Questions by Arjun / GO Mechanical

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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 $\...

asked Feb 15, 2022

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GATE Mechanical 2022 Set 1 | Question: 7
The figure shows a schematic of a simple Watt governor mechanism with the spindle $O_{1}O_{2}$ rotating at an angular velocity $\omega$ about a vertical axis. The balls at $P$ and $S$ have equal mass. Assume that there is no friction anywhere and all ... If $\omega$ is doubled, the value of $h$ will be _________________ $\text{mm}$. $50$ $100$ $150$ $200$

The figure shows a schematic of a simple Watt governor mechanism with the spindle $O_{1}O_{2}$ rotating at an angular velocity $\omega$ about a vertical axis. The balls a...

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GATE Mechanical 2022 Set 1 | Question: 8
A square threaded screw is used to lift a load $W$ by applying a force $F$. Efficiency of square threaded screw is expressed as The ratio of work done by $W$ per revolution to work done by $F$ per revolution $\frac{W}{F}$ $\frac{F}{W}$ The ratio of work done by $F$ per revolution to work done by $W$ per revolution

A square threaded screw is used to lift a load $W$ by applying a force $F$. Efficiency of square threaded screw is expressed asThe ratio of work done by $W$ per revolutio...

asked Feb 15, 2022

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GATE Mechanical 2022 Set 1 | Question: 9
A $\text{CNC}$ worktable is driven in a linear direction by a lead screw connected directly to a stepper motor. The pitch of the lead screw is $5$ $\text{mm}$. The stepper motor completes one full revolution upon receiving $600$ ... stepper motor is $20$ $\text{kHz}$ $10$ $\text{kHz}$ $3$ $\text{kHz}$ $15$ $\text{kHz}$

A $\text{CNC}$ worktable is driven in a linear direction by a lead screw connected directly to a stepper motor. The pitch of the lead screw is $5$ $\text{mm}$. The steppe...

asked Feb 15, 2022

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GATE Mechanical 2022 Set 1 | Question: 10
The type of fit between a mating shaft of diameter $25.0 ^{+0.010}_{- 0.010}$ $\text{mm}$ and a hole of diameter $25.015 ^{+0.015}_{- 0.015}$ $\text{mm}$ is __________________. Clearance Transition Interference Linear

The type of fit between a mating shaft of diameter $25.0 ^{+0.010}_{- 0.010}$ $\text{mm}$ and a hole of diameter $25.015 ^{+0.015}_{- 0.015}$ $\text{mm}$ is ____________...

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GATE Mechanical 2022 Set 1 | Question: 11
In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource is positive negative zero infinity

In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource ispositivenegativezeroinfinity

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GATE Mechanical 2022 Set 1 | Question: 12
Which one of the following is NOT a form of inventory? Raw materials Work-in-process materials Finished goods $\text{CNC}$ Milling Machines

Which one of the following is NOT a form of inventory?Raw materialsWork-in-process materialsFinished goods$\text{CNC}$ Milling Machines

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GATE Mechanical 2022 Set 1 | Question: 13
The Clausius inequality holds good for any process any cycle only reversible process only reversible cycle

The Clausius inequality holds good forany processany cycleonly reversible processonly reversible cycle

asked Feb 15, 2022

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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 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: 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 1 | Question: 17
Which of the following heat treatment processes is/are used for surface hardening of steels? Carburizing Cyaniding Annealing Carbonitriding

Which of the following heat treatment processes is/are used for surface hardening of steels?CarburizingCyanidingAnnealingCarbonitriding

asked Feb 15, 2022

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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 1 | Question: 19
Which of the following methods can improve the fatigue strength of a circular mild steel $\text{(MS)}$ shaft? Enhancing surface finish Shot peening of the shaft Increasing relative humidity Reducing relative humidity

Which of the following methods can improve the fatigue strength of a circular mild steel $\text{(MS)}$ shaft?Enhancing surface finishShot peening of the shaftIncreasing r...

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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 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: 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 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 1 | Question: 24
A polytropic process is carried out from an initial pressure of $110$ $\text{kPa}$ and volume of $5\; m^{3}$ to a final volume of $2.5\; m^{3}$. The polytropic index is given by $n = 1.2$. The absolute value of the work done during the process is ______________ $\text{kJ}$ (round off to $2$ decimal places).

