← MES Jr. Grade
Past Questions
Distinguish Tresca failure theory and Von Mises yield theory with five important points.
On the motors with low starting torque, the type of the clutch to be used is:
A)
Multiple-plate clutch
B)
Cone clutch
C)
Centrifugal clutch
D)
Single-plate clutch with both sides effective
A centrifugal clutch is an automatic clutch that engages based on the rotational speed of the driving member. In motors with low starting torque, the motor cannot handle a sudden load at zero or low speed; if a manual clutch (like a single-plate or cone clutch) were engaged immediately, the motor might stall or fail to start due to the high initial load. The centrifugal clutch solves this by remaining disengaged while the motor accelerates to a specific speed where it has developed sufficient torque to handle the load. Once the motor reaches this critical speed, centrifugal force pushes the weights/shoes against the drum, gradually engaging the clutch. This ensures a smooth transition and prevents the motor from stalling during the startup phase.
Other options are incorrect because:
- a. Multiple-plate clutches are used where high torque transmission is required in a compact space.
- b. Cone clutches provide high torque transmission due to the wedge effect but are not automatic.
- d. Single-plate clutches are standard manual clutches and do not provide the automatic speed-dependent engagement required for low starting torque motors.
A hollow shaft has greater strength and stiffness than solid shaft of equal weight. Explain.
A circle drawn with centre as the cam centre and radius equal to the distance between the cam centre and the point on the pitch curve at which the pressure angle is maximum, is called:
A)
base circle
B)
pitch circle
C)
prime circle
D)
none of these
In cam mechanism design, different circles are defined to describe the geometry of the cam:
1. **Base Circle**: The smallest circle that can be drawn to the cam profile. It is the circle from which the cam profile is generated.
2. **Pitch Curve**: The locus of the center of the roller (if a roller follower is used) as it moves in contact with the cam.
3. **Prime Circle**: This is the smallest circle drawn with the cam center as the center and a radius equal to the distance between the cam center and the point on the pitch curve where the pressure angle is maximum. Essentially, it is the circle that passes through the point on the pitch curve closest to the cam center (for a radial follower). It is used to determine the minimum size of the cam to ensure the pressure angle does not exceed a permissible limit.
4. **Pressure Angle**: The angle between the direction of the follower's motion and the normal to the pitch curve. To keep this angle low (to prevent jamming), the prime circle radius is often adjusted.
Since the question specifically describes the circle passing through the point on the pitch curve associated with the maximum pressure angle (or the minimum distance from the center to the pitch curve), it refers to the Prime Circle.
According to the Lewis equation which one of the following is correct?
A)
Pinion is always weaker than gear.
B)
Pinion is weaker than gear if both are made up of same material
C)
Gear is weaker than pinion if both are made up of same material
D)
Gear is always weaker than pinion
The Lewis equation for the beam strength of a gear tooth 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. The Lewis form factor (Y) depends on the number of teeth on the gear. For a given module and material, the form factor Y increases as the number of teeth increases. In a gear pair, the pinion is the smaller gear and thus has fewer teeth than the gear. Consequently, the Lewis form factor for the pinion (Yp) is smaller than that for the gear (Yg). Since the strength of the tooth is directly proportional to the form factor, the pinion tooth is weaker than the gear tooth when both are made of the same material and have the same face width and module. Therefore, the design of a gear drive is usually governed by the strength of the pinion.
In a cone pulley, if the sum of radii of the pulleys on the driving and driven shafts is constant, then:
A)
open belt drive is recommended
B)
cross belt drive is recommended
C)
both open belt drive and cross belt drive are recommended
D)
the drive is recommended depending upon the torque transmitted
In a cone pulley system, multiple pulleys of different diameters are mounted on the shafts to provide different speed ratios. For the system to function efficiently without needing to adjust the center distance between the shafts for every speed change, the length of the belt must remain constant for all pulley pairs.
1. For an **Open Belt Drive**, the length of the belt (L) is approximately given by: L ≈ 2C + 1.57(r1 + r2) + (r1 - r2)² / 4C, where C is the center distance and r1, r2 are the radii of the pulleys. If the sum of the radii (r1 + r2) is constant, the length of the belt remains nearly constant regardless of which pair of pulleys is engaged.
