Question 1

Assuming constant temperature condition and air to be an ideal gas, the variation in atmospheric pressure with height calculated from fluid statics is

Accepted Answer

exponential. The variation in atmospheric pressure with height is exponential because, under constant temperature and assuming air behaves as an ideal gas, the pressure decreases exponentially as altitude increases due to the balance of gravitational force and the gas laws.

Question 2

A hollow cylinder has length L, inner radius r1, outer radius r2, and thermal conductivity k. The thermal resistance of the cylinder for radial conduction is

Accepted Answer

ln(r2 / r1) / 2 kL. The correct option is based on the formula for thermal resistance in cylindrical coordinates, which accounts for the logarithmic relationship between the inner and outer radii. This formula reflects how heat flows radially through the material, with the resistance being proportional to the natural logarithm of the ratio of the outer radius to the inner radius, divided by the product of thermal conductivity and length.

Question 3

Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the outer cylinder is Ro and that of the inner cylinder is Ri. The radiation view factor of the outer cylinder onto itself is

Accepted Answer

1 - Ri / Ro. The correct option, 1 - Ri / Ro, represents the fraction of the total radiation emitted by the outer cylinder that is not intercepted by the inner cylinder, effectively capturing the geometric relationship between the two cylinders.

Question 4

The internal energy of an ideal gas is a function of

Accepted Answer

temperature only. The internal energy of an ideal gas depends solely on its temperature because, for an ideal gas, the internal energy is related to the kinetic energy of the gas molecules, which is directly influenced by temperature.

Question 5

In the phase diagram shown in the figure, four samples of the same composition are heated to temperatures marked by a, b, c and d.

At which temperature will a sample get solutionized the fastest?

Accepted Answer

d. At temperature d, the sample is at the highest temperature, which typically allows for the most rapid diffusion and dissolution of solute atoms into the solvent, leading to faster solutionizing.

Question 6

The welding process which uses a blanket of fusible granular flux is

Accepted Answer

submerged arc welding. Submerged arc welding involves the use of a granular flux that covers the weld area, protecting it from contamination and allowing for deeper penetration and a smoother finish.

Question 7

The value of true strain produced in compressing a cylinder to half its original length is

Accepted Answer

-0.69. True strain is calculated using the natural logarithm of the ratio of the original length to the final length. When a cylinder is compressed to half its original length, the true strain is negative, reflecting the reduction in length, and evaluates to approximately -0.69.

Question 8

Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions 2R × L at the bottom of an open tank as shown in the figure. The head of the plug has the shape of a semi-cylinder of radius R. The tank is filled with a liquid of density ρ up to the tip of the

Accepted Answer

2ρR²gL (1 − π/4). The correct option accounts for the pressure exerted by the liquid on the plug, which is influenced by both the rectangular area and the semi-circular shape of the plug. The term (1 − π/4) arises from the geometry of the semi-cylinder, reflecting the effective area that contributes to the force on the plug, leading to the correct calculation of the hydrostatic pressure.

Question 9

In a binary system of A and B, a liquid of 20% A (80% B) is coexisting with a solid of 70% A (30% B). For an overall composition having 40% A, the fraction of solid is

Accepted Answer

(A) 0.40. By the lever rule, fraction of solid = (overall - liquid)/(solid - liquid) = (40-20)/(70-20) = 20/50 = 0.40. The stored value 0.50 is incorrect.

Question 10

For the situation shown in the figure below the expression for H in terms of r, R and D is

Accepted Answer

H = (R + r) + √(2D(R + r) - D²). The correct option accurately represents the relationship between the heights and distances in the given geometric configuration, incorporating both the sum of the radii and the derived expression that accounts for the spatial arrangement of the elements involved.

Question 11

A rigid link PQ is undergoing plane motion as shown in the figure (Vp and VQ are non-zero). VQP is the relative velocity of point Q with respect to point P. Which one of the following is TRUE?

Accepted Answer

VQP has only one component perpendicular to PQ. In plane motion of a rigid link, the relative velocity between two points on the link can be analyzed using the concept of instantaneous rotation about a point. Since the link is rigid, the relative velocity VQP must be perpendicular to the line connecting points P and Q, which means it has only one component that is perpendicular to PQ.

