List of top Mechanical Engineering Questions asked in GATE ME

The figure shows a block of mass \(m = 20\) kg attached to a pair of identical linear springs, each having a spring constant \(k = 1000\) N/m. The block oscillates on a frictionless horizontal surface. Assuming free vibrations, the time taken by the block to complete ten oscillations is ............... seconds. (Rounded off to two decimal places) Take \(\pi = 3.14\). 

Consider a unidirectional fluid flow with the velocity field given by
\(V(x, y, z, t) = u(x, t)\ \hat{i}\)
where \(u(0, t) = 1\). If the spatially homogeneous density field varies with time \(t\) as
\(\rho(t) = 1 + 0.2e^{-t}\), the value of \(u(2,1)\) is ................ (Rounded off to two decimal places).
Assume all quantities to be dimensionless.

An explosion at time \(t = 0\) releases energy \(E\) at the origin in a space filled with a gas of density \(\rho\). Subsequently, a hemispherical blast wave propagates radially outwards as shown in the figure. 
Let \(R\) denote the radius of the front of the hemispherical blast wave. The radius \(R\) follows the relationship \(R = k t^a E^b \rho^c\), where \(k\) is a dimensionless constant. The value of exponent \(a\) is ................ 
(Rounded off to one decimal place) 

 

The figure shows two fluids held by a hinged gate. The atmospheric pressure is \(P_a\) = 100 kPa. The moment per unit width about the base of the hinge is ............... kNm/m. (Rounded off to one decimal place) 
Take the acceleration due to gravity to be g = 9.8 m/s². 

 

An optical flat is used to measure the height difference between a reference slip gauge A and a slip gauge B. Upon viewing via the optical flat using a monochromatic light of wavelength 0.5 \(\mu\)m, 12 fringes were observed over a length of 15 mm of gauge B. If the gauges are placed 45 mm apart, the height difference of the gauges is ............... \(\mu\)m. (Answer in integer) 

A solid part (see figure) of polymer material is to be fabricated by additive manufacturing (AM) in square-shaped layers starting from the bottom of the part working upwards. The nozzle diameter of the AM machine is a/10 mm and the nozzle follows a linear serpentine path parallel to the sides of the square layers with a feed rate of a/5 mm/min. Ignore any tool path motions other than those involved in adding material, and any other delays between layers or the serpentine scan lines. The time taken to fabricate this part is ............... minutes. (Answer in integer) 

 

A coordinate measuring machine (CMM) is used to determine the distance between Surface SP and Surface SQ of an approximately cuboidal shaped part. Surface SP is declared as the datum as per the engineering drawing used for manufacturing this part. The CMM is used to measure four points P1, P2, P3, P4 on Surface SP, and four points Q1, Q2, Q3, Q4 on Surface SQ as shown. A regression procedure is used to fit the necessary planes. The distance between the two fitted planes is ............... mm. (Answer in integer) 

A CNC machine has one of its linear positioning axes as shown in the figure, consisting of a motor rotating a lead screw, which in turn moves a nut horizontally on which a table is mounted. The motor moves in discrete rotational steps of 50 steps per revolution. The pitch of the screw is 5 mm and the total horizontal traverse length of the table is 100 mm. What is the total number of controllable locations at which the table can be positioned on this axis? 

 

In an ideal orthogonal cutting experiment (see figure), the cutting speed V is 1 m/s, the rake angle of the tool \(\alpha = 5^\circ\), and the shear angle, \(\phi\), is known to be \(45^\circ\). Applying the ideal orthogonal cutting model, consider two shear planes PQ and RS close to each other. As they approach the thin shear zone (shown as a thick line in the figure), plane RS gets sheared with respect to PQ (point R1 shears to R2, and S1 shears to S2). Assuming that the perpendicular distance between PQ and RS is \(\delta = 25 \, \mu\text{m}\), what is the value of shear strain rate (in \(s^{-1}\)) that the material undergoes at the shear zone? 

