Past Questions — 2010

A laminated leaf spring consists of several strips (leaves) of varying lengths stacked together. When a load is applied, the spring bends. If all the leaves were of the same length, the stress would be concentrated primarily at the center (the point of application of the load), leading to premature failure at that point while the ends of the leaves remain under-stressed. By providing strips of different lengths (graduated lengths), the bending moment is distributed more uniformly across the length of the spring. This ensures that the stress is distributed equally among the various leaves, maximizing the material efficiency and increasing the overall life and load-carrying capacity of the spring. - Option (b) 'light weight' is a secondary benefit of optimizing material, but not the primary engineering reason for varying lengths. - Option (c) 'ease in installing' is incorrect as varying lengths actually make the assembly more complex than using uniform strips.

High Speed Steel (HSS) is an alloy steel specifically designed to maintain its hardness and cutting edge even at elevated temperatures generated during high-speed machining. Tungsten (W) is a primary alloying element in HSS. It forms hard, stable carbides (such as WC) that resist softening at high temperatures. This property is known as 'red hardness' or 'hot hardness.' While other elements like Chromium provide wear resistance and corrosion resistance, and Vanadium improves grain refinement and wear resistance, Tungsten is specifically credited with providing the hot hardness necessary for the tool to operate at high speeds without losing its temper. - Option b (toughness) is generally provided by the balance of carbon and alloying elements, but tungsten actually tends to decrease toughness if present in excess. - Option c (wear resistance) is provided by various carbides, including those formed by Vanadium and Chromium. - Option d (cold hardness) is a general property of hardened steels, not the specific purpose of adding Tungsten in HSS.

The Coriolis component of acceleration occurs when a point moves along a path that is itself rotating. Mathematically, it is expressed as 2vω, where 'v' is the velocity of the point relative to the rotating frame and 'ω' is the angular velocity of that frame. 1. In a Quick Return Mechanism (specifically the Crank and Slotted Lever mechanism used in shapers), the slider moves along the slotted lever. Since the slider has a velocity (v) relative to the lever and the lever itself is rotating (ω), a Coriolis acceleration component is generated. This is a classic textbook example of Coriolis acceleration in machine theory. 2. In a simple Four Bar Chain mechanism, the links are rigid; there is no point moving relative to a rotating link, so no Coriolis component exists. 3. In a standard Slider Crank mechanism, the piston moves relative to the cylinder (which is stationary) and the connecting rod rotates, but there is no point moving along a rotating link in the same manner as the slotted lever mechanism. Therefore, Coriolis acceleration is not encountered in the basic slider crank.

Bearing liners (or bearing shells) require materials with specific properties: low friction, high embeddability (the ability to allow small grit particles to sink into the material to avoid scratching the shaft), and conformability. 1. **Babbitt Metal (Option d):** This is a white-metal alloy typically consisting of tin or lead mixed with antimony and copper. It is specifically engineered for use as a lining for bearings because it is soft enough to conform to the shaft and embed contaminants, yet strong enough to support the load under lubrication. It is the standard material for high-load, low-speed sliding bearings. 2. **Gun Metal (Option a):** A type of bronze (copper-tin-zinc). While used for bushings and valves, it is harder than Babbitt metal and lacks the same embeddability for high-precision liner applications. 3. **Bronze (Option b):** A general category of copper alloys. While used for many bearing types (like sleeve bearings), 'Babbitt' is the more specialized answer for 'liner' materials specifically designed for wear and protection of the shaft. 4. **Bell Metal (Option c):** A high-tin bronze used primarily for bells and some heavy-duty bearings, but it is too brittle and hard to be used as a general-purpose bearing liner compared to Babbitt metal.

Iron exhibits allotropy, meaning it exists in different crystal structures depending on the temperature. 1. Alpha-iron (α-Fe): This is the stable form of iron at room temperature (up to 912°C). It possesses a Body-Centered Cubic (BCC) structure. In this arrangement, there is one atom at each corner of the cube and one atom at the center of the cube. 2. Gamma-iron (γ-Fe): Also known as austenite, this form exists between 912°C and 1394°C and possesses a Face-Centered Cubic (FCC) structure. 3. Delta-iron (δ-Fe): This form exists from 1394°C up to the melting point (1538°C) and reverts to a Body-Centered Cubic (BCC) structure. Therefore, alpha iron is specifically characterized by a body-centered cubic lattice.

Bending stress σ=M y /I, inversely proportional to section modulus (I/y).

