Question 1

Q.9 In vibration isolation, which one of the following statements is NOT correct regarding Transmissibility (T)?

Accepted Answer

(B) T can be always reduced by using higher damping at any excitation frequency. Option B is incorrect because while increasing damping can reduce transmissibility, it does not guarantee a reduction at all excitation frequencies, especially in certain conditions where damping may not effectively mitigate resonance effects.

Question 2

A thin plate of uniform thickness is subject to pressure as shown in the figure below. Under the assumption of plane stress, which one of the following is correct?

Accepted Answer

Normal stress is zero in the z-direction. In a plane stress condition, the stress in the thickness direction (z-direction) is assumed to be negligible, leading to a normal stress of zero in that direction. This simplification is valid for thin plates where the in-plane stresses dominate.

Question 3

For laminar forced convection over a flat plate, if the free stream velocity increases by a factor of 2, the average heat transfer coefficient

Accepted Answer

rises by a factor of √2. In laminar forced convection over a flat plate, the average heat transfer coefficient is proportional to the square root of the free stream velocity. Therefore, when the velocity doubles, the heat transfer coefficient increases by a factor of the square root of 2.

Question 4

A pure substance at 8 MPa and 400 °C is having a specific internal energy of 2864 kJ/kg and a specific volume of 0.03432 m³/kg. Its specific enthalpy (in kJ/kg) is ______

Accepted Answer

3138.56. Specific enthalpy h = u + p*v. With u=2864 kJ/kg, p=8000 kPa, v=0.03432 m3/kg: p*v = 274.56 kJ/kg, so h = 2864 + 274.56 = 3138.56 kJ/kg.

Question 5

A component can be produced by any of the four processes I, II, III and IV. The fixed cost and the variable cost for each of the processes are listed below.
Process | Fixed cost (in Rs.) | Variable cost per piece (in Rs.)
I | 20 | 3
II | 50 | 1
III | 40 | 2
IV | 10 | 4
The most economical

Accepted Answer

II. Process II is the most economical choice because it has the lowest total cost when considering both fixed and variable costs for producing 100 pieces, resulting in a total cost of Rs. 150, which is less than the total costs of the other processes.

Question 6

The flatness of a machine bed can be measured using

Accepted Answer

Auto collimator. An auto collimator is specifically designed to measure angular deviations and flatness with high precision by utilizing a collimated light beam, making it the most suitable option for assessing the flatness of a machine bed.

Question 7

A robot arm PQ with end coordinates P(0,0) and Q(2,5) rotates counter clockwise about P in the X Y plane by 90°. The new coordinate pair of the end point is

Accepted Answer

(-5,2). When the robot arm PQ rotates counterclockwise by 90° around point P(0,0), the coordinates of point Q(2,5) transform according to the rotation matrix for 90° counterclockwise, resulting in the new coordinates (-5,2).

Question 8

The following four unconventional machining processes are available in a shop floor. The most appropriate one to drill a hole of square cross section of 6 mm × 6 mm and 25 mm deep is

Accepted Answer

Electro Discharge Machining. Electro Discharge Machining (EDM) is ideal for creating precise shapes and features, such as a square cross-section, in hard materials. It uses electrical discharges to remove material, making it suitable for intricate designs and deep holes.

Question 9

The relationship between true strain (ε_T) and engineering strain (ε_E) in a uniaxial tension test is given as

Accepted Answer

ε_T = ln(1 + ε_E). The correct option shows that true strain is derived from engineering strain using the natural logarithm, reflecting how true strain accounts for the continuous change in length during deformation, while engineering strain is based on the original length.

Question 10

The flexural rigidity (EI) of a cantilever beam is assumed to be constant over the length of the beam shown in figure. If a load P and bending moment PL/2 are applied at the free end of the beam then the value of the slope at the free end is

Accepted Answer

PL² / EI. A tip load P gives end slope PL^2/(2EI). A tip moment M = PL/2 gives end slope ML/EI = PL^2/(2EI). Superposing, total slope = PL^2/(2EI) + PL^2/(2EI) = PL^2/EI, the second option.

Question 11

What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring constants are denoted by k1 and k2 as shown below.

Accepted Answer

√((k1 + k2)/m). The natural frequency of a spring-mass system is determined by the total effective spring constant and the mass. In this case, since the springs are in series, their combined effect leads to the formula √((k1 + k2)/m), which accurately reflects the system's oscillatory behavior.

Question 12

Consider laminar flow of water over a flat plate of length 1 m. If the boundary layer thickness at a distance of 0.25 m from the leading edge of the plate is 8 mm, the boundary layer thickness (in mm), at a distance of 0.75 m, is

Accepted Answer

14. The boundary layer thickness in laminar flow over a flat plate increases with the square root of the distance from the leading edge. Given that the thickness at 0.25 m is 8 mm, we can use the relationship to find that at 0.75 m, the thickness increases to approximately 14 mm.

