GATE Technical: GATE 2022 (ME Set-1) Mechanical Engineering questions with solutions

Q1. The figure shows a schematic of a simple Watt governor mechanism with the spindle O1O2 rotating at an angular velocity ω about a vertical axis. The balls at P and S have equal mass. Assume that there is no friction anywhere and all other components are massless and rigid. The vertical distance between the horizontal plane of rotation of the balls and the pivot O1 is denoted by h. The value of h = 400 mm at a certain ω. If ω is doubled, the value of h will be ________ mm.

1. 50
2. 100
3. 150
4. 200

Answer: 100

For a Watt governor, h = g/omega^2, so h is inversely proportional to omega squared. Doubling omega divides h by 4, giving 400/4 = 100 mm.

Q2. A square threaded screw is used to lift a load W by applying a force F. Efficiency of square threaded screw is expressed as

1. The ratio of work done by W per revolution to work done by F per revolution
2. W/F
3. F/W
4. The ratio of work done by F per revolution to work done by W per revolution

Answer: The ratio of work done by W per revolution to work done by F per revolution

The efficiency of a square threaded screw is determined by comparing the useful work output (work done by the load W) to the work input (work done by the applied force F) per revolution, which reflects how effectively the screw converts input force into lifting work.

Q3. The type of fit between a mating shaft of diameter 25.0^(+0.010)_(-0.010) mm and a hole of diameter 25.015^(+0.015)_(-0.015) mm is __________.

1. Clearance
2. Transition
3. Interference
4. Linear

Answer: Transition

Shaft 24.990-25.010, hole 25.000-25.030. Max clearance = 25.030-24.990 = +0.040 (clearance), min = 25.000-25.010 = -0.010 (interference). Since the assembly can give both clearance and interference, it is a transition fit.

Q4. In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource is

1. positive
2. negative
3. zero
4. infinity

Answer: zero

The shadow price represents the value of an additional unit of a resource in a linear programming problem. If a resource is not fully utilized, it means that increasing its availability does not improve the objective function, resulting in a shadow price of zero.

Q5. Which one of the following is NOT a form of inventory?

1. Raw materials
2. Work-in-process materials
3. Finished goods
4. CNC Milling Machines

Answer: CNC Milling Machines

CNC Milling Machines are equipment used in the manufacturing process, not a type of inventory. Inventory refers specifically to the goods and materials that a business holds for the purpose of resale or production.

Q6. The Clausius inequality holds good for

1. any process
2. any cycle
3. only reversible process
4. only reversible cycle

Answer: any cycle

The Clausius inequality applies to any thermodynamic cycle, as it establishes that the change in entropy for a cycle is always greater than or equal to zero, regardless of whether the process is reversible or irreversible.

Q7. Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following statement(s) is/are TRUE? (A) A body subjected to hydrostatic pressure has no shear stress. (B) If a long solid steel rod is subjected to tensile load, then its volume increases. (C) Maximum shear stress theory is suitable for failure analysis of brittle materials. (D) If a portion of a beam has zero shear force, then the corresponding portion of the elastic curve of the beam is always straight.

1. A body subjected to hydrostatic pressure has no shear stress.
2. If a long solid steel rod is subjected to tensile load, then its volume increases.
3. Maximum shear stress theory is suitable for failure analysis of brittle materials.
4. If a portion of a beam has zero shear force, then the corresponding portion of the elastic curve of the beam is always straight.

Answer: A body subjected to hydrostatic pressure has no shear stress.

In a hydrostatic pressure scenario, the stress is uniformly distributed in all directions, resulting in only normal stresses and no shear stresses acting on the material. This is a fundamental characteristic of hydrostatic conditions.

Q8. Which of the following heat treatment processes is/are used for surface hardening of steels? (A) Carburizing (B) Cyaniding (C) Annealing (D) Carbonitriding

1. Carburizing
2. Cyaniding
3. Annealing
4. Carbonitriding

Answer: Carburizing

Carburizing is a heat treatment process that increases the carbon content on the surface of steel, enhancing its hardness and wear resistance, making it ideal for surface hardening.

Q9. Which of the following additive manufacturing technique(s) can use a wire as a feedstock material?

1. Stereolithography
2. Fused deposition modeling
3. Selective laser sintering
4. Directed energy deposition processes

Answer: Directed energy deposition processes

Directed energy deposition processes utilize a wire feedstock, allowing for the precise addition of material during the manufacturing process, which is essential for creating complex geometries and repairing existing components.

