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GATE Mechanical 2022 Set 2 | Question: 28
A linear elastic structure under plane stress condition is subjected to two sets of loading, $\text{I}$ and $\text{II}$. The resulting states of stress at a point corresponding to these two loadings are as shown in the figure below. If these two sets of loading are applied ... $\sigma /2$ $\sigma \left ( 1-1/\sqrt{2} \right )$
A linear elastic structure under plane stress condition is subjected to two sets of loading, $\text{I}$ and $\text{II}$. The resulting states of stress at a point corresp...
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GATE Mechanical 2022 Set 1 | Question: 20
The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condition. The exit plane shown in the figure is located within the nozzle. If the ... through the nozzle will increase. Mach number at the exit plane of the nozzle will become more than unity.
The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condi...
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GATE Mechanical 2022 Set 2 | Question: 16
A square plate is supported in four different ways (configurations $(P)$ to $(S)$ as shown in the figure). A couple moment $C$ is applied on the plate. Assume all the members to be rigid and mass-less, and all joints to ... one or more of the following support configurations? Configuration $(P)$ Configuration $(Q)$ Configuration $(R)$ Configuration $(S)$
A square plate is supported in four different ways (configurations $(P)$ to $(S)$ as shown in the figure). A couple moment $C$ is applied on the plate. Assume all the mem...
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GATE Mechanical 2022 Set 2 | Question: 12
Which one of the following $\text{CANNOT}$ impart linear motion in a $\text{CNC}$ machine? Linear motor Ball screw Lead screw Chain and sprocket
Which one of the following $\text{CANNOT}$ impart linear motion in a $\text{CNC}$ machine?Linear motorBall screwLead screwChain and sprocket
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GATE Mechanical 2022 Set 2 | Question: 37
The lengths of members $\text{BC}$ and $\text{CE}$ in the frame shown in the figure are equal. All the members are rigid and lightweight, and the friction at the joints is negligible. Two forces of magnitude $Q> 0$ are applied as shown, each at the ... the following members do not carry any load (force)? $\text{AB}$ $\text{CD}$ $\text{EF}$ $\text{GH}$
The lengths of members $\text{BC}$ and $\text{CE}$ in the frame shown in the figure are equal. All the members are rigid and lightweight, and the friction at the joints i...
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GATE Mechanical 2022 Set 1 | Question: 28
A planar four-bar linkage mechanism with $3$ revolute kinematic pairs and $1$ prismatic kinematic pair is shown in the figure, where $AB \perp CE$ and $FD \perp CE$. The $T$-shaped link $\text{CDEF}$ is constructed such that the ... $\text{AG and CDEF}$ on the border of Grashof and non-Grashof chains with uncertain configuration(s)
A planar four-bar linkage mechanism with $3$ revolute kinematic pairs and $1$ prismatic kinematic pair is shown in the figure, where $AB \perp CE$ and $FD \perp CE$. The ...
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GATE Mechanical 2022 Set 1 | Question: 14
A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field in the fluid is $\vec{V} = \left ( 2x\right ) \hat{i} + \left ( y + 3t \right )\hat{j}$, and the temperature field ... by the probe at $\left ( x = 1, y = 1, t = 1 \right )$ is _____________. $4$ $0$ $18$ $14$
A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field in the fluid is $\ve...
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GATE Mechanical 2022 Set 2 | Question: 20
A rope with two mass-less platforms at its two ends passes over a fixed pulley as shown in the figure. Discs with narrow slots and having equal weight of $20\: N$ each can be placed on the platforms. The number of discs placed ... $\text{(ii)}$ of the figure) required to prevent downward motion of the left side platform is _____________________(in integer).
A rope with two mass-less platforms at its two ends passes over a fixed pulley as shown in the figure. Discs with narrow slots and having equal weight of $20\: N$ each ca...
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GATE Mechanical 2022 Set 2 | Question: 7
A massive uniform rigid circular disc is mounted on a frictionless bearing at the end $E$ of a massive uniform rigid shaft $\text{AE}$ which is suspended horizontally in a uniform gravitational field by two identical light inextensible strings ... about the positive $y$-axis direction rotate slowly (compared to $\omega$) about the negative $y$-axis direction
A massive uniform rigid circular disc is mounted on a frictionless bearing at the end $E$ of a massive uniform rigid shaft $\text{AE}$ which is suspended horizontally in ...