Question 13

For the CNC part programming, match Group A with Group B:

Group A
P: circular interpolation, counter clock wise
Q: dwell
R: circular interpolation, clock wise
S: point to point countering

Group B
I: G 02
II: G 03
III: G 04
IV: G 00

Accepted Answer

(B) P-II, Q-III, R-I, S-IV. Option B is correct because it accurately matches the G-code commands with their respective functions: G 02 (P) represents circular interpolation in a counterclockwise direction, G 03 (R) is for clockwise circular interpolation, G 04 (Q) indicates dwell, and G 00 (S) is used for point-to-point rapid positioning.

Question 14

A hole of 20 mm diameter is to be drilled in a steel block of 40 mm thickness. The drilling is performed at rotational speed of 400 rpm and feed rate of 0.1 mm/rev. The required approach and over run of the drill together is equal to the radius of drill. The drilling time (in minute) is

Accepted Answer

1.25. The drilling time is calculated based on the total distance the drill must travel, including the hole depth and the approach and overrun, divided by the feed rate. Given the parameters, the total distance is effectively 40 mm (depth) plus 10 mm (approach and overrun), and with a feed rate of 0.1 mm/rev at 400 rpm, the total time comes out to 1.25 minutes.

Question 15

A rectangular hole of size 100 mm × 50 mm is to be made on a 5 mm thick sheet of steel having ultimate tensile strength and shear strength of 500 MPa and 300 MPa, respectively. The hole is made by punching process. Neglecting the effect of clearance, the punching force (in kN) is

Accepted Answer

450. Punching force = sheared perimeter * thickness * shear strength. Perimeter = 2(100+50)=300 mm. F = 300 mm * 5 mm * 300 MPa = 450000 N = 450 kN.

Question 16

In a statically determinate plane truss, the number of joints (j) and the number of members (m) are related by

Accepted Answer

m = 2j − 3. The correct option reflects the relationship derived from the equilibrium conditions of a statically determinate truss, where the number of members is determined by the number of joints minus three, accounting for the two-dimensional nature of the structure and the three equilibrium equations available.

Question 17

Which one of the following is used to convert a rotational motion into a translational motion?

Accepted Answer

Rack and pinion gears. Rack and pinion gears are specifically designed to convert rotational motion from the pinion gear into linear motion along the rack, making them ideal for applications requiring this transformation.

Question 18

As the temperature increases, the thermal conductivity of a gas
(A) increases
(B) decreases
(C) remains constant
(D) increases up to a certain temperature and then decreases

Accepted Answer

(A). As temperature rises, the kinetic energy of gas molecules increases, leading to more frequent and energetic collisions, which enhances the transfer of heat and thus increases thermal conductivity.

Question 19

A flow field which has only convective acceleration is
(A) a steady uniform flow
(B) an unsteady uniform flow
(C) a steady non-uniform flow
(D) an unsteady non-uniform flow

Accepted Answer

(C). A steady non-uniform flow indicates that the flow characteristics do not change over time (steady) but vary across different locations in the flow field (non-uniform), which aligns with the presence of convective acceleration.

Question 20

Match Group A with Group B:
Group A: P: Biot number, Q: Grashof number, R: Prandtl number, S: Reynolds number
Group B: 1: Ratio of buoyancy to viscous force, 2: Ratio of inertia force to viscous force, 3: Ratio of momentum to thermal diffusivities, 4: Ratio of internal thermal resistance t

Accepted Answer

P-4, Q-1, R-3, S-2. The correct option matches each dimensionless number with its defining ratio: the Biot number (P) relates internal thermal resistance to boundary layer thermal resistance (4), the Grashof number (Q) compares buoyancy to viscous forces (1), the Prandtl number (R) is the ratio of momentum to thermal diffusivities (3), and the Reynolds number (S) represents the ratio of inertia to viscous forces (2).

Question 21

Kaplan water turbine is commonly used when the flow through its runner is
(A) axial and the head available is more than 100 m
(B) axial and the head available is less than 10 m
(C) radial and the head available is more than 100 m
(D) mixed and the head available is about 50 m

Accepted Answer

(B). The Kaplan turbine is designed for low-head applications, typically under 10 meters, where the flow is axial, making it suitable for efficient operation in such conditions.

Question 22

The total number of decision variables in the objective function of an assignment problem of size n × n (n jobs and n machines) is

Accepted Answer

n². In an assignment problem of size n × n, each job can be assigned to each machine, resulting in n jobs having n possible assignments each, which totals to n² decision variables.

