Past Questions — 2010

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.

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.

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.

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

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.

In a cantilever beam (a beam fixed at one end and free at the other), the bending moment is caused by the applied load. For a point load 'P' applied at the free end (tip) of a beam of length 'L', the bending moment 'M' at any distance 'x' from the free end is given by M = P * x. The maximum bending moment occurs where 'x' is maximum, which is at the fixed support (x = L), where M_max = P * L. Since the bending stress (σ = My/I) is directly proportional to the bending moment, the maximum stress is developed at the fixed support. Failure in beams typically occurs where the internal stress exceeds the material's strength; therefore, the beam will fail at the support where the bending moment and resulting stresses are highest.

Principal planes have zero shear stress; max shear occurs at 45° to principals.

In a belt drive system, the belt speed (v) is the linear velocity of the belt. For a driver pulley with diameter D1 and angular velocity ω1, the belt speed is given by v = (π * D1 * N1) / 60, where N1 is the speed in RPM. However, the question asks for the proportionality of the 'belt speed' in the context of the relationship between the driver and driven pulleys. Usually, in these types of competitive exam questions, 'belt speed' refers to the speed ratio or the relative speed of the driven pulley (N2) compared to the driver pulley (N1). The fundamental equation for belt drives (assuming no slip) is: N1 * D1 = N2 * D2 Rearranging for the speed of the driven pulley (N2): N2 = N1 * (D1 / D2) However, if the question is interpreted as the ratio of the driven speed to the driver speed (the speed multiplier/reduction), it is D1/D2. But looking at the options provided, if we are looking for the relationship of the output speed relative to the input, and the options are structured as they are, we must evaluate the velocity ratio. Wait, let's re-evaluate: The linear belt speed (v) is the same for both pulleys (v = πD1N1 = πD2N2). If the question asks what the belt speed is proportional to in terms of the diameters for a given driven speed, v ∝ D2. If it asks for the speed ratio (N2/N1), it is D1/D2. Given the options provided in many technical exams for this specific question, there is often a confusion between 'belt speed' (linear) and 'driven pulley speed' (angular). If the question implies the ratio of the driven speed to the driver speed (N2/N1), the answer is D1/D2. If the question asks for the ratio of driver speed to driven speed (N1/N2), the answer is D2/D1. In the context of the MPSC 2010 paper, the intended answer for the speed ratio (Driver/Driven) is D2/D1. This represents the 'velocity ratio' (VR = N1/N2 = D2/D1).

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.

Hooke's law linear stress-strain holds only up to limit of proportionality, beyond which deviation starts.

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.

Backlash is the amount of clearance between mating gear teeth on the line of action. It is necessary to prevent jamming due to thermal expansion, manufacturing tolerances, and lubrication requirements. 1. **Module (a):** The module determines the size of the gear teeth. Larger modules result in larger teeth, which typically require a larger absolute amount of backlash to accommodate manufacturing tolerances and ensure smooth operation without interference. 2. **Pitch Line Velocity (b):** As gears rotate at higher speeds, the teeth experience centrifugal forces and, more importantly, thermal expansion due to friction and heat generation. To prevent the teeth from jamming (binding) as they expand thermally at high pitch line velocities, a greater amount of backlash must be provided. 3. **Tooth Profile (c):** While the profile (e.g., involute) determines how the gears mesh, the 'required' amount of backlash is a functional design decision based on the physical size (module) and the operating conditions (velocity/temperature), rather than the shape of the curve itself. Therefore, since both the physical dimensions (module) and the operational heat/expansion factors (pitch line velocity) dictate the necessary clearance, the correct answer is both module and pitch line velocity.

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 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.

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.

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.

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.

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.

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.

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.

Iron (Fe) is an allotropic metal, meaning it exists in different crystal structures depending on the temperature. The three primary phases of pure iron are: 1. Alpha-iron (α-iron): Stable from room temperature up to 912°C; it has a Body-Centred Cubic (BCC) structure. 2. Gamma-iron (γ-iron), also known as austenite: Stable between 912°C and 1394°C; it has a Face-Centred Cubic (FCC) structure. 3. Delta-iron (δ-iron): Stable between 1394°C and the melting point (1538°C); it reverts to a Body-Centred Cubic (BCC) structure. Therefore, gamma iron is specifically characterized by a face-centred cubic (FCC) arrangement. Option (a) refers to alpha and delta iron, and option (c) is not a standard phase for pure iron under normal atmospheric pressure.

The question asks for the property that allows a material to return to its original shape and size after the applied load is removed. 1. **Elasticity (Option b):** This is the fundamental property of a material that enables it to undergo deformation under an applied load and return to its original dimensions once the load is removed. This occurs as long as the material is stressed within its elastic limit. 2. **Plasticity (Option a):** This is the opposite of elasticity. It is the property by which a material undergoes permanent deformation without rupture after the load is removed. If a material is stressed beyond its elastic limit, it enters the plastic region. 3. **Ductility (Option c):** This is the property of a material (usually metals) that allows it to be drawn into thin wires. It is a measure of how much a material can deform plastically before fracturing under tensile stress. 4. **Malleability (Option d):** This is the property of a material that allows it to be hammered or rolled into thin sheets without cracking. It is a measure of plastic deformation under compressive stress. Therefore, the correct property described is elasticity.

In a milling machine, the cutting tool (specifically the milling cutter) is mounted on a shaft called the arbor. The arbor is a precision-ground shaft that holds the cutter and is driven by the machine's spindle to provide the necessary rotational motion for material removal. Breakdown of options: - a. Tool holder: While general tools are held by holders, in the specific context of milling (especially horizontal milling), the primary mounting shaft is the arbor. - b. Arbor: Correct. It is the specific component designed to hold and rotate the milling cutter. - c. Spindle: The spindle is the main rotating shaft of the machine. While the arbor is inserted into or driven by the spindle, the tool itself is mounted on the arbor. - d. Column: The column is the main vertical structural support of the milling machine and does not hold the cutting tool.

In arc welding, an electric arc is established between the electrode and the workpiece. The process begins when the electrode touches the workpiece, creating a short circuit. As the electrode is slightly withdrawn, the air gap is ionized. The continuous flow of electric current through this ionized gas (plasma) maintains the arc, which generates the intense heat required to melt the base metal and the filler electrode. While voltage is necessary to initiate the arc (open-circuit voltage) and electrical energy is the overall power source, it is specifically the flow of current (amperage) that sustains the arc and determines the heat input. Contact resistance is a factor during the initial strike but does not 'create' or maintain the arc itself.