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GATE Mechanical 2022 Set 2 | Question: 14
Consider a steady flow through a horizontal divergent channel, as shown in the figure, with supersonic flow at the inlet. The direction of flow is from left to right. Pressure at location $B$ is observed to be higher than that at an ... flow rate is constant, velocity at $B$ is lower than velocity at $A$ Normal shock Viscous effect Boundary layer separation
Consider a steady flow through a horizontal divergent channel, as shown in the figure, with supersonic flow at the inlet. The direction of flow is from left to right.Pres...
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GATE Mechanical 2022 Set 2 | Question: 17
Consider sand casting of a cube of edge length $a$. A cylindrical riser is placed at the top of the casting. Assume solidification time, $t_{s} \:\alpha\: V/A$, where $V$ is the volume and $A$ is the total surface area dissipating heat. If the top of the ... /radii of riser is/are acceptable? $\dfrac{a}{3}$ $\dfrac{a}{2}$ $\dfrac{a}{4}$ $\dfrac{a}{6}$
Consider sand casting of a cube of edge length $a$. A cylindrical riser is placed at the top of the casting. Assume solidification time, $t_{s} \:\alpha\: V/A$, where $V$...
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GATE Mechanical 2022 Set 1 | Question: 22
A rigid uniform annular disc is pivoted on a knife edge $A$ in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner ... of circumference to diameter of a circle, then $\beta = $ ____________________ (round off to $2$ decimal places).
A rigid uniform annular disc is pivoted on a knife edge $A$ in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in ...
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GATE Mechanical 2022 Set 2 | Question: 22
An electric car manufacturer underestimated the January sales of car by $20$ units, while the actual sales was $120$ units. If the manufacturer uses exponential smoothing method with a smoothing constant of $\alpha = 0.2$, then the sales forecast for the month of February of the same year is ____________ units (in integer).
An electric car manufacturer underestimated the January sales of car by $20$ units, while the actual sales was $120$ units. If the manufacturer uses exponential smoothing...
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GATE Mechanical 2022 Set 1 | Question: 23
Electrochemical machining operations are performed with tungsten as the tool, and copper and aluminum as two different workpiece materials. Properties of copper and aluminum are given in the table below. ... $\text{MRR}$ of aluminum will be _______________________ $\text{mg/s}$ (round-off to two decimal places)
Electrochemical machining operations are performed with tungsten as the tool, and copper and aluminum as two different workpiece materials. Properties of copper and alumi...
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GATE Mechanical 2022 Set 2 | Question: 15
Which of the following non-dimensional terms is an estimate of Nusselt number? Ratio of internal thermal resistance of a solid to the boundary layer thermal resistance Ratio of the rate at which internal energy is ... to the rate of conduction heat transfer Non-dimensional temperature gradient Non-dimensional velocity gradient multiplied by Prandtl number
Which of the following non-dimensional terms is an estimate of Nusselt number?Ratio of internal thermal resistance of a solid to the boundary layer thermal resistanceRati...
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GATE Mechanical 2022 Set 2 | Question: 5
A polynomial $\varphi \left ( s \right ) = a_{n}s^{n} + a_{n-1}s^{n-1} + \cdots + a_{1}s+a_{0}$ of degree $n>3$ with constant real coefficients $a_{n}, a_{n-1}, \:\dots a_{0}$ has triple roots at $s = -\sigma$. Which one of the following ... $\frac{d^{3}\varphi \left ( s \right )}{ds^{3}} = 0$ at $s = -\sigma$
A polynomial $\varphi \left ( s \right ) = a_{n}s^{n} + a_{n-1}s^{n-1} + \cdots + a_{1}s+a_{0}$ of degree $n>3$ with constant real coefficients $a_{n}, a_{n-1}, \:\dots a...
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GATE Mechanical 2022 Set 1 | Question: 25
A flat plate made of cast iron is exposed to a solar flux of $600\; W/m^{2}$ at an ambient temperature of $25^{\circ}C$. Assume that the entire solar flux is absorbed by the plate. Cast iron has a low ... the aforementioned conditions, the radiation equilibrium temperature of the plate is _____________$^{\circ}C$ (round off to the nearest integer).