A polytropic process is carried out from an initial pressure of $110$ $\text{kPa}$ and volume of $5\; m^{3}$ to a final volume of $2.5\; m^{3}$. The polytropic index is g...

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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: 26
The value of the integral $\oint \left ( \frac{6z}{2z^{4} - 3z^{3} + 7z^{2} - 3z + 5 } \right )dz$ evaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole $z = i$, where $i$ is the imaginary unit, is $\left ( -1 + i \right )\pi$ $\left ( 1 + i \right )\pi$ $2\left ( 1 - i \right )\pi$ $\left ( 2 + i \right )\pi$

The value of the integral $$\oint \left ( \frac{6z}{2z^{4} - 3z^{3} + 7z^{2} - 3z + 5 } \right )dz$$ evaluated over a counter-clockwise circular contour in the complex pl...

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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 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: 29
Consider a forced single degree-of-freedom system governed by $\ddot{\chi }\left ( t \right ) + 2 \zeta \omega _{n}\dot{\chi }\left ( t \right ) +\omega _{n}^{2}\chi(t)= \omega _{n}^{2} \cos \left ( \omega t \right )$, where $\zeta$ and $\omega_{n}$ ... $\omega _{d} < \omega _{n} = \omega _{p}$ $\omega _{d} < \omega _{n} < \omega _{p}$

Consider a forced single degree-of-freedom system governed by $\ddot{\chi }\left ( t \right ) + 2 \zeta \omega _{n}\dot{\chi }\left ( t \right ) +\omega _{n}^{2}\chi(t)= ...

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GATE Mechanical 2022 Set 1 | Question: 30
A bracket is attached to a vertical column by means of two identical rivets $U$ and $V$ separated by a distance of $2a = 100\; mm$, as shown in the figure. The permissible shear stress of the rivet material is $50$ $\text{MPa}$. If a ... cross-sectional area of each of the rivets to avoid failure is ________________$mm^2$. $800$ $25$ $100\sqrt{7}$ $200$

A bracket is attached to a vertical column by means of two identical rivets $U$ and $V$ separated by a distance of $2a = 100\; mm$, as shown in the figure. The permissibl...

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GATE Mechanical 2022 Set 1 | Question: 31
In $Fe-Fe_{3}C$ phase diagram, the eutectoid composition is $0.8$ weight $\%$ of carbon at $725^{\circ}C$. The maximum solubility of carbon in $\alpha$-ferrite phase is $0.025$ weight $\%$ of carbon. A steel sample, having no other ... of pro-eutectoid $\alpha$-ferrite in the above steel sample at room temperature is $0.387$ $0.864$ $0.475$ $0.775$

In $Fe-Fe_{3}C$ phase diagram, the eutectoid composition is $0.8$ weight $\%$ of carbon at $725^{\circ}C$. The maximum solubility of carbon in $\alpha$-ferrite phase is $...

asked Feb 15, 2022

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GATE Mechanical 2022 Set 1 | Question: 32
Activities $A$ to $K$ are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is to be completed in the minimum possible time, the latest finish time for the activity $G$ is _______________ ... $5$ $10$ $8$ $9$

Activities $A$ to $K$ are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is ...

asked Feb 15, 2022

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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 (...

asked Feb 15, 2022

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GATE Mechanical 2022 Set 1 | Question: 34
Consider steady, one-dimensional compressible flow or a gas in a pipe or diameter $1\; m$. At one location in the pipe, the density and velocity are $1\; kg/m^{3}$ and $100\; m/s$, respectively. At a downstream location in the pipe, the ... the gas on the pipe between these two locations is ________________$N$. $350 \pi^{2}$ $750 \pi$ $1000 \pi$ $3000$

Consider steady, one-dimensional compressible flow or a gas in a pipe or diameter $1\; m$. At one location in the pipe, the density and velocity are $1\; kg/m^{3}$ and $1...

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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: 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 1 | Question: 37
Let a random variable $X$ follow Poisson distribution such that $\text{Prob (X = 1) = Prob (X = 2)}$. The value of $\text{Prob (X = 3)}$ is ______________ (round off to $2$ decimal places).