Question 23

Demand during lead time with associated probabilities is shown below:
Demand: 50, 70, 75, 80, 85
Probability: 0.15, 0.14, 0.21, 0.20, 0.30
Expected demand during lead time is -------

Accepted Answer

75. Expected demand = 50(0.15)+70(0.14)+75(0.21)+80(0.20)+85(0.30) = 7.5+9.8+15.75+16+25.5 = 74.55, which rounds to about 75. The closest option is 75 (index 2), not 80.

Question 24

Within the Heat Affected Zone (HAZ) in a fusion welding process, the work material undergoes

Accepted Answer

microstructural changes but does not melt. The Heat Affected Zone (HAZ) experiences changes in microstructure due to the heat from the welding process, but the material itself does not reach melting temperatures, allowing it to retain its solid form.

Question 25

The principle of material removal in Electrochemical machining is

Accepted Answer

Faraday's laws. Faraday's laws govern the amount of material removed during electrochemical machining by relating the mass of the material removed to the electric charge passed through the electrolyte, making them fundamental to the process.

Question 26

Q.24 Match the heat treatment processes (Group A) and their associated effects on properties (Group B) of medium carbon steel

Group A
P: Tempering
Q: Quenching
R: Annealing
S: Normalizing

Group B
I: Strengthening and grain refinement
II: Inducing toughness
III: Hardening
IV: Softening

Accepted Answer

P-II, Q-III, R-IV, S-I. Tempering reduces brittleness and enhances toughness after hardening, which is why it is matched with inducing toughness. Quenching is a rapid cooling process that increases hardness, hence its association with hardening. Annealing softens the material, making it easier to work with, while normalizing refines the grain structure, leading to improved strength.

Question 27

Q.25 In a rolling process, the maximum possible draft, defined as the difference between the initial and the final thickness of the metal sheet, mainly depends on which pair of the following parameters?

P: Strain
Q: Strength of the work material
R: Roll diameter
S: Roll velocity
T: Coeffi

Accepted Answer

R, T. The maximum possible draft in a rolling process is primarily influenced by the roll diameter, as larger rolls can accommodate greater thickness reductions, and the coefficient of friction, which affects the grip between the rolls and the material being processed, enabling effective deformation.

Question 28

Consider an ordinary differential equation dx/dt = 4t + 4. If x = x0 at t = 0, the increment in x calculated using Runge-Kutta fourth order multi-step method with a step size of Δt = 0.2 is

Accepted Answer

0.88. Since dx/dt = 4t+4 is linear in t, RK4 reproduces the exact integral over the step: increment = integral_0^0.2 (4t+4) dt = 2(0.2^2)+4(0.2) = 0.08+0.8 = 0.88 (index 3), not 0.44.

Question 29

It is desired to avoid interference in a pair of spur gears having a 20° pressure angle. With increase in pinion to gear speed ratio, the minimum number of teeth on the pinion

Accepted Answer

increases. As the speed ratio between the pinion and gear increases, the pinion must have more teeth to maintain proper engagement and avoid interference, especially with a 20° pressure angle, which requires a minimum number of teeth to ensure smooth operation.

Question 30

A frame is subjected to a load P as shown in the figure. The frame has a constant flexural rigidity EI. The effect of axial load is neglected. The deflection at point A due to the applied load P is

Accepted Answer

(D) 4 P L³ / 3 EI. The correct option reflects the cumulative effect of the applied load on the frame's deflection, considering the geometry and boundary conditions of the frame, which results in a deflection that is four times the standard deflection for a simple beam under a point load.

Question 31

Consider the following statements regarding streamline(s):
(i) It is a continuous line such that the tangent at any point on it shows the velocity vector at that point
(ii) There is no flow across streamlines
(iii) dx/u = dy/v = dz/w is the differential equation of a streamline, where u, v

Accepted Answer

(i), (ii), (iii). Statements (i), (ii), and (iii) accurately describe the properties of streamlines in fluid dynamics. (i) indicates that streamlines represent the direction of flow, (ii) confirms that fluid does not cross streamlines, and (iii) provides the mathematical relationship that defines a streamline based on velocity components.

Question 32

Two infinite parallel plates are placed at a certain distance apart. An infinite radiation shield is inserted between the plates without touching any of them to reduce heat exchange between the plates. A assume that the emissivities of plates and radiation shield are equal. The ratio of th

Accepted Answer

(A) 1/2. For two infinite parallel plates with N radiation shields of equal emissivity, the net heat exchange is reduced by a factor 1/(N+1). With one shield (N=1) the ratio of heat exchange with shield to without shield is 1/2.

GATE Technical: MECHANICAL - ME questions with solutions

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