A flat plate made of cast iron is exposed to a solar flux of $600\; W/m^{2}$ at an ambient temperature of $25^{\circ}C$. Assume that the entire solar flux is absorbed by ...
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GATE Mechanical 2022 Set 1 | Question: 27
An $L$-shaped elastic member $\text{ABC}$ with slender arms $\text{AB}$ and $\text{BC}$ of uniform cross-section is clamped at end $A$ and connected to a pin at end $C$. The pin remains in continuous contact with and is constrained to move in a smooth ... $\frac{5P}{8}$, and upwards $\frac{P}{4}$, and downwards $\frac{3P}{4}$, and upwards
An $L$-shaped elastic member $\text{ABC}$ with slender arms $\text{AB}$ and $\text{BC}$ of uniform cross-section is clamped at end $A$ and connected to a pin at end $C$. ...
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GATE Mechanical 2022 Set 2 | Question: 4
Given $\int_{-\infty }^{\infty } e^{-x^{2}} dx = \sqrt{\pi }.$ If $a$ and $b$ are positive integers, the value of $\int_{-\infty }^{\infty } e^{-a\left ( x+b \right )^{2}} dx$ is _______________. $\sqrt{\pi a}$ $\sqrt{\frac{\pi }{a}}$ $b\sqrt{\pi a}$ $b\sqrt{\frac{\pi }{a}}$
Given $\int_{-\infty }^{\infty } e^{-x^{2}} dx = \sqrt{\pi }.$If $a$ and $b$ are positive integers, the value of $\int_{-\infty }^{\infty } e^{-a\left ( x+b \right )^{2}}...
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GATE Mechanical 2022 Set 1 | Question: 18
Which of the following additive manufacturing technique(s) can use a wire as a feedstock material? Stereolithography Fused deposition modeling Selective laser sintering Directed energy deposition processes
Which of the following additive manufacturing technique(s) can use a wire as a feedstock material?StereolithographyFused deposition modelingSelective laser sinteringDirec...
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GATE Mechanical 2022 Set 2 | Question: 8
A structural member under loading has a uniform state of plane stress which is usual notations is given by $\sigma _{x} = 3P, \sigma _{y} = -2P$ and $\tau_{xy} = \sqrt{2}P$, where $P>0$. The yield strength of the material is $350$ ... maximum distortion energy theory) is $70$ $\text{MPa}$ $90$ $\text{MPa}$ $120$ $\text{MPa}$ $75$ $\text{MPa}$
A structural member under loading has a uniform state of plane stress which is usual notations is given by $\sigma _{x} = 3P, \sigma _{y} = -2P$ and $\tau_{xy} = \sqrt{2}...
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GATE Mechanical 2022 Set 2 | Question: 9
Fluidity of a molten alloy during sand casting depends on its solidification range. The phase diagram of a hypothetical binary alloy of components $A$ and $B$ is shown in the figure with its eutectic composition and temperature. All the lines in this phase diagram, ... the solidification range is $400^{\circ}C$ $250^{\circ}C$ $800^{\circ}C$ $150^{\circ}C$
Fluidity of a molten alloy during sand casting depends on its solidification range. The phase diagram of a hypothetical binary alloy of components $A$ and $B$ is shown in...
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GATE Mechanical 2022 Set 1 | Question: 36
The system of linear equations in real $\left ( x,y \right )$ given by $\left ( x \: y \right )\begin{bmatrix} 2 &5 - 2 \alpha \\ \alpha & 1 \end{bmatrix} = \left ( 0\:0 \right )$ involves a real parameter $\alpha$ and has infinitely many non-trivial solutions for special ... $\alpha$? $x = 2, y = -2$ $x = -1, y = 4$ $x = 1, y = 1$ $x = 4, y = -2$
The system of linear equations in real $\left ( x,y \right )$ given by $$\left ( x \: y \right )\begin{bmatrix} 2 &5 - 2 \alpha \\ \alpha & 1 \end{bmatrix} = \left ( 0\:0...
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GATE Mechanical 2022 Set 2 | Question: 11
Match the additive manufacturing technique in Column $\text{I}$ with its corresponding input material in Column $\text{II}$. Additive manufacturing technique (Column $\text{I}$) Input material (Column $\text{II}$) $P$ Fused deposition modelling $1$ Photo sensitive liquid resin $Q$ Laminated object ... $P -2, Q -3, R -1$ $P -4, Q -1, R -4$
Match the additive manufacturing technique in Column $\text{I}$ with its corresponding input material in Column $\text{II}$. Additive manufacturing technique (Column $\t...
