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

Q1. The correct sequence of machining large diameter through hole is

1. drilling, boring, reaming
2. boring, drilling, reaming
3. drilling, reaming, boring
4. boring, reaming, drilling

Answer: drilling, boring, reaming

The correct sequence starts with drilling to create the initial hole, followed by boring to achieve the desired diameter and finish, and finally reaming to enhance the hole's accuracy and surface quality.

Q2. In modern CNC machine tools, the backlash has been eliminated by

1. preloaded ballscrews
2. rack and pinion
3. ratchet and pinion
4. slider crank mechanism

Answer: preloaded ballscrews

Preloaded ballscrews are designed to minimize or eliminate backlash by applying a constant force that keeps the balls in contact with the screw threads, ensuring precise movement and positioning in CNC machines.

Q3. In which of the following pairs of cycles isothermal process?

1. Diesel cycle and Otto cycle
2. Carnot cycle and Stirling cycle
3. Brayton cycle and Rankine cycle
4. Bell-Coleman cycle and Vapour compression refrigeration cycle

Answer: Carnot cycle and Stirling cycle

The Carnot cycle and Stirling cycle both involve isothermal processes where heat is absorbed and released at constant temperatures, making them idealized cycles for studying thermodynamic efficiency.

Q4. Superheated steam at 1500 kPa, has a specific volume of 2.75 m³/kmol and compressibility factor (Z) of 0.95. The temperature of steam is ____ °C (round off to the nearest integer).

1. 522
2. Reynolds number and Prandtl number
3. Biot number and Froude number
4. Nusselt number and Grashoff number

Answer: 522

The correct option is 522 °C because, using the provided specific volume and compressibility factor, we can apply the ideal gas law and steam tables to determine the temperature of superheated steam at the given pressure.

Q5. An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate of Q̇1 to the ambient air. If the thermal conductivity of the fin material is doubled, while keeping everything else constant, the rate of steady-state heat transfer from the fin becomes Q̇2. The ratio Q̇2/Q̇1 is

1. √2
2. 2
3. 1/√2
4. 1/2

Answer: √2

For an infinitely long fin, Q=sqrt(h*P*k*A_c)*theta, so Q is proportional to sqrt(k). Doubling k gives Q2/Q1=sqrt(2). Stored '2' is wrong.

Q6. A cantilever beam of length, L, and flexural rigidity, EI, is subjected to an end moment, M, as shown in the figure. The deflection of the beam at x = L/2 is

1. M L² / (8 E I)
2. M L² / (16 E I)
3. M L² / (24 E I)
4. M L² / (32 E I)

Answer: M L² / (8 E I)

A cantilever with an end moment M has deflection y(x) = M x^2/(2EI). At x = L/2, y = M(L/2)^2/(2EI) = M L^2/(8EI). Stored M L^2/(16EI) is wrong.

Q7. Shear stress distribution on the cross-section of the coil wire in a helical compression spring is shown in the figure. This shear stress distribution represents

1. direct shear stress in the coil wire cross-section
2. torsional shear stress in the coil wire cross-section
3. combined direct shear and torsional shear stress in the coil wire cross-section
4. combined direct shear and torsional shear stress with stress concentration at inside edge of the coil wire cross-section

Answer: combined direct shear and torsional shear stress with stress concentration at inside edge of the coil wire cross-section

The correct option indicates that both direct shear and torsional shear stresses are present in the coil wire, particularly highlighting the stress concentration at the inside edge, which is typical in helical springs due to their geometry and loading conditions.

Q8. The fundamental thermodynamic relation is dU = TdS + τdL, where T is the temperature and τ is the tension in the rubber band. Which one of the following relations is correct?

1. (A) τ = (∂U/∂S)L
2. (B) (∂T/∂L)S = (∂τ/∂S)L
3. (C) (∂T/∂S)L = (∂τ/∂L)S
4. (D) T = (∂U/∂S)τ

Answer: (B) (∂T/∂L)S = (∂τ/∂S)L

Option B is correct because it reflects the relationship between temperature and tension in a system where entropy is held constant, demonstrating how changes in one variable affect the other under those specific conditions.