2. For a **Cross Belt Drive**, the length of the belt is approximately: L ≈ 2C + 1.57(r1 + r2) + (r1 + r2)² / 4C. While this also depends on the sum of radii, the geometry of a cross belt drive is generally not used for cone pulleys because the belt would have to cross over the other pulleys on the shaft, leading to interference and mechanical impracticality.
Therefore, when the sum of the radii of the pulleys on the driving and driven shafts is constant, an open belt drive is recommended because it allows the same belt to be used for all speed combinations without adjusting the center distance.
A concentrated mass m is attached at the centre of a rod of length 2L as shown in the figure. The rod is kept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude of vibration, neglecting the weights of the rod and spring, the undamped natural frequency of the system is:
A)
k/m
B)
2k/m
C)
k/2m
D)
4k/m
Option B is correct: 2k/m.
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.
Every material obeys the Hooke’s law within:
A)
Elastic limit
B)
Plastic limit
C)
Limit of proportionality
D)
None of these
Option C is correct: Limit of proportionality.
The ratio of the ultimate stress to the design stress is known as:
A)
elastic limit
B)
strain
C)
factor of safety
D)
bulk modulus
In machine design, the 'Factor of Safety' (FoS) is a design margin used to ensure that a structure or component can handle more than its intended load to account for uncertainties in material properties, loading conditions, and manufacturing tolerances. It is mathematically defined as the ratio of the failure stress (Ultimate Stress or Yield Stress, depending on the material) to the allowable stress (Design Stress or Working Stress).
Formula: Factor of Safety = Ultimate Stress / Design Stress.
Why other options are incorrect:
- a. Elastic Limit: This is the maximum stress a material can withstand without permanent deformation; it is a material property, not a ratio of stresses.
- b. Strain: This is the ratio of change in dimension to the original dimension (deformation), not a ratio of stresses.
- d. Bulk Modulus: This is a measure of a substance's resistance to uniform compression (ratio of volumetric stress to volumetric strain).
Derive the expression for thermal stress when expansion of a body is fully restrained.
In the figure, Pinion 1 runs at 1750 rpm and transmits 2.5 kW to idler gear 2. The teeth are out on the 20° full depth system and have a module of 2.5 mm. The resultant shaft reaction on the idler gear is
A)
581 N
B)
340 N
C)
480 N
D)
608 N
Option D is correct: 608 N.
The Poisson’s ratio for steel varies from:
A)
0.21 to 0.25
B)
0.25 to 0.33
C)
0.33 to 0.38
D)
0.38 to 0.45
Poisson's ratio (ν) is the ratio of lateral strain to longitudinal strain when a material is stretched or compressed. For most structural metals, this value typically falls between 0.25 and 0.35. Specifically for steel, the standard accepted range in strength of materials and engineering textbooks is approximately 0.27 to 0.30, which fits squarely within the range of 0.25 to 0.33.
- Option (a) 0.21 to 0.25 is generally too low for standard structural steel.
- Option (c) 0.33 to 0.38 is more characteristic of aluminum or some copper alloys.
- Option (d) 0.38 to 0.45 is characteristic of highly plastic materials or rubber (which approaches 0.5 for incompressible materials).
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.
Whirling Speed of a shaft coincides with the natural frequency of its:
A)
longitudinal vibration
B)
transverse vibration
C)
torsional vibration
D)
coupled bending torsional vibration
Whirling of a shaft occurs when the shaft rotates at a speed that excites its lateral (transverse) vibrations. This phenomenon happens when the rotational speed of the shaft coincides with the natural frequency of transverse vibration. At this critical speed, the centrifugal force caused by a slight eccentricity (offset between the geometric center and the center of mass) causes the shaft to deflect or 'bow' outward, leading to high-amplitude vibrations.
Why other options are incorrect:
- Longitudinal vibration (a) refers to vibrations along the axis of the shaft, which is not caused by rotation/whirling.
- Torsional vibration (c) refers to the twisting of the shaft about its axis, governed by the shear modulus and polar moment of inertia, not the lateral stiffness.
- Coupled bending torsional vibration (d) is a complex mode where both bending and twisting occur, but the fundamental definition of 'whirling speed' specifically refers to the transverse (bending) mode.
If the value of Poisson’s ratio is zero, then it means that:
A)
The material is rigid
B)
The material is perfectly plastic
C)
There is no longitudinal strain in the material
D)
The longitudinal strain in the material is infinite
Poisson's ratio (ν) is defined as the ratio of lateral strain to longitudinal strain: ν = -(lateral strain / longitudinal strain).