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GATE Mechanical 2022 Set 2 | Question: 13
Which one of the following is an intensive property of a thermodynamic system? Mass Density Energy Volume
Which one of the following is an intensive property of a thermodynamic system?MassDensityEnergyVolume
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GATE Mechanical 2022 Set 1 | Question: 6
A uniform light slender beam $\text{AB}$ of section modulus $\text{EI}$ is pinned by a frictionless joint $A$ to the ground and supported by a light inextensible cable $\text{CB}$ to hang a weight $W$ as shown. If the maximum value of $W$ ... $\beta$ is $0.0924\:m^{-2}$ $0.0713\:m^{-2}$ $0.1261\:m^{-2}$ $0.1417\:m^{-2}$
A uniform light slender beam $\text{AB}$ of section modulus $\text{EI}$ is pinned by a frictionless joint $A$ to the ground and supported by a light inextensible cable $\...
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GATE Mechanical 2022 Set 2 | Question: 18
Which of these processes involve$(s)$ melting in metallic workpieces? Electrochemical machining Electric discharge machining Laser beam machining Electron beam machining
Which of these processes involve$(s)$ melting in metallic workpieces?Electrochemical machiningElectric discharge machiningLaser beam machiningElectron beam machining
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GATE Mechanical 2022 Set 2 | Question: 2
Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point $(1, 2, 3)$. The surface integral $\int _{A} \vec{F}.d\vec{A}$ of a vector field $\vec{F} = 3x\hat{i} + 5y\hat{j} + 6z\hat{k}$ over the entire surface $A$ of the cube is _____________. $14$ $27$ $28$ $31$
Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point $(1, 2, 3)$. The surface integral $\int _{A} \vec{F}.d\vec{A}$ ...
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GATE Mechanical 2022 Set 2 | Question: 6
Which one of the following is the definition of ultimate tensile strength $\text{(UTS)}$ obtained from a stress-strain test on a metal specimen? Stress value where the stress-strain curve transitions from elastic ... -sectional area The maximum load attained divided by the corresponding instantaneous cross-sectional area Stress where the specimen fractures
Which one of the following is the definition of ultimate tensile strength $\text{(UTS)}$ obtained from a stress-strain test on a metal specimen?Stress value where the str...
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GATE Mechanical 2022 Set 2 | Question: 3
Consider the definite integral $\int_{1}^{2} \left ( 4x^{2} + 2x + 6 \right )dx.$ Let $I_{e}$ be the exact value of the integral. If the same integral is estimated using Simpson's rule with $10$ equal subintervals, the value is $I_{S}$. The percentage error is defined ... $e$ is $2.5$ $3.5$ $1.2$ $0$
Consider the definite integral$$\int_{1}^{2} \left ( 4x^{2} + 2x + 6 \right )dx.$$Let $I_{e}$ be the exact value of the integral. If the same integral is estimated using ...
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GATE Mechanical 2022 Set 1 | Question: 16
Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following statement(s) is/are TRUE? A body subjected to hydrostatic pressure ... a beam has zero shear force, then the corresponding portion of the elastic curve of the beam is always straight.
Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the foll...
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GATE Mechanical 2022 Set 2 | Question: 10
A shaft of diameter $25_{-0.07}^{-0.04}$ $\text{mm}$ is assembled in a hole of diameter $25_{-0.00}^{+0.02}$ $\text{mm}$. Match the allowance and limit parameter in Column $\text{I}$ with its corresponding quantitative value in Column $\text{II}$ for this shaft-hole assembly. Allowance ... $P -1, Q -3, R -2$ $P -1, Q -3 R -4$ $P -3, Q -1, R -2$
A shaft of diameter $25_{-0.07}^{-0.04}$ $\text{mm}$ is assembled in a hole of diameter $25_{-0.00}^{+0.02}$ $\text{mm}$. Match the allowance and limit parameter in Colum...
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GATE Mechanical 2022 Set 1 | Question: 40
Two rigid massless rods $PR$ and $RQ$ are joined at frictionless pin-joint $R$ and are resting on ground at $P$ and $Q$, respectively, as shown in the figure. A vertical force $F$ acts on the pin $R$ ... friction at $Q$ to that at $P\left(\mu_{Q}/\mu_{P}\right)$ is ___________________ (round off to two decimal places).