Question 12

Which of the bearings given below SHOULD NOT be subjected to a thrust load?

Accepted Answer

Cylindrical (straight) roller bearing. Cylindrical (straight) roller bearings are designed primarily to handle radial loads and are not suitable for thrust loads due to their geometry, which lacks the necessary contact angles to effectively manage axial forces.

Question 13

For a certain two-dimensional incompressible flow, velocity field is given by 2xy î − y² ĵ. The streamlines for this flow are given by the family of curves

Accepted Answer

xy² = constant. The streamlines of a flow are determined by the relationship between the velocity components. In this case, the velocity field indicates that the change in y with respect to x is proportional to y², leading to the conclusion that the product xy² remains constant along the streamlines.

Question 14

Grashof number signifies the ratio of

Accepted Answer

buoyancy force to viscous force. The Grashof number is a dimensionless quantity that compares the buoyancy forces, which drive fluid motion due to density differences, to the viscous forces that resist this motion, thereby indicating the relative importance of these forces in natural convection scenarios.

Question 15

A beam of length L is carrying a uniformly distributed load w per unit length. The flexural rigidity of the beam is EI. The reaction at the simple support at the right end is

Accepted Answer

3wL/8. A beam fixed at one end and simply (propped) supported at the other carrying a UDL w is a propped cantilever. Compatibility (zero deflection at the prop) gives the reaction at the simple support as 3wL/8, not wL/2.

Question 16

For a two-dimensional flow, the velocity field is u = (x)/(x²+y²)î + (y)/(x²+y²)ĵ, where î and ĵ are the basis vectors in the x-y Cartesian coordinate system. Identify the CORRECT statements from below.
(1) The flow is incompressible.
(2) The flow is unsteady.
(3) y-component of accele

Accepted Answer

(B) (1) and (3). The flow is incompressible because the divergence of the velocity field is zero, indicating that the density remains constant. The y-component of acceleration is correctly derived from the velocity field, confirming that statement (3) is accurate.

Question 17

A cuboidal part has to be accurately positioned first, arresting six degrees of freedom and then clamped in a fixture, to be used for machining. Locating pins in the form of cylinders with hemi-spherical tips are to be placed on the fixture for positioning. Four different configurations of

Accepted Answer

Configuration P1 arrests 6 degrees of freedom, while Configurations P2 and P4 are over-constrained and Configuration P3 is under-constrained.. Configuration P1 effectively restricts all six degrees of freedom necessary for stable positioning, while the other configurations either add unnecessary constraints (over-constrained) or fail to provide sufficient support (under-constrained), making P1 the only correct choice.

Question 18

The effective stiffness of a cantilever beam of length L and flexural rigidity EI subjected to a transverse tip load W is

Accepted Answer

3EI/L³. The effective stiffness of a cantilever beam under a transverse load is derived from its deflection characteristics, where the stiffness is defined as the load divided by the deflection at the tip. For a cantilever beam, the relationship shows that the effective stiffness is three times the flexural rigidity divided by the cube of the length, hence 3EI/L³.

Question 19

The S-N curve from a fatigue test for steel is shown. Which one of the options gives the endurance limit?

Accepted Answer

S₄. The endurance limit is defined as the maximum stress level below which a material can endure an infinite number of loading cycles without failing. In the S-N curve, S₄ represents this threshold for the steel, indicating the stress level where fatigue failure does not occur.

Question 20

Air (density = 1.2 kg/m³, kinematic viscosity = 1.5×10⁻⁵ m²/s) flows over a flat plate with a free-stream velocity of 2 m/s. The wall shear stress at a location 15 mm from the leading edge is τ_w. What is the wall shear stress at a location 30 mm from the leading edge?

Accepted Answer

τ_w / √2. The wall shear stress in a laminar flow over a flat plate decreases with distance from the leading edge, specifically following the relationship that it is inversely proportional to the square root of the distance from the leading edge. Therefore, at 30 mm, the wall shear stress is reduced to τ_w / √2 compared to its value at 15 mm.

Question 21

Consider incompressible laminar flow of a constant property Newtonian fluid in an isothermal circular tube. The flow is steady with fully-developed temperature and velocity profiles. The Nusselt number for this flow depends on

Accepted Answer

neither the Reynolds number nor the Prandtl number. In fully-developed laminar flow in a circular tube, the Nusselt number is constant and determined solely by the geometry and flow conditions, not by the Reynolds or Prandtl numbers, which influence heat transfer in other flow regimes.