In a centrifugal governor, the sleeve moves up or down based on the balance between the centrifugal force (generated by the rotating fly-balls) and the downward force (usually provided by a spring or the weight of the balls). 1. When the speed of the governor increases, the centrifugal force increases, pushing the sleeve upward. 2. When the speed decreases, the centrifugal force decreases, and the sleeve moves downward. 3. For the sleeve to be in a state of equilibrium at a specific speed (constant speed), the net force acting on the sleeve must be zero. According to Newton's First Law of Motion, if an object (the sleeve) is at rest or moving at a constant velocity (constant position in the case of a governor running at a steady state), the vector sum of all forces acting upon it must be zero. Therefore, for a governor running at a constant speed, the sleeve remains at a fixed position, meaning the upward centrifugal force is exactly balanced by the downward restoring force, resulting in a net force of zero.

In the context of Value Engineering (VE) and Value Analysis (VA), 'Value' is defined as the ratio of the function of a product or service to the cost required to achieve that function. The fundamental formula used in Value Engineering is: Value = Function / Cost. This means that value can be increased either by improving the function (performance/utility) without increasing the cost, or by reducing the cost while maintaining the same level of function. - Option (b) 'purchase value' refers to the acquisition cost, which is only one part of the cost equation. - Option (c) 'saleable value' refers to the market price or resale value, which is a commercial metric rather than an engineering value metric. - Option (a) correctly identifies the relationship between the utility (function) and the resources expended (cost).

A planer is a large machine tool used to produce flat surfaces. To specify the capacity or 'size' of a planer, one must define the maximum dimensions of the workpiece it can accommodate. This is determined by two primary factors: 1) The size of the table (specifically the length and width), which determines the maximum length and width of the workpiece that can be clamped and moved during the reciprocating stroke. 2) The height of the cross rail (or the distance between the table and the cross rail), which determines the maximum height of the workpiece that can be machined. While stroke length is a characteristic of the machine's operation, the overall 'size' specification of the machine as a piece of equipment is defined by the physical envelope it can handle, which is the table dimensions and the cross rail height.

When a nut is tightened onto a bolt, the nut pulls the bolt head (or the bolted joint) toward it. This action creates a clamping force that compresses the materials between the nut and the bolt head. According to Newton's Third Law, as the nut exerts a compressive force on the joint, the joint exerts an equal and opposite force on the bolt. This results in the bolt being stretched along its longitudinal axis. In mechanics of materials, a load that tends to stretch or elongate a body is defined as a tensile load. Therefore, the bolt is subjected to tension. - Option (a) Compression is incorrect because the bolt is being stretched, not squeezed. - Option (c) Shear is incorrect because the primary load resulting from tightening is axial, not transverse (perpendicular to the axis). - Option (d) is incorrect as tension is the primary load experienced.

The shear stress ($ au$) induced in a circular shaft subjected to a torque ($T$) is governed by the torsion formula: $\tau = \frac{T \cdot r}{J}$, where $T$ is the applied torque, $r$ is the radial distance from the center of the shaft, and $J$ is the polar moment of inertia. From this formula, it is evident that the shear stress is directly proportional to the radius ($r$). Therefore: 1. At the center of the shaft ($r = 0$), the shear stress is zero. 2. As the distance from the center increases, the shear stress increases linearly. 3. At the outer surface or circumference ($r = R$), the shear stress reaches its maximum value. This linear distribution explains why option (c) is correct and options (a) and (b) are incorrect.

PERT (Program Evaluation and Review Technique) is a project management tool used primarily for projects where activity durations are uncertain. To account for this uncertainty, PERT uses a probabilistic approach involving three time estimates for each activity: 1. Optimistic Time (to): The minimum time required to complete an activity if everything goes perfectly. 2. Most Likely Time (tm): The most realistic time estimate, representing the duration that would occur most frequently if the activity were repeated many times. 3. Pessimistic Time (tp): The maximum time required if significant delays or obstacles occur. These three estimates are used to calculate the Expected Time (te) using the formula: te = (to + 4tm + tp) / 6. In contrast, CPM (Critical Path Method) typically uses a single-time (deterministic) estimate, making option 'a' incorrect. Options 'b' and 'd' are not standard practices in project management network analysis.

In the Theory of Machines, a kinematic pair is classified based on the type of contact between the two mating elements: 1. **Lower Pair**: When two elements have surface contact (area contact) while in motion, it is called a lower pair. Examples include sliding pairs (piston and cylinder), turning pairs (shaft in a bearing), and screw pairs. 2. **Higher Pair**: When two elements have point or line contact during motion, it is called a higher pair. Examples include gear teeth in mesh, cam and follower, or ball bearings. Analyzing the options: - Option (a) is incorrect because higher pairs involve point or line contact. - Option (b) is correct as surface contact is the defining characteristic of a lower pair. - Option (c) is incorrect because 'surface pair' is not a standard technical term used in kinematic classification. - Option (d) is incorrect because a rolling pair is a specific type of contact (often a higher pair if it's a ball/roller) and does not encompass all surface contact pairs.