Two rigid massless rods $PR$ and $RQ$ are joined at frictionless pin-joint $R$ and are resting on ground at $P$ and $Q$, respectively, as shown in the figure. A vertical ...
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GATE Mechanical 2022 Set 2 | Question: 1
$F(t)$ is a periodic square wave function as shown. It takes only two values, $4$ and $0$, and stays at each of these values for $1$ second before changing. What is the constant term in the Fourier series expansion of $F(t)$? $1$ $2$ $3$ $4$
$F(t)$ is a periodic square wave function as shown. It takes only two values, $4$ and $0$, and stays at each of these values for $1$ second before changing. What is the c...
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GATE Mechanical 2022 Set 2 | Question: 53
Consider steady state, one-dimensional heat conduction in an infinite slab of thickness $2L (L = 1\:m)$ as shown in the figure. The conductivity $(k)$ of the material varies with temperature as $\text{k = CT}$, where $T$ ... of the slab are maintained at $600\: K$, then the temperature at $X = 0$ is _______________ $K$ (in integer).
Consider steady state, one-dimensional heat conduction in an infinite slab of thickness $2L (L = 1\:m)$ as shown in the figure. The conductivity $(k)$ of the material var...
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GATE Mechanical 2022 Set 1 | Question: 21
The plane of the figure represents a horizontal plane. A thin rigid rod at rest is pivoted without friction about a fixed vertical axis passing through $O$. Its mass moment of inertia is equal to $0.1\; kg.cm^{2}$ about $O$. A ... and sticks to it. Immediately after the impact, the angular velocity of the rod is ______________ $\text{rad/s}$ (in integer).
The plane of the figure represents a horizontal plane. A thin rigid rod at rest is pivoted without friction about a fixed vertical axis passing through $O$. Its mass mome...
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GATE Mechanical 2022 Set 1 | Question: 35
Consider a rod of uniform thermal conductivity whose one end $(x = 0)$ is insulated and the other end $(x =L)$ is exposed to flow of air at temperature $T_{\infty}$ with convective heat transfer coefficient $h$. The cylindrical surface of the rod is insulated so that the heat ...
Consider a rod of uniform thermal conductivity whose one end $(x = 0)$ is insulated and the other end $(x =L)$ is exposed to flow of air at temperature $T_{\infty}$ with ...
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GATE Mechanical 2022 Set 1 | Question: 15
In the following two-dimensional momentum equation for natural convection over a surface immersed in a quiescent fluid at temperature $T_{\infty}$ ($g$ is the gravitational acceleration, $\beta$ is the volumetric thermal expansion ... viscous force. Ratio of buoyancy force to viscous force. Viscous force per unit mass. Buoyancy force per unit mass.
In the following two-dimensional momentum equation for natural convection over a surface immersed in a quiescent fluid at temperature $T_{\infty}$ ($g$ ...
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GATE Mechanical 2022 Set 1 | Question: 33
A solid spherical bead of lead (uniform density= $11000 \; kg/m^{3}$) of diameter $d = 0.1\; mm$ sinks with a constant velocity $V$ in a large stagnant pool of a liquid (dynamic viscosity = $1.1 \times 10^{-3}\; kg \cdot m^{-1} \cdot s^{-1}$). The ... $V$ is ____________ $m/s$. $\frac{1}{24}$ $\frac{1}{6}$ $\frac{1}{18}$ $\frac{1}{12}$
A solid spherical bead of lead (uniform density= $11000 \; kg/m^{3}$) of diameter $d = 0.1\; mm$ sinks with a constant velocity $V$ in a large stagnant pool of a liquid (...
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GATE Mechanical 2022 Set 2 | Question: 25
Wien's law is stated as follows: $\lambda _{m}T = C$, where $C$ is $2898$ $\mu m \cdot K$ and $\lambda_{m}$ is the wavelength at which the emissive power of a black body is maximum for a given ... $K$ (round off to the nearest integer).
Wien's law is stated as follows: $\lambda _{m}T = C$, where $C$ is $2898$ $\mu m \cdot K$ and $\lambda_{m}$ is the wavelength at which the emissive power of a black body ...
Arjun
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Arjun
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Feb 15, 2022
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