Q10. Which of the following methods can improve the fatigue strength of a circular mild steel (MS) shaft?

1. Enhancing surface finish
2. Shot peening of the shaft
3. Increasing relative humidity
4. Reducing relative humidity

Answer: Shot peening of the shaft

Shot peening introduces compressive residual stresses on the surface of the shaft, which helps to counteract the tensile stresses that contribute to fatigue failure, thereby improving its fatigue strength.

Q11. Consider a forced single degree-of-freedom system governed by x¨(t) + 2ζωₙ x˙(t) + ωₙ² x(t) = ωₙ² cos(ωt), where ζ and ωₙ are the damping ratio and undamped natural frequency of the system, respectively, while ω is the forcing frequency. The amplitude of the forced steady state response of this system is given by [(1 − r²)² + (2ζr)²]−1/2, where r = ω/ωₙ. The peak amplitude of this response occurs at a frequency ω = ωₚ. If ω_d denotes the damped natural frequency of this system, which one of the following options is true?

1. ωₚ < ω_d < ωₙ
2. ωₚ = ω_d < ωₙ
3. ω_d < ωₙ = ωₚ
4. ω_d < ωₙ < ωₚ

Answer: ωₚ < ω_d < ωₙ

The peak amplitude of the forced response occurs at a frequency lower than the damped natural frequency, which is itself less than the undamped natural frequency. This relationship indicates that as the system is damped, the frequency at which resonance occurs shifts, confirming that ωₚ is less than ω_d, which in turn is less than ωₙ.

Q12. In Fe-Fe3C phase diagram, the eutectoid composition is 0.8 weight % of carbon at 725 °C. The maximum solubility of carbon in α-ferrite phase is 0.025 weight % of carbon. A steel sample, having no other alloying element except 0.5 weight % of carbon, is slowly cooled from 1000 °C to room temperature. The fraction of pro-eutectoid α-ferrite in the above steel sample at room temperature is

1. 0.387
2. 0.864
3. 0.475
4. 0.775

Answer: 0.387

The fraction of pro-eutectoid α-ferrite can be calculated using the lever rule, which considers the composition of the steel sample and the eutectoid point. Since the steel has 0.5 weight % carbon, which is less than the eutectoid composition of 0.8 weight %, it will form pro-eutectoid α-ferrite before reaching the eutectoid transformation, resulting in a calculated fraction of approximately 0.387.

Q13. Activities A to K are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is to be completed in the minimum possible time, the latest finish time for the activity G is __________ hours. Activity | Time (hours) | Immediate predecessors A | 2 | — B | 3 | — C | 2 | — D | 4 | A E | 5 | B F | 4 | B G | 3 | C H | 10 | D, E I | 5 | F J | 8 | G K | 3 | H, I, J

1. 5
2. 10
3. 8
4. 9

Answer: 10

Forward pass gives project duration 21 (path B-E-H-K). Backward pass: K LS=18, so J LF=18, J LS=10, hence G LF=J LS=10. The latest finish time of G is 10, not 9.

Q14. Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m³ and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ________ N.

1. 350π²
2. 750π
3. 1000π

Answer: 750π

The force exerted by the gas on the pipe can be calculated using the momentum equation, which relates the change in momentum to the pressure drop and the area of the pipe. Given the increase in velocity and the pressure drop, the resulting force is determined to be 750π N, which corresponds to the net effect of the pressure and velocity changes in the flow.

Q15. Consider a rod of uniform thermal conductivity whose one end (x = 0) is insulated and the other end (x = L) is exposed to flow of air at temperature T∞ with convective heat transfer coefficient h. The cylindrical surface of the rod is insulated so that the heat transfer is strictly along the axis of the rod. The rate of internal heat generation per unit volume inside the rod is given as q̇ = cos(2πx/L). The steady state temperature at the mid-location of the rod is given as TA. What will be the temperature at the same location, if the convective heat transfer coefficient increases to 2h?

1. TA + q̇L/(2h)
2. 2TA
3. TA
4. TA (1 − q̇L/(4πh)) + q̇L/(4πh) T∞

Answer: TA

The temperature at the mid-location of the rod remains unchanged at TA because the increase in the convective heat transfer coefficient does not affect the steady-state temperature distribution established by the internal heat generation and the boundary conditions. The insulated end prevents any heat loss, and the steady state is defined by the balance of internal generation and heat loss at the exposed end.