In material science, specifically in the study of the Iron-Carbon equilibrium diagram, pure iron exists in different allotropic forms (crystal structures) depending on the temperature: 1. Alpha-iron (α-Fe): Ferrite, which is Body-Centered Cubic (BCC), stable from room temperature up to 912°C. 2. Gamma-iron (γ-Fe): Austenite, which is Face-Centered Cubic (FCC), stable between 912°C and 1394°C. 3. Delta-iron (δ-Fe): Delta-ferrite, which returns to a Body-Centered Cubic (BCC) structure, stable from 1394°C (approximately 1400°C) up to the melting point of iron. The melting point of pure iron is approximately 1538°C to 1539°C. Therefore, Delta iron occurs in the narrow temperature range between roughly 1400°C and 1539°C. Analysis of options: - Option (a) is incorrect because room temperature iron is Alpha-iron. - Option (b) is incorrect because above the melting point, iron exists as a liquid. - Option (c) is correct as it aligns with the stability range of the Delta phase.

Monel metal is a group of alloys primarily composed of nickel (Ni) and copper (Cu). The most common grade, Monel 400, typically consists of approximately 63% nickel and 31% copper, with small amounts of iron, manganese, carbon, and silicon. It is highly valued in engineering for its excellent corrosion resistance, particularly in seawater and marine environments, and its high strength. Analysis of other options: - Option b (nickel and molybdenum): While molybdenum is added to some specialized nickel alloys (like Hastelloy) to improve corrosion resistance, it is not the primary constituent of Monel. - Option c (zinc, tin and lead): These are common alloying elements for brass (copper-zinc) or bronze (copper-tin), but they are not the defining constituents of Monel metal.

A Hooke's joint, also known as a Universal joint (U-joint), is used to connect two shafts whose axes intersect at a small angle. The mechanism consists of two Y-shaped components called 'forks' and a central cross-shaped piece called a 'spider' or 'cross'. Each fork is connected to one of the shafts, and the two forks are linked together by the cross. The cross allows the forks to rotate independently of each other while transmitting torque, enabling the joint to operate even as the angle between the shafts changes during rotation. Therefore, the joint consists of exactly two forks.

In the Theory of Machines, a 'mechanism' is defined as a combination of rigid or resistant bodies (links) so shaped and connected that they move with definite relative motion with respect to each other. To achieve a constrained motion that can transmit or transform motion (the primary purpose of a mechanism), a minimum of four links is required. For example, the simplest possible mechanism is the four-bar chain. A system with only two links (a binary joint) or three links (a triangular frame) is either a simple joint or a rigid structure (truss) and cannot provide the relative motion necessary to be classified as a mechanism. Therefore, a mechanism must consist of four or more links.

The correct answer is buttress threads. Here is the detailed technical reasoning: 1. **Buttress Threads**: These are specifically designed for applications where the force (and thus the stress) is applied in only one direction. They have one face perpendicular (or nearly perpendicular) to the axis of the screw and the other face sloping. This design allows them to withstand very high axial loads in one direction while providing high efficiency, making them ideal for components like artillery breech blocks or screw jacks where the load is unidirectional. 2. **Square Threads**: These are used for power transmission because they have the highest efficiency (no radial pressure). However, they are designed to handle loads in both directions and are difficult to manufacture. 3. **Acme Threads**: These are a modification of square threads with a 29° angle. They are stronger and easier to manufacture than square threads and are used in lead screws of lathes. Like square threads, they are designed for bidirectional loads. 4. **Metric Threads**: These are standard V-threads (60° angle) primarily used for fastening purposes. They are not optimized for high-power transmission in a single direction. Therefore, for applications where stresses are encountered in one direction only, the buttress thread is the most efficient and appropriate choice.

A double slider crank chain consists of four links: two sliders and two connecting links. In this mechanism, two sliders move along perpendicular guides. If we analyze the motion of any point on the link connecting the two sliders (the coupling link), its coordinates (x, y) can be expressed in terms of the positions of the sliders. Specifically, if the sliders move along the X and Y axes, the distance between them remains constant (the length of the link). This geometric constraint follows the equation x² + y² = L², where L is the length of the link. However, for any point other than the sliders themselves on that connecting link, the locus is an ellipse. This is a fundamental principle used in the construction of 'Elliptical Trammels,' a device specifically designed to draw a perfect ellipse using a double slider crank mechanism.