1. Analysis of ν = 0: If Poisson's ratio is zero, it means that when a material is stretched or compressed in one direction, there is no change in its dimensions in the directions perpendicular to the applied force (lateral strain = 0).
2. Material Behavior: A material that does not exhibit lateral contraction when stretched (or lateral expansion when compressed) is characteristic of certain specialized materials like cork. In the context of theoretical material science and plasticity, a 'perfectly plastic' material (specifically in the context of plastic flow or incompressible materials in some contexts, though usually, perfectly plastic refers to the stress-strain curve) is often contrasted with elastic materials. However, more accurately, a material with ν = 0 is one where the volume changes purely based on the longitudinal strain without any compensating lateral movement.
3. Evaluating Options:
- Option (a) 'The material is rigid': Incorrect. A rigid material would have zero strain in all directions, making the ratio 0/0 (undefined), not specifically 0.
- Option (c) 'There is no longitudinal strain': Incorrect. If longitudinal strain were zero, the ratio would be undefined (division by zero).
- Option (d) 'The longitudinal strain is infinite': Incorrect. This is physically impossible for real materials and would make the ratio zero, but it is not the definition of a material property.
- Option (b) 'The material is perfectly plastic': In many technical exam contexts for Civil Engineering, materials that do not exhibit the 'Poisson effect' (like cork) are associated with specific plastic or cellular behaviors. While 'perfectly plastic' usually refers to the stress-strain relationship (constant stress), in the specific context of these multiple-choice options, it is the only viable choice as it describes a material that does not behave according to linear elastic Poisson's laws. Note: In some advanced texts, a material with ν = 0 is simply called a 'non-Poissonian' material, but among the given choices, (b) is the standard intended answer for this specific question pattern in competitive exams.
Figure shows a rolled steel beam of an unsymmetrical I-section. If the maximum bending stress in the beam section is not to exceed 40 MPa, find the moment, which the beam can resist.
What do you understand by the instantaneous centre of rotation (centro) in kinematic of machines? Answer briefly.
The ratio of the maximum displacement of the forced vibration to the deflection due to the static force is known as:
A)
damping factor
B)
damping coefficient
C)
logarithmic decrement
D)
magnification factor
In the study of forced vibrations, the 'Magnification Factor' (also known as the Amplification Factor) is defined as the ratio of the steady-state amplitude of the forced vibration (maximum displacement, X) to the static deflection (δst) caused by the force. Mathematically, it is expressed as MF = X / δst.
Why other options are incorrect:
- a. Damping factor (ζ): This is a dimensionless measure describing how oscillations in a system decay after a disturbance.
- b. Damping coefficient (c): This is a constant that represents the viscous damping force per unit velocity (measured in N-s/m).
- c. Logarithmic decrement (δ): This is the natural logarithm of the ratio of any two successive amplitudes in a free damped vibration system.
Write the précis of the provided passage regarding free speech, democracy, and the necessity of opposition in about one-third of its original length.
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.
Quantization noise power is inversely proportional to:
A)
Sampling rate
B)
Signal power
C)
Square of number of quantization levels
D)
Bandwidth
In a uniform quantizer, the quantization noise power (also known as quantization error variance) is given by the formula: Pq = (Δ^2) / 12, where Δ is the step size. The step size Δ is defined as Δ = (Vmax - Vmin) / L, where (Vmax - Vmin) is the full-scale range of the signal and L is the number of quantization levels. Substituting Δ into the power formula, we get: Pq = ((Vmax - Vmin)^2) / (12 * L^2). From this expression, it is evident that the quantization noise power (Pq) is inversely proportional to the square of the number of quantization levels (L^2). Increasing the number of levels reduces the step size, thereby reducing the noise power. Options a, b, and d are incorrect because the noise power depends on the resolution of the quantizer (L), not on the sampling rate, the signal power, or the bandwidth of the system.
A 555 timer is used in astable mode with R1 = 2 kV, R2 = 5 kV, and C = 0.1 mF. Calculate the frequency of oscillation and duty cycle.
Explain with figure the working of a snubber Circuit used in SCR subjected to Rs and Cs.
Explain the concept of differential amplifier. Derive expressions for differential gain and common-mode gain.