Question 22

A heat engine extracts heat (Q_H) from a thermal reservoir at a temperature of 1000 K and rejects heat (Q_L) to a thermal reservoir at a temperature of 100 K, while producing work (W). Which one of the combinations of (Q_H, Q_L and W) given is allowed?

Accepted Answer

Q_H = 2000 J, Q_L = 750 J, W = 1250 J. This combination satisfies the first law of thermodynamics, where the work done by the engine (W) is equal to the heat extracted from the hot reservoir (Q_H) minus the heat rejected to the cold reservoir (Q_L), confirming that W = Q_H - Q_L.

Question 23

Two surfaces P and Q are to be joined together. In which of the given joining operation(s), there is no melting of the two surfaces P and Q for creating the joint?

(A) Arc welding
(B) Brazing
(C) Adhesive bonding
(D) Spot welding

Accepted Answer

(C) Adhesive bonding. Adhesive bonding involves using a substance to bond two surfaces together without melting them, unlike welding or brazing, which require heat to create a joint.

Question 24

In a metal casting process to manufacture parts, both patterns and moulds provide shape by dictating where the material should or should not go. Which of the option(s) given correctly describe(s) the mould and the pattern?

Accepted Answer

Patterns can be used to make moulds.. Patterns are used to create moulds by providing the shape that the molten material will take when poured into the mould, making option D correct.

Question 25

A spherical ball weighing 2 kg is dropped from a height of 4.9 m onto an immovable rigid block as shown in the figure. If the collision is perfectly elastic, what is the momentum vector of the ball (in kg m/s) just after impact? Take the acceleration due to gravity to be g = 9.8 m/s². Opti

Accepted Answer

19.6 ĵ. The momentum vector just after impact is directed vertically upward, as the ball rebounds after the perfectly elastic collision. The magnitude of the momentum is calculated using the formula p = mv, where the velocity just before impact is determined by the height from which it was dropped, resulting in a momentum of 19.6 kg m/s in the ĵ direction.

Question 26

Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and cross-sectional area of the cylinder is A. The fluid inside the cylinder is air (considered as a perfect gas), with γ being the ratio of the specific heat at constant pressure to the s

Accepted Answer

P0 A (L2 - L1). The work done by the piston on the atmosphere is determined by the pressure exerted by the atmosphere (P0) and the change in volume as the piston moves from L1 to L2. Since the process is adiabatic and the piston is moving against atmospheric pressure, the work is calculated as the atmospheric pressure multiplied by the cross-sectional area and the distance moved, which is represented by P0 A (L2 - L1).

Question 27

A cylindrical rod of length h and diameter d is placed inside a cubic enclosure of side length L. S denotes the inner surface of the cube. The view-factor Fₛ-s is

Accepted Answer

1 - (πdh + πd²/2) / 6L². The view-factor Fₛ-s represents the fraction of radiation leaving the cylindrical rod that is intercepted by the inner surface of the cube. Since the rod does not occupy the entire volume of the cube, the view-factor is less than 1, and the correct option accounts for the area of the rod relative to the cube's surface area.

Question 28

In an ideal orthogonal cutting experiment (see figure), the cutting speed V is 1 m/s, the rake angle of the tool α = 5°, and the shear angle, φ, is known to be 45°.

Applying the ideal orthogonal cutting model, consider two shear planes PQ and RS close to each other. As they approach the t

Accepted Answer

5.20 × 10⁴. The shear strain rate is calculated using the formula that relates the cutting speed, the shear angle, and the distance between shear planes. Given the parameters, the calculation yields a shear strain rate of 5.20 × 10⁴ s⁻¹, which reflects the high rate of deformation in the thin shear zone during the cutting process.

Question 29

Cylindrical bars P and Q have identical lengths and radii, but are composed of different linear elastic materials. The Young's modulus and coefficient of thermal expansion of Q are twice the corresponding values of P. Assume the bars to be perfectly bonded at the interface, and their weigh

Accepted Answer

σ1 = σ2. The correct option is that the stresses in both bars are equal (σ1 = σ2) because they are perfectly bonded and experience the same temperature change, leading to equal stress distribution despite differing material properties.