In the context of pig iron and steel metallurgy, sulphur is considered an impurity. Sulphur reacts with iron to form iron sulphide (FeS). These sulphide inclusions typically concentrate at the grain boundaries of the metal. This presence of sulphur increases the hardness and brittleness of the material. Specifically, sulphur contributes to a phenomenon known as 'hot shortness' (brittleness at high temperatures), which makes the metal difficult to work or forge. Because it inhibits the sliding of grain boundaries and increases internal stress/resistance to deformation, it makes the pig iron harder and more brittle. Why other options are incorrect: - b. soft: Sulphur increases brittleness and hardness; it does not soften the metal. - c. ductile: Ductility is the ability to be drawn into wires. Sulphur significantly reduces ductility by promoting brittle fracture. - d. malleable: Malleability is the ability to be hammered into sheets. Sulphur makes the metal brittle, meaning it will crack rather than deform under compression, thus reducing malleability.

In the study of Strength of Materials, strain energy is the energy stored in a body due to deformation. 1. **Resilience**: This is the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered. It is the strain energy stored up to any point within the elastic limit. 2. **Proof Resilience**: This is the maximum energy that can be absorbed by a body per unit volume without permanent deformation. In other words, it is the strain energy stored when the material is stressed up to its elastic limit (or proportional limit). Since it is the 'maximum' energy stored within the elastic range, it is the correct answer. 3. **Toughness**: This is the total energy absorbed by a material up to the point of fracture. It includes both elastic and plastic deformation. While it is a 'maximum' energy, it refers to the energy until failure, not the stored energy typically associated with resilience. 4. **Impact Energy**: This refers to the energy absorbed by a material during a high-strain rate loading (like a Charpy or Izod test), which is a measure of toughness rather than a specific property of stored strain energy. Therefore, the maximum strain energy that can be stored (specifically within the elastic limit) is known as proof resilience.

In materials science and strength of materials, 'fatigue' refers to the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. The key characteristic of fatigue is that failure (or yielding/fracture) occurs at a stress level significantly lower than the ultimate tensile strength or the yield strength measured under static (monotonic) loading. This is because cyclic stresses cause microscopic cracks to initiate and propagate over time, weakening the material's internal structure. Therefore, the effective stress level at which a material fails under fatigue loading is lower than the yield point observed during a standard static load test. Option (a) is incorrect because fatigue specifically reduces the load-bearing capacity. Option (b) is incorrect because cyclic loading never increases the strength of a material relative to its static yield point.

To determine which quantity has no unit, we analyze the dimensions and definitions of each option: 1. **Kinematic Viscosity (a):** It is defined as the ratio of dynamic viscosity to density. Its SI unit is square meters per second (m²/s) or Stokes (St). It has dimensions [L²/T]. 2. **Surface Tension (b):** It is defined as the force per unit length acting on the surface of a liquid. Its SI unit is Newtons per meter (N/m). It has dimensions [MT⁻²]. 3. **Strain (c):** In the context of Strength of Materials, strain is defined as the ratio of the change in dimension (e.g., change in length $\Delta L$) to the original dimension (e.g., original length $L$). Since it is a ratio of two identical physical quantities (length/length), the units cancel out, making it a dimensionless quantity with no unit. 4. **Elasticity (d):** Elasticity (specifically the Modulus of Elasticity) is the ratio of stress to strain. Since stress has units of pressure (N/m² or Pascals) and strain is dimensionless, the unit of elasticity is the Pascal (Pa). It has dimensions [ML⁻¹T⁻²]. Therefore, Strain is the only quantity among the options that is dimensionless and has no unit.

White cast iron is characterized by the absence of graphite. In this material, the carbon is chemically combined with iron to form a hard, brittle intermetallic compound called iron carbide, also known as cementite (Fe3C). This occurs due to rapid cooling or a low silicon content, which prevents the carbon from precipitating as graphite. Because the surface of the fractured metal appears white (due to the presence of cementite and pearlite) rather than grey (due to graphite), it is termed 'white cast iron'. Analysis of other options: - a. Free carbon: This is a general term and not a specific metallurgical phase in cast iron. - b. Graphite: This is the form carbon takes in 'Grey Cast Iron'. - d. White carbon: This is not a standard metallurgical term for carbon in cast iron.

A helical gear is essentially a spur gear with teeth that are cut at an angle (the helix angle) relative to the axis of the gear. When you take a transverse section (a cross-section perpendicular to the axis of the gear), the curvature of the teeth and the profile of the gear appear exactly as they would in a spur gear. In a spur gear, the teeth are parallel to the axis, so any section perpendicular to the axis is identical to the gear's basic profile. Therefore, the transverse section of a helical gear is identical to that of a spur gear. Comparison with other options: - Bevel gears have conical shapes used for intersecting shafts, so their sections are not identical to helical transverse sections. - Worm gears consist of a worm (screw) and a worm wheel, which have entirely different geometries and tooth profiles compared to the transverse section of a helical gear.