GATE Technical: Mechanical Engineering (ME, Set-2) questions with solutions

Q1. The size distribution of the powder particles used in Powder Metallurgy process can be determined by

1. Laser scattering
2. Laser reflection
3. Laser absorption
4. Laser penetration

Answer: Laser scattering

Laser scattering is effective for determining particle size distribution because it analyzes the way laser light is scattered by particles, providing detailed information about their size and distribution.

Q2. In a CNC machine tool, the function of an interpolator is to generate

1. signal for the lubrication pump during machining
2. error signal for tool radius compensation during machining
3. NC code from the part drawing during post processing
4. reference signal prescribing the shape of the path

Answer: reference signal prescribing the shape of the path

The interpolator in a CNC machine generates a reference signal that defines the precise path the tool should follow, ensuring accurate movement and positioning during machining.

Q3. The machining process that involves thermal energy is

1. Abrasive Jet Machining
2. Chemical Machining
3. Electrochemical Machining
4. Laser Beam Machining

Answer: Laser Beam Machining

Laser Beam Machining utilizes focused laser energy to melt or vaporize material, making it a thermal process that effectively cuts or engraves various materials.

Q4. The allowance provided in between a hole and a shaft is calculated from the difference between

1. lower limit of the shaft and the upper limit of the hole
2. upper limit of the shaft and the upper limit of the hole
3. upper limit of the shaft and the lower limit of the hole
4. lower limit of the shaft and the lower limit of the hole

Answer: upper limit of the shaft and the lower limit of the hole

The allowance is determined by the difference between the upper limit of the shaft and the lower limit of the hole, as this reflects the maximum clearance or fit between the two components, ensuring proper assembly and function.

Q5. For a two-dimensional, incompressible flow having velocity components u and v in the x and y directions, respectively, the expression ∂(u²)/∂x + ∂(uv)/∂y can be simplified to

1. u ∂u/∂x + v ∂u/∂y
2. u ∂v/∂x + v ∂v/∂y
3. ∂u/∂x + ∂v/∂y
4. u ∂u/∂y + v ∂v/∂x

Answer: u ∂u/∂x + v ∂u/∂y

The correct option is derived from applying the product rule of differentiation to the terms u² and uv, leading to the simplification that expresses the change in kinetic energy per unit volume in terms of the velocity components and their gradients.

Q6. Which of the following is responsible for eddy viscosity (or turbulent viscosity) in a turbulent boundary layer on a flat plate?

1. Nikuardse stresses
2. Reynolds stresses
3. Boussinesq stresses
4. Prandtl stresses

Answer: Reynolds stresses

Reynolds stresses arise from the fluctuations in velocity within a turbulent flow, and they represent the momentum transfer due to these fluctuations, which is essential for defining eddy viscosity in turbulent boundary layers.

Q7. The controlling force curves P, Q and R for a spring controlled governor are shown in the figure, where r1 and r2 are any two radii of rotation.

1. P – Stable; Q – Isochronous; R – Unstable
2. P – Isochronous; Q – Stable; R – Unstable
3. P – Stable; Q – Isochronous; R – Unstable
4. P – Stable; Q – Unstable; R – Isochronous

Answer: P – Stable; Q – Isochronous; R – Unstable

Option A is correct because the characteristics of the curves indicate that curve P maintains stability at varying speeds, curve Q achieves constant speed regardless of load (isochronous), and curve R shows instability as the radius of rotation increases.

Q8. The von Mises stress at a point is proportional to the square root of the

1. total strain energy per unit volume
2. plastic strain energy per unit volume
3. dilatational strain energy per unit volume
4. distortional strain energy per unit volume

Answer: distortional strain energy per unit volume

The von Mises stress is derived from the distortional strain energy, which reflects the material's response to shear deformation. It is specifically designed to predict yielding under complex loading conditions, making it directly related to the distortional component of strain energy.

Q9. A factory produces m (i = 1, 2,..., m) products, each of which requires processing on n (j = 1, 2,..., n) workstations. Let a_ij be the amount of processing time that one unit of the i^th product requires on the j^th workstation. Let the revenue from selling one unit of the i^th product be r_i and h_i be the holding cost per unit per time period for the i^th product. The planning horizon consists of T (t = 1, 2,..., T) time periods. The minimum demand that must be satisfied in time period t is d_it, and the capacity of j^th workstation in time period t is c_jt. Consider the aggregate planning formulation below, with decision variables S_it (amount of product i sold in time period t), X_it (amount of product i manufactured in time period t) and I_it (amount of product i held in inventory at the end of time period t). max ∑ₜ₌₁^(T)∑_(i=1)^(m)(r_iS_(it)-h_iI_(it)) subject to S_it ≥ d_it ∀ i,t < capacity constraint > < inventory balance constraint > X_it, S_it, I_it ≥ 0; I_i0 = 0 The capacity constraints and inventory balance constraints for this formulation are

1. ∑_(i=1)^(m) a_(ij)X_(it) ≤ c_(jt), ∀ j,t and I_(it)=I_(i,t-1)+X_(it)-S_(it), ∀ i,t
2. ∑_(j=1)ⁿ a_(ij)X_(it) ≤ c_(jt), ∀ i,t and I_(it)=I_(i,t-1)+X_(it)-S_(it), ∀ i,t
3. ∑_(i=1)^(m) a_(ij)X_(it) ≤ c_(jt), ∀ j,t and I_(it)=I_(i,t-1)+S_(it)-X_(it), ∀ i,t
4. ∑_(j=1)ⁿ a_(ij)X_(it) ≤ c_(jt), ∀ i,t and I_(it)=I_(i,t-1)+S_(it)-X_(it), ∀ i,t

Answer: ∑_(i=1)^(m) a_(ij)X_(it) ≤ c_(jt), ∀ j,t and I_(it)=I_(i,t-1)+X_(it)-S_(it), ∀ i,t

The correct option accurately represents the capacity constraints by summing the processing times of all products on each workstation to ensure they do not exceed the available capacity, while the inventory balance constraint correctly reflects the relationship between production, sales, and inventory levels over time.