Question 30

The velocity field of a two-dimensional, incompressible flow is given by V = 2 sinh x î + v(x,y) ĵ where î and ĵ denote the unit vectors in x and y directions, respectively. If v(x,0) = cosh x, then v(0,−1) is

Accepted Answer

3. Incompressibility: dv/dy = -du/dx = -2cosh x, so v = -2y cosh x + f(x). With v(x,0)=cosh x, f(x)=cosh x, giving v = cosh x (1-2y). Then v(0,-1) = 1*(1+2) = 3, so option '3' (not '1').

Question 31

Consider incompressible laminar flow over a flat plate with freestream velocity of u∞. The Nusselt number corresponding to this flow velocity is Nu1. If the freestream velocity is doubled, the Nusselt number changes to Nu2. Choose the correct option for Nu2/Nu1.

Accepted Answer

√2. The Nusselt number is proportional to the square root of the Reynolds number for laminar flow over a flat plate. When the freestream velocity is doubled, the Reynolds number increases by a factor of 2, leading to a Nusselt number that is proportional to the square root of this increase, resulting in Nu2/Nu1 being √2.

Question 32

A furnace can supply heat steadily at 1200 K at a rate of 24000 kJ/min. The maximum amount of power (in kW) that can be produced by using the heat supplied by this furnace in an environment at 300 K is

Accepted Answer

300. The maximum power output can be calculated using the Carnot efficiency formula, which is based on the temperatures of the heat source and sink. The efficiency is given by 1 - (T_sink/T_source), and when applied to the given temperatures, it results in a maximum power output of 300 kW.

Question 33

Which one of the following statements regarding a Rankine cycle is FALSE?

Accepted Answer

Cycle efficiency increases as boiler pressure decreases.. The statement is false because increasing the boiler pressure actually enhances the cycle efficiency by allowing the working fluid to absorb more heat, leading to a higher thermal efficiency. Lowering the boiler pressure would reduce the temperature difference between the heat source and the working fluid, thus decreasing efficiency.

Question 34

Which one of the following failure theories is the most conservative design approach against fatigue failure?

Accepted Answer

Soderberg line. The Soderberg line is considered the most conservative design approach against fatigue failure because it incorporates both the yield strength and the endurance limit, ensuring a greater safety margin by accounting for the effects of mean stress on fatigue life.

Question 35

The phases present in pearlite are

Accepted Answer

ferrite and cementite. Pearlite is a microstructure in steel that consists of alternating layers of ferrite and cementite, which form during the slow cooling of austenite. This combination provides a balance of strength and ductility in the material.

Question 36

The “Earing” phenomenon in metal forming is associated with

Accepted Answer

deep drawing. Earing occurs during deep drawing due to the anisotropic nature of the metal, leading to uneven stretching and the formation of raised edges, or 'ears', around the perimeter of the drawn part.

Question 37

The grinding wheel used to provide the best surface finish is

Accepted Answer

A 80L 5V. The 80L 5V grinding wheel has a finer grit size, which allows for a smoother finish on the workpiece compared to the coarser options, making it ideal for achieving a high-quality surface finish.

Question 38

The allowance provided to a pattern for easy withdrawal from a sand mold is

Accepted Answer

shake allowance. Shake allowance is the extra space given in a mold to facilitate the easy removal of the pattern without damaging it, ensuring that the final casting can be produced accurately.

Question 39

The most suitable electrode material used for joining low alloy steels using Gas Metal Arc Welding (GMAW) process is

Accepted Answer

low alloy steel. Low alloy steel is the most suitable electrode material for joining low alloy steels in GMAW because it ensures compatibility in composition and properties, leading to strong and reliable welds that maintain the integrity of the base materials.

Question 40

The preparatory functions in Computer Numerical Controlled (CNC) machine programming are denoted by the alphabet

Accepted Answer

G. In CNC programming, preparatory functions, which control the movement and operation of the machine, are designated by the letter 'G'. These codes instruct the machine on how to perform specific tasks, such as linear interpolation or circular interpolation.

