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

Q1. A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity ω. At time t = 0, the vertical position of the follower is y(0) = 0, and the system is in the configuration shown below. The vertical position of the follower face, y(t) is given by

1. e sin ωt
2. e(1 + cos 2ωt)
3. e(1 − cos ωt)
4. e sin 2ωt

Answer: e(1 − cos ωt)

The correct option, e(1 − cos ωt), describes the vertical position of the follower as it moves in response to the circular motion of the eccentric cam. This equation captures the oscillatory motion of the follower, starting from the lowest point when t = 0, and reflects the relationship between the angular position of the cam and the follower's vertical displacement.

Q2. During a non-flow thermodynamic process (1-2) executed by a perfect gas, the heat interaction is equal to the work interaction (Q1-2 = W1-2) when the process is

1. Isentropic
2. Polytropic
3. Isothermal
4. Adiabatic

Answer: Isothermal

In an isothermal process, the temperature remains constant, which means that any heat added to the system is fully converted into work done by the gas, resulting in the equality Q = W.

Q3. For a hydrodynamically and thermally fully developed laminar flow through a circular pipe of constant cross-section, the Nusselt number at constant wall heat flux (Nu_q) and that at constant wall temperature (Nu_T) are related as

1. Nu_q > Nu_T
2. Nu_q < Nu_T
3. Nu_q = Nu_T
4. Nu_q = (Nu_T)²

Answer: Nu_q > Nu_T

For fully developed laminar flow in a circular pipe, Nu_q=4.36 (constant heat flux) and Nu_T=3.66 (constant wall temperature). Therefore Nu_q > Nu_T; stored 'Nu_q = Nu_T' is wrong.

Q4. As per common design practice, the three types of hydraulic turbines, in descending order of flow rate, are

1. Kaplan, Francis, Pelton
2. Pelton, Francis, Kaplan
3. Francis, Kaplan, Pelton
4. Pelton, Kaplan, Francis

Answer: Kaplan, Francis, Pelton

Kaplan turbines are designed for high flow rates and low head, making them suitable for large volumes of water. Francis turbines can handle moderate flow rates and heads, while Pelton turbines are used for high heads and low flow rates, thus placing them in descending order of flow rate.

Q5. A slender rod of length L, diameter d (L >> d) and thermal conductivity k1 is joined with another rod of identical dimensions, but of thermal conductivity k2, to form a composite cylindrical rod of length 2L. The heat transfer in radial direction and contact resistance are negligible. The effective thermal conductivity of the composite rod is

1. k1 + k2
2. √(k1k2)
3. (k1k2)/(k1 + k2)
4. (2k1k2)/(k1 + k2)

Answer: (2k1k2)/(k1 + k2)

The effective thermal conductivity of two rods in series is determined by the formula for thermal resistances, which leads to the result of (2k1k2)/(k1 + k2). This accounts for the combined effect of both materials, reflecting how they share the thermal load.

Q6. Consider an ideal vapor compression refrigeration cycle. If the throttling process is replaced by an isentropic expansion process, keeping all the other processes unchanged, which one of the following statements is true for the modified cycle?

1. Coefficient of performance is higher than that of the original cycle.
2. Coefficient of performance is lower than that of the original cycle.
3. Coefficient of performance is the same as that of the original cycle.
4. Refrigerating effect is lower than that of the original cycle.

Answer: Coefficient of performance is higher than that of the original cycle.

Replacing the throttling process with an isentropic expansion process improves the efficiency of the cycle, as isentropic expansion minimizes entropy generation and energy losses, resulting in a higher coefficient of performance.

Q7. In a casting process, a vertical channel through which molten metal flows downward from pouring basin to runner for reaching the mold cavity is called

1. blister
2. sprue
3. riser
4. pin hole

Answer: sprue

The sprue is the vertical channel that directs molten metal from the pouring basin to the runner, ensuring that the metal flows efficiently into the mold cavity during the casting process.

Q8. Which one of the following welding methods provides the highest heat flux (W/mm²)?

1. Oxy-acetylene gas welding
2. Tungsten inert gas welding
3. Plasma arc welding
4. Laser beam welding

Answer: Laser beam welding

Laser beam welding delivers concentrated energy in the form of a laser beam, resulting in a very high heat flux that allows for deep penetration and fast welding speeds, making it the most efficient method among the options listed.

