulo 16, 32 ≡ 0, so the counter returns to 0000 after 27 pulses. Hence option (a) is the mathematically correct result. However, since the options given include 0000 as (a), that is the correct choice. The other options are incorrect because 0001, 0010, and 0011 correspond to decimal 1, 2, and 3 respectively, not the modulo-16 result of 0.