Question 41

A set of jobs U, V, W, X, Y, Z arrive at time t = 0 to a production line consisting of two work stations in series. Each job must be processed by both work stations in sequence (i.e., the first followed by the second). The process times (in minutes) for each job on each workstation in the

Accepted Answer

W-X-Z-V-Y-U. The sequence W-X-Z-V-Y-U minimizes the makespan by prioritizing jobs with shorter processing times on the first workstation, allowing for a more efficient flow through both workstations and reducing idle time.

Question 42

A queueing system has one single server work station that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Poisson distribution with a mean of 5 jobs/hour. The service time of the server is exponentially distributed with a mean of 6 minutes. I

Accepted Answer

0.50. lambda = 5 jobs/hr; mean service 6 min gives mu = 10 jobs/hr, so utilization rho = 5/10 = 0.5. The probability the server is idle is P0 = 1 - rho = 0.5, option 2. The stored 0.83 is wrong.

Question 43

In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same friction factor. The pipes connecting points W, N, and S with point J have an equal length L. The pipe connecting points J and E has a length 10L. The pressures at the ends N,

Accepted Answer

Both I and II are True. Both statements are true because the flow rate in the longer pipe connecting J and E is reduced due to the longer length and equal friction factor, resulting in a flow rate of Q/21. Additionally, since the pressures at points N, E, and S are equal, the pressure difference between J and N must match the pressure difference between J and E, confirming the second statement.

Question 44

Steady, compressible flow of air takes place through an adiabatic converging-diverging nozzle, as shown in the figure. For a particular value of pressure difference across the nozzle, a stationary normal shock wave forms in the diverging section of the nozzle. If E and F denote the flow co

Accepted Answer

Specific entropy at E is lower than the specific entropy at F. In a normal shock wave, the flow experiences an increase in entropy due to irreversible processes, which means that the specific entropy downstream of the shock (at point F) is higher than upstream (at point E). This aligns with the thermodynamic principles governing shock waves in compressible flow.

Question 45

In a laboratory experiment using a scaled down model to measure scour at a bridge pier, the Froude number is important. The ratio of the prototype length to the model length is 100. If the velocity of the model is 1 m s⁻¹, the velocity (in m s⁻¹) of the prototype is

Accepted Answer

10. The Froude number is a dimensionless parameter that relates the inertial forces to gravitational forces in fluid flow. Since the model length is scaled down by a factor of 100, to maintain dynamic similarity, the velocity of the prototype must be scaled by the square root of the length ratio, which is √100 = 10. Therefore, if the model velocity is 1 m/s, the prototype velocity must be 10 m/s.

Question 46

A rigid, thermally-insulated tank undergoes stirring as shown in the figure below. Which one of the following options is correct?

Accepted Answer

Both the enthalpy and the entropy of the air increase. Stirring the air in a thermally-insulated tank introduces mechanical energy into the system, which increases both the enthalpy due to the added energy and the entropy as the air molecules become more disordered.

Question 47

In a psychrometric chart, one axis represents dry-bulb temperature. The axis, that is perpendicular to the dry-bulb temperature axis, represents

Accepted Answer

specific humidity. The axis perpendicular to the dry-bulb temperature on a psychrometric chart represents specific humidity, which indicates the amount of water vapor present in the air relative to the mass of dry air.

Question 48

Among the following surface hardening processes, steel is heated to the lowest temperature in

Accepted Answer

nitriding. Nitriding involves heating steel to a lower temperature compared to the other processes, typically around 500-550°C, which allows for the diffusion of nitrogen into the surface without significantly altering the core properties of the steel.

Question 49

The welding process commonly used for fabricating tailor-welded blanks of dissimilar thickness for automotive applications is

Accepted Answer

laser welding. Laser welding is preferred for fabricating tailor-welded blanks of dissimilar thickness because it provides precise control over the heat input, allowing for minimal distortion and the ability to join different materials effectively.

Question 50

The yield stress of a metal in uniaxial tension is 200 MPa. According to von Mises yield criterion, the yield stress (in MPa) of the metal in pure shear is closest to

Accepted Answer

115.5. By the von Mises criterion, the shear yield stress equals the tensile yield stress divided by sqrt(3): 200/1.732 = 115.5 MPa. The stored 141.4 (which is 200/sqrt(2)) is wrong; the answer is 115.5 MPa.

GATE Technical: Mechanical Engineering (ME) questions with solutions

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