GATE Technical: Mechanical Engineering questions with solutions

Q1. A block of mass 10 kg rests on a horizontal floor. The acceleration due to gravity is 9.81 m/s². The coefficient of static friction between the floor and the block is 0.2. A horizontal force of 10 N is applied on the block as shown in the figure. The magnitude of force of friction (in N) on the block is ____

1. 2
2. 10
3. 19.62
4. 0

Answer: 10

Maximum static friction = mu*N = 0.2*10*9.81 = 19.62 N. The applied 10 N is less than this, so the block stays at rest and friction exactly balances the applied force at 10 N.

Q2. A cylindrical rod of diameter 10 mm and length 1.0 m is fixed at one end. The other end is twisted by an angle of 10° by applying a torque. If the maximum shear strain in the rod is p×10⁻³, then p is equal to ____ (round off to two decimal places).

1. 0.87
2. 1.75
3. 8.73
4. 17.45

Answer: 0.87

gamma = r*theta/L with r=0.005 m, theta=10 deg=0.17453 rad, L=1 m gives gamma=0.005*0.17453=8.727e-4=0.8727e-3, so p=0.87. The stored 1.75 is wrong.

Q3. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of points P and R are Vp and Vr, in the x and y directions, respectively. The magnitude of the angular velocity of the body is

1. 2Vr
2. 2Vp
3. Vr/√3
4. Vp/√3

Answer: 2Vr

The angular velocity of a rigid body can be determined by the relationship between the linear velocities of its points and the distance from the axis of rotation. In this case, since edge QR is parallel to the x-axis and the body is moving, the angular velocity is twice the velocity of point R (2Vr) due to the geometry of the triangle and the distribution of velocities.

Q4. Hardendability of steel is a measure of

1. the ability to harden when it is cold worked
2. the maximum hardness that can be obtained when it is austenitized and then quenched
3. the depth to which required hardening is obtained when it is austenitized and then quenched
4. the ability to retain its hardness when it is heated to elevated temperatures

Answer: the depth to which required hardening is obtained when it is austenitized and then quenched

Hardendability specifically refers to how deeply a steel can be hardened through the process of austenitizing followed by quenching, indicating the effectiveness of the heat treatment in achieving hardness throughout the material.

Q5. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase in

1. viscosity
2. surface tension
3. freezing range
4. degree of superheat

Answer: degree of superheat

Increasing the degree of superheat raises the temperature of the molten metal above its melting point, which reduces its viscosity and enhances fluidity, allowing it to flow more easily into molds.

Q6. The cold forming process in which a hardened tool is pressed against a workpiece (when there is relative motion between the tool and the workpiece) to produce a roughened surface with a regular pattern is

1. Roll forming
2. Strip rolling
3. Knurling
4. Chamfering

Answer: Knurling

Knurling is a cold forming process that creates a textured pattern on a workpiece by pressing a hardened tool against it while both are in relative motion, resulting in a roughened surface that enhances grip.

Q7. The most common limit gage used for inspecting the hole diameter is

1. Snap gage
2. Ring gage
3. Plug gage
4. Master gage

Answer: Plug gage

A plug gage is specifically designed to measure the internal diameter of holes, making it the most common tool for this purpose due to its accuracy and ease of use.

Q8. The transformation matrix for mirroring a point in x - y plane about the line y = x is given by

1. [1 0] [0 -1]
2. [-1 0] [0 1]
3. [0 1] [1 0]
4. [0 -1] [-1 0]

Answer: [0 1] [1 0]

The correct transformation matrix swaps the x and y coordinates, which reflects points across the line y = x. This effectively mirrors any point in the x-y plane about that line.

Q9. Consider two concentric circular cylinders of different materials M and N in contact with each other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder system is subjected to internal pressure P. Let (u_r^M, u_θ^M) and (σ_rr^M, σ_θθ^M) denote the radial and tangential displacement and stress components, respectively, in material M. Similarly, (u_r^N, u_θ^N) and (σ_rr^N, σ_θθ^N) denote the radial and tangential displacement and stress components, respectively, in material N. The boundary conditions that need to be satisfied at the frictionless interface between the two cylinders are:

1. u_r^M = u_r^N and σ_rr^M = σ_rr^N only
2. u_r^M = u_r^N and σ_rr^M = σ_rr^N and u_θ^M = u_θ^N and σ_θθ^M = σ_θθ^N
3. u_θ^M = u_θ^N and σ_θθ^M = σ_θθ^N only
4. σ_rr^M = σ_rr^N and σ_θθ^M = σ_θθ^N only

Answer: u_r^M = u_r^N and σ_rr^M = σ_rr^N only

At the frictionless interface between the two materials, the radial displacements must be equal to ensure continuity, and the radial stresses must also be equal to maintain equilibrium. The tangential components do not need to match because there is no friction to enforce that condition.

Q10. A prismatic, straight, elastic cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is L, Young’s modulus E, and area moment of inertia I, the magnitude of the maximum deflection is

1. qL⁴/15EI
2. qL⁴/30EI
3. qL⁴/10EI
4. qL⁴/60EI

Answer: qL⁴/30EI

The maximum deflection of a cantilever beam under a linearly distributed load can be derived using beam theory, specifically the formula for deflection due to such loading conditions. The correct option, qL⁴/30EI, accurately represents the relationship between the load intensity, beam length, material properties, and geometric properties, confirming it as the appropriate solution.