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GATE Mechanical 2021 Set 1 | Question: 46
In the vicinity of the triple point, the equation of liquid-vapour boundary in the $\text{P-T}$ phase diagram for ammonia is $ \ln p=24.38-3063/T$, where $\text{P}$ is pressure (in $\text{Pa}$) and $\text{T}$ is temperature (in ... $\text{K}$ ($\textit{round off to one decimal place}$).
In the vicinity of the triple point, the equation of liquid-vapour boundary in the $\text{P-T}$ phase diagram for ammonia is $ \ln p=24.38-3063/T$, where $\text{P}$ is pr...
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Feb 22, 2021
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GATE Mechanical 2024 | Question: 38
Consider a slab of $20 \mathrm{~mm}$ thickness. There is a uniform heat generation of $\dot{q}=100 \mathrm{MW} / \mathrm{m}^{3}$ ... state heat conduction, the location of the maximum temperature from the left face will be at ________ $\mathrm{mm}$ (answer in integer).
Consider a slab of $20 \mathrm{~mm}$ thickness. There is a uniform heat generation of $\dot{q}=100 \mathrm{MW} / \mathrm{m}^{3}$ inside the slab. The left and right faces...
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Feb 16
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GATE Mechanical 2022 Set 1 | Question: 53
A steady two-dimensional flow field is specified by the stream function $\psi = kx^{3}y,$ where $x$ and $y$ are in meter and the constant $k = 1 \:m^{-2}\:s^{-1}$. The magnitude of acceleration at a point $(x, y) = (1\;m, 1\;m)$ is _______________ $m/s^{2}$ (round off to $2$ decimal places).
A steady two-dimensional flow field is specified by the stream function $$\psi = kx^{3}y,$$ where $x$ and $y$ are in meter and the constant $k = 1 \:m^{-2}\:s^{-1}$. The ...
Arjun
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Arjun
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Feb 15, 2022
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GATE Mechanical 2021 Set 1 | Question: 29
The fundamental thermodynamic relation for a rubber band is given by $dU=TdS+\tau dL$, where $\text{T}$ is the absolute temperature, $\text{S}$ is the entropy, $\tau$ is the tension in the rubber band, and $\text{L}$ is the length of the rubber band. ... $T=\left ( \frac{\partial U}{\partial S} \right )_{\tau}$
The fundamental thermodynamic relation for a rubber band is given by $dU=TdS+\tau dL$, where $\text{T}$ is the absolute temperature, $\text{S}$ is the entropy, $\tau$ is ...
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gatecse
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Feb 22, 2021
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GATE Mechanical 2021 Set 1 | Question: 38
An orthogonal cutting operation is performed using a single point cutting tool with a rake angle of $12^{\circ}$ on a lathe. During turning, the cutting force and the friction force are $\text{1000 N}$ and $\text{600 N}$, respectively. If the ... $\text{N}$ ($\textit{round off to two decimal places}$).
An orthogonal cutting operation is performed using a single point cutting tool with a rake angle of $12^{\circ}$ on a lathe. During turning, the cutting force and the fri...
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gatecse
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Feb 22, 2021
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GATE Mechanical 2024 | Question: 46
A solid massless cylindrical member of $50 \mathrm{~mm}$ diameter is rigidly attached at one end, and is subjected to an axial force $P=100 \mathrm{kN}$ and a torque $T=600 \mathrm{~N}$. $\mathrm{m}$ at the other end as shown. Assume that ... yield stress as $300$ $\mathrm{MPa}$, the factor of safety in the design is ________ (rounded off to $1$ decimal place).
A solid massless cylindrical member of $50 \mathrm{~mm}$ diameter is rigidly attached at one end, and is subjected to an axial force $P=100 \mathrm{kN}$ and a torque $T=6...
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admin
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Feb 16
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GATE Mechanical 2024 | Question: 42
The Levai type-$\text{A}$ train illustrated in the figure has gears with module $m=8 \mathrm{~mm} /$ tooth. Gears $2$ and $3$ have $19$ and $24$ teeth respectively. Gear $2$ is fixed and internal gear $4$ ... $\text{rev/min}$. (rounded off to $2$ decimal places)
The Levai type-$\text{A}$ train illustrated in the figure has gears with module $m=8 \mathrm{~mm} /$ tooth. Gears $2$ and $3$ have $19$ and $24$ teeth respectively. Gear ...
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admin
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Feb 16
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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...
Arjun
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Arjun
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Feb 15, 2022
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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...
Arjun
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Arjun
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Feb 15, 2022
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GATE Mechanical 2024 | Question: 35
Consider an air-standard Brayton cycle with adiabatic compressor and turbine, and a regenerator, as shown in the figure. Air enters the compressor at $100 \mathrm{kPa}$ and $300 \mathrm{~K}$ and exits the compressor at $600 \mathrm{kPa}$ ... volume is $c_{p} / c_{v}=1.4$. The thermal efficiency of the cycle is $\%$ ________ (answer in integer).
Consider an air-standard Brayton cycle with adiabatic compressor and turbine, and a regenerator, as shown in the figure. Air enters the compressor at $100 \mathrm{kPa}$ a...
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Feb 16
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GATE Mechanical 2024 | Question: 49
A band brake shown in the figure has a coefficient of friction of $0.3$. The band can take a maximum force of $1.5 \mathrm{kN}$. The maximum braking force $\text{(F)}$ that can be safely applied is ___________ $\mathrm{N}$ (rounded off to the nearest integer).