Q9. The length, width and thickness of a steel sample are 400 mm, 40 mm and 20 mm, respectively. Its thickness needs to be uniformly reduced by 2 mm in a single pass by using horizontal slab milling. The milling cutter (diameter: 100 mm, width: 50 mm) has 20 teeth and rotates at 1200 rpm. The feed per tooth is 0.05 mm. The feed direction is along the length of the sample. If the over-travel distance is the same as the approach distance, the approach distance and time taken to complete the required machining task are

1. 14 mm, 18.4 s
2. 21 mm, 28.9 s
3. 21 mm, 39.4 s
4. 14 mm, 21.4 s

Answer: 14 mm, 21.4 s

Approach (and over-travel) distance = sqrt(d(D-d)) = sqrt(2*98) = 14 mm. Feed rate = 0.05*20*1200 = 1200 mm/min = 20 mm/s, total travel = 400+14+14 = 428 mm, time = 428/20 = 21.4 s. Answer is 14 mm, 21.4 s.

Q10. A car having weight W is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height h from the ground, midway between the front and rear wheels. The distance between the front and rear wheels is l. The acceleration of the car is a, and acceleration due to gravity is g. The reactions on the front wheels (R_f) and rear wheels (R_r) are given by

1. R_f = R_r = W/2 - (W/g)(h/l)a
2. R_f = W/2 + (W/g)(h/l)a; R_r = W/2 - (W/g)(h/l)a
3. R_f = W/2 - (W/g)(h/l)a; R_r = W/2 + (W/g)(h/l)a
4. R_f = R_r = W/2 + (W/g)(h/l)a

Answer: R_f = W/2 - (W/g)(h/l)a; R_r = W/2 + (W/g)(h/l)a

The correct option reflects the distribution of forces on the front and rear wheels due to the car's acceleration. As the car accelerates, the weight shifts towards the rear, decreasing the load on the front wheels and increasing it on the rear wheels, which is accurately represented in the equations.

Q11. The rotor of a turbojet engine of an aircraft has a mass 180 kg and polar moment of inertia 10 kg·m² about the rotor axis. The rotor rotates at a constant speed of 1100 rad/s in the clockwise direction when viewed from the front of the aircraft. The aircraft while flying at a speed of 800 km per hour takes a turn with a radius of 1.5 km to the left. The gyroscopic moment exerted by the rotor on the aircraft structure and the direction of motion of the nose when the aircraft turns, are

1. 1629.6 N·m and the nose goes up
2. 1629.6 N·m and the nose goes down
3. 162.9 N·m and the nose goes up
4. 162.9 N·m and the nose goes down

Answer: 1629.6 N·m and the nose goes down

The gyroscopic moment is calculated using the formula for gyroscopic precession, which results in a value of 1629.6 N·m. When the aircraft turns left, the gyroscopic effect causes the nose to pitch down due to the direction of the angular momentum vector and the applied force from the turn.

Q12. A plane-strain compression (forging) of a block is shown in the figure. The strain in the z-direction is zero. The yield strength (S_y) in uniaxial tension/compression of the material of the block is 300 MPa and it follows the Tresca (maximum shear stress) criterion. Assume that the entire block has started yielding. At a point where σₓ = 40 MPa (compressive) and τ_xy = 0, the stress component σ_y is

1. 340 MPa (compressive)
2. 340 MPa (tensile)
3. 260 MPa (compressive)
4. 260 MPa (tensile)

Answer: 340 MPa (compressive)

According to the Tresca criterion, yielding occurs when the maximum shear stress reaches a critical value. Given that the yield strength is 300 MPa and the stress state indicates a compressive stress of 40 MPa in the x-direction, the corresponding stress in the y-direction must be 340 MPa (compressive) to satisfy the yield condition, ensuring that the difference between the principal stresses does not exceed the yield strength.

Q13. In orthogonal turning of a cylindrical tube of wall thickness 5 mm, the axial and the tangential cutting forces were measured as 1259 N and 1601 N, respectively. The measured chip thickness after machining was found to be 0.3 mm. The rake angle was 10° and the axial feed was 100 mm/min. The rotational speed of the spindle was 1000 rpm. Assuming the material to be perfectly plastic and Merchant’s first solution, the shear strength of the material is closest to

1. 722 MPa
2. 920 MPa
3. 200 MPa
4. 875 MPa

Answer: 920 MPa

The correct option is 920 MPa because it is derived from Merchant's equation, which relates cutting forces, chip thickness, and shear strength. By applying the given forces and parameters, the calculated shear strength aligns with this value, confirming it as the closest estimate.