Let a random variable $X$ follow Poisson distribution such that $$\text{Prob (X = 1) = Prob (X = 2)}$$. The value of $\text{Prob (X = 3)}$ is ______________ (round off t...

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GATE Mechanical 2022 Set 1 | Question: 38
Consider two vectors: $\vec{a} = 5 i + 7j + 2k$$\vec{b} = 3 i - j + 6k$ Magnitude of the component of $\vec{a}$ orthogonal to $\vec{b}$ in the plane containing the vectors $\vec{a}$ and $\vec{b}$ is _____________ (round off to $2$ decimal places).

Consider two vectors: $$\vec{a} = 5 i + 7j + 2k$$$$\vec{b} = 3 i - j + 6k$$Magnitude of the component of $\vec{a}$ orthogonal to $\vec{b}$ in the plane containing the vec...

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GATE Mechanical 2022 Set 1 | Question: 39
A structure, along with the loads applied on it, is shown in the figure. Self-weight of all the members is negligible and all the pin joints are friction-less. $AE$ is a single member that contains pin $C$. Likewise, $BE$ is a ... and $FH$ are overlapping rigid members. The magnitude of the force carried by member $CI$ is ______________ $kN$ (in integer).

A structure, along with the loads applied on it, is shown in the figure. Self-weight of all the members is negligible and all the pin joints are friction-less. $AE$ is a ...

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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 1 | Question: 41
A cylindrical disc of $\text{mass m = 1 kg}$ and $\text{radius r = 0.15 m}$ was spinning at $\omega =5\; rad/s$ when it was placed on a flat horizontal surface and released (refer to the figure). Gravity $g$ acts ... of the center of the disc, when it starts rolling without slipping, will be __________________$m/s$ (round off to $2$ decimal places).

A cylindrical disc of $\text{mass m = 1 kg}$ and $\text{radius r = 0.15 m}$ was spinning at $\omega =5\; rad/s$ when it was placed on a flat horizontal surface and releas...

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GATE Mechanical 2022 Set 1 | Question: 42
A thin-walled cylindrical pressure vessel has mean wall thickness of $t$ and nominal radius of $r$. The Poisson's ratio of the wall material is $1/3$. When it was subjected to some internal pressure, its nominal perimeter in the cylindrical portion increased ... $\%$ (round off to $3$ decimal places).

A thin-walled cylindrical pressure vessel has mean wall thickness of $t$ and nominal radius of $r$. The Poisson's ratio of the wall material is $1/3$. When it was subject...

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GATE Mechanical 2022 Set 1 | Question: 43
A schematic of an epicyclic gear train is shown in the figure. The sun $\text{(gear 1)}$ and planet $\text{(gear 2)}$ are external, and the ring gear $\text{(gear 3)}$ is internal. Gear $1$, gear $3$ and arm $OP$ are ... $\text{(ccw)}$, the magnitude of angular velocity of arm $OP$ is _____________________ $\text{rpm}$ (in integer)

A schematic of an epicyclic gear train is shown in the figure. The sun $\text{(gear 1)}$ and planet $\text{(gear 2)}$ are external, and the ring gear $\text{(gear 3)}$ is...

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GATE Mechanical 2022 Set 1 | Question: 44
Under orthogonal cutting condition, a turning operation is carried out on a metallic workpiece at a cutting speed of $4\; m/s$. The orthogonal rake angle of the cutting tool is $5^{\circ}$ ... condition is $1000$ $\text{MPa}$, then the cutting force is _________________ $N$ (round off to one decimal place).

Under orthogonal cutting condition, a turning operation is carried out on a metallic workpiece at a cutting speed of $4\; m/s$. The orthogonal rake angle of the cutting t...

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GATE Mechanical 2022 Set 1 | Question: 45
A $1$ $\text{mm}$ thick cylindrical tube, $100$ $\text{mm}$ in diameter, is orthogonally turned such that the entire wall thickness of the tube is cut in a single pass. The axial feed of the tool is $1$ ... of feed force towards power. The power required to carry out this operation is _______________ $kW$ (round off to one decimal place).

A $1$ $\text{mm}$ thick cylindrical tube, $100$ $\text{mm}$ in diameter, is orthogonally turned such that the entire wall thickness of the tube is cut in a single pass. T...

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