A band brake shown in the figure has a coefficient of friction of $0.3$. The band can take a maximum force of $1.5 \mathrm{kN}$. The maximum braking force $\text{(F)}$ th...
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4.4k
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admin
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Feb 16
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GATE Mechanical 2024 | Question: 45
A vibratory system consists of mass $m$, a vertical spring of stiffness $2 k$ and a horizontal spring of stiffness $k$. The end $\mathrm{A}$ of the horizontal spring is given a horizontal motion $x_{A}=a \sin \omega t$. The other end ... the oscillations of mass $m$ tend to become excessively large is ___________ $\mathrm{rad} / \mathrm{s}$ (answer in integer).
A vibratory system consists of mass $m$, a vertical spring of stiffness $2 k$ and a horizontal spring of stiffness $k$. The end $\mathrm{A}$ of the horizontal spring is g...
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admin
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Feb 16
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GATE Mechanical 2024 | Question: 40
Consider a hemispherical furnace of diameter $\text{D}=6 \mathrm{~m}$ with a flat base. The dome of the furnace has an emissivity of $0.7$ and the flat base is a blackbody. The base and the dome are maintained at uniform temperature of $300 \mathrm{~K}$ ... -Boltzmann constant $=5.67 \times 10^{-8} \mathrm{~W} /\left(\mathrm{m}^{2} \mathrm{~K}^{4}\right)$
Consider a hemispherical furnace of diameter $\text{D}=6 \mathrm{~m}$ with a flat base. The dome of the furnace has an emissivity of $0.7$ and the flat base is a blackbod...
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4.4k
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admin
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Feb 16
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GATE Mechanical 2024 | Question: 54
A flat surface of a $\text{C}60$ steel having dimensions of $100 \mathrm{~mm}$ (length) $\times 200 \mathrm{~mm}$ (width) is produced by a $\text{HSS}$ slab mill cutter. The $8$ -toothed cutter has $100 \mathrm{~mm}$ diameter ... is $2 \mathrm{~mm}$. The machining time required to remove the entire stock is ________ minutes (rounded off to $2$ decimal places).
A flat surface of a $\text{C}60$ steel having dimensions of $100 \mathrm{~mm}$ (length) $\times 200 \mathrm{~mm}$ (width) is produced by a $\text{HSS}$ slab mill cutter. ...
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admin
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Feb 16
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GATE Mechanical 2024 | Question: 39
A condenser is used as a heat exchanger in a large steam power plant in which steam is condensed to liquid water. The condenser is a shell and tube heat exchanger which consists of $1$ shell and $20,000$ tubes. Water flows through each of the ... $3$ decimal places).
A condenser is used as a heat exchanger in a large steam power plant in which steam is condensed to liquid water. The condenser is a shell and tube heat exchanger which c...
admin
4.4k
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admin
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Feb 16
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GATE Mechanical 2024 | Question: 47
The figure shows a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an angle $\alpha=60^{\circ}$ with the horizontal. The closed vessel has a wall thickness of $10 \mathrm{~mm}$ ... magnitude of the normal stress acting on the weld is __________ $\mathrm{MPa}$ (rounded off to $1$ decimal place).
The figure shows a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an angle $\alpha=60^{\circ}$ with the horizontal. The c...
admin
4.4k
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admin
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Feb 16
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GATE Mechanical 2024 | Question: 34
Let $\text{X}$ be a continuous random variable defined on $[0,1]$ such that its probability density function $f(x)=1$ for $0 \leq x \leq 1$ and $0$ otherwise. Let $Y=\log _{\mathrm{e}}(X+1)$. Then the expected value of $\text{Y}$ is ___________. (rounded off to $2$ decimal places)
Let $\text{X}$ be a continuous random variable defined on $[0,1]$ such that its probability density function $f(x)=1$ for $0 \leq x \leq 1$ and $0$ otherwise. Let $Y=\log...
admin
4.4k
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admin
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Feb 16
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GATE Mechanical 2024 | Question: 44
At the instant when $\text{OP}$ is vertical and $\text{AP}$ is horizontal, the link $\text{OD}$ is rotating counter clockwise at a constant rate $\omega=7 \mathrm{rad} / \mathrm{s}$. Pin $\mathrm{P}$ on link $\text{OD}$ slides in ... velocity of link $\text{ABC}$ for this instant is ______________$\mathrm{rad} / \mathrm{s}$ (rounded off to $2$ decimal places).
At the instant when $\text{OP}$ is vertical and $\text{AP}$ is horizontal, the link $\text{OD}$ is rotating counter clockwise at a constant rate $\omega=7 \mathrm{rad} / ...
admin
4.4k
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admin
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Feb 16
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GATE Mechanical 2024 | Question: 48
A three-hinge arch $\text{ABC}$ in the form of a semi-circle is shown in the figure. The arch is in static equilibrium under vertical loads of $\text{P}=100 \mathrm{kN}$ and $\text{Q}=50 \mathrm{kN}$. Neglect friction at all the hinges. The magnitude of the horizontal reaction at $\text{B}$ is __________ $\mathrm{kN}$ (rounded off to $1$ decimal place).
A three-hinge arch $\text{ABC}$ in the form of a semi-circle is shown in the figure. The arch is in static equilibrium under vertical loads of $\text{P}=100 \mathrm{kN}$ ...
admin
4.4k
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admin
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Feb 16
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