 

The figure shows a thin-walled open-top cylindrical vessel of radius \(r\) and wall thickness \(t\). The vessel is held along the brim and contains a constant-density liquid to height \(h\) from the base. Neglect atmospheric pressure, the weight of the vessel and bending stresses in the vessel walls. Which one of the plots depicts qualitatively CORRECT dependence of the magnitudes of axial wall stress (\(\sigma_1\)) and circumferential wall stress (\(\sigma_2\)) on \(y\)? 

A beam of length L is loaded in the xy-plane by a uniformly distributed load, and by a concentrated tip load parallel to the z-axis, as shown in the figure. The resulting bending moment distributions about the y and the z axes are denoted by \(M_y\) and \(M_z\), respectively. Which one of the options given depicts qualitatively CORRECT variations of \(M_y\) and \(M_z\) along the length of the beam? 

The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity \(\omega_1\). A rigid bar PQ is pinned to the wheel at P while the end Q slides on the floor. What is the angular velocity \(\omega_2\) of the bar PQ? 

A vector field \[ \mathbf{B}(x, y, z) = x \mathbf{\hat{i}} + y \mathbf{\hat{j}} - 2z \mathbf{\hat{k}} \] is defined over a conical region having height \(h = 2\), base radius \(r = 3\) and axis along z, as shown in the figure. The base of the cone lies in the x-y plane and is centered at the origin. If \(\mathbf{n}\) denotes the unit outward normal to the curved surface S of the cone, the value of the integral \[ \iint_S \mathbf{B} \cdot \mathbf{n} \, dS \] equals ................ (Answer in integer) 

Two meshing spur gears 1 and 2 with diametral pitch of 8 teeth per mm and an angular velocity ratio \(|\omega_2|/|\omega_1| = 1/4\), have their centers 30 mm apart. The number of teeth on the driver (gear 1) is ................ (Answer in integer) 

Which of the plot(s) shown is/are valid Mohr's circle representations of a plane stress state in a material? (The center of each circle is indicated by O.) 

 

A beam is undergoing pure bending as shown in the figure. The stress (\(\sigma\))-strain (\(\epsilon\)) curve for the material is also given. The yield stress of the material is \(\sigma_Y\). Which of the option(s) given represent(s) the bending stress distribution at cross-section AA after plastic yielding? 

 

The S-N curve from a fatigue test for steel is shown. Which one of the options gives the endurance limit? 

 

The options show frames consisting of rigid bars connected by pin joints. Which one of the frames is non-rigid? 

 

The effective stiffness of a cantilever beam of length L and flexural rigidity EI subjected to a transverse tip load W is 

 

A cuboidal part has to be accurately positioned first, arresting six degrees of freedom and then clamped in a fixture, to be used for machining. Locating pins in the form of cylinders with hemi-spherical tips are to be placed on the fixture for positioning. Four different configurations of locating pins are proposed as shown. Which one of the options given is correct? 

 

Which one of the options given represents the feasible region of the linear programming model: 
Maximize \(45X_1 + 60X_2\) 
\(X_1 \le 45\) 
\(X_2 \le 50\) 
\(10X_1 + 10X_2 \ge 600\) 
\(25X_1 + 5X_2 \le 750\) 

 

With reference to the Economic Order Quantity (EOQ) model, which one of the options given is correct? 

 

The figure shows the plot of a function over the interval [-4, 4]. Which one of the options given CORRECTLY identifies the function? 

 

The velocity field of a certain two-dimensional flow is given by
\(V(x, y) = k(x\hat{i} - y\hat{j})\)
where \(k = 2 \text{ s}^{-1}\). The coordinates x and y are in meters. Assume gravitational effects to be negligible.
If the density of the fluid is 1000 kg/m³ and the pressure at the origin is 100 kPa, the pressure at the location (2 m, 2 m) is ............... kPa.
(Answer in integer)
A cylindrical bar has a length L = 5 m and cross section area S = 10 m². The bar is made of a linear elastic material with a density \(\rho\) = 2700 kg/m³ and Young's modulus E = 70 GPa. The bar is suspended as shown in the figure and is in a state of uniaxial tension due to its self-weight.
The elastic strain energy stored in the bar equals ............... J. (Rounded off to two decimal places)
Take the acceleration due to gravity as g = 9.8 m/s².