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Recent questions tagged gateme-2023
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GATE Mechanical 2023 | Question: 29
A beam of length $L$ is loaded in the $x y-$ 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 $y$ ... Which one of the options given depicts qualitatively $\text{CORRECT}$ variations of $M_y$ and $M_z$ along the length of the beam?
A beam of length $L$ is loaded in the $x y-$ plane by a uniformly distributed load, and by a concentrated tip load parallel to the $z$-axis, as shown in the figure. The r...
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GATE Mechanical 2023 | Question: 32
Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and cross-sectional area of the cylinder is $A$. The fluid inside the cylinder is air (considered as a perfect gas), with $\gamma$ being the ratio of the specific heat at ... $P_1 A L_1 \ln \frac{L_1}{L_2}$ $\frac{\left(P_2 L_2-P_1 L_1\right) A}{(1-\gamma)}$
Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and cross-sectional area of the cylinder is $A$. The fluid inside th...
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GATE Mechanical 2023 | Question: 33
A cylindrical rod of length $h$ and diameter $d$ is placed inside a cubic enclosure of side length $L. S$ denotes the inner surface of the cube. The view-factor $F_{S-S}$ is $0$ $1$ $\frac{\left(\pi d h+\pi d^2 / 2\right)}{6 L^2}$ $1-\frac{\left(\pi d h+\pi d^2 / 2\right)}{6 L^2}$
A cylindrical rod of length $h$ and diameter $d$ is placed inside a cubic enclosure of side length $L. S$ denotes the inner surface of the cube. The view-factor $F_{S-S}$...
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GATE Mechanical 2023 | Question: 34
In an ideal orthogonal cutting experiment (see figure), the cutting speed $V$ is $1 \mathrm{~m} / \mathrm{s}$, 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, ... at the shear zone? $1.84 \times 10^4$ $5.20 \times 10^4$ $0.71 \times 10^4$ $1.30 \times 10^4$
In an ideal orthogonal cutting experiment (see figure), the cutting speed $V$ is $1 \mathrm{~m} / \mathrm{s}$, the rake angle of the tool $\alpha=5^{\circ}$, and the shea...
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GATE Mechanical 2023 | Question: 35
A $\text{CNC}$ 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 ... total number of controllable locations at which the table can be positioned on this axis? $5000$ $2$ $1000$ $500$
A $\text{CNC}$ 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 ...
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GATE Mechanical 2023 | Question: 36
Cylindrical bars $\mathrm{P}$ and $\mathrm{Q}$ have identical lengths and radii, but are composed of different linear elastic materials. The Young's modulus and coefficient of thermal expansion of $\mathrm{Q}$ ... $\mathrm{P}$ and $\mathrm{Q}$ moves to the right after heating $\sigma_1<\sigma_2$ $\sigma_1=\sigma_2$
Cylindrical bars $\mathrm{P}$ and $\mathrm{Q}$ have identical lengths and radii, but are composed of different linear elastic materials. The Young's modulus and coefficie...
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GATE Mechanical 2023 | Question: 37
A very large metal plate of thickness $d$ and thermal conductivity $k$ is cooled by a stream of air at temperature $T_{\infty}=300 \mathrm{~K}$ with a heat transfer coefficient $h$, as shown in the figure. The centerline temperature of the plate is $T_{\mathrm{P}}$. In ...
A very large metal plate of thickness $d$ and thermal conductivity $k$ is cooled by a stream of air at temperature $T_{\infty}=300 \mathrm{~K}$ with a heat transfer coeff...
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GATE Mechanical 2023 | Question: 38
The smallest perimeter that a rectangle with area of $4$ square units can have is __________ units. (Answer in integer)
The smallest perimeter that a rectangle with area of $4$ square units can have is __________ units. (Answer in integer)
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GATE Mechanical 2023 | Question: 39
Consider the second-order linear ordinary differential equation $ x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}-y=0, \quad x \geq 1 $ with the initial conditions $ y(x=1)=6,\left.\quad \frac{d y}{d x}\right|_{x=1}=2 . $ The value of $y$ at $x=2$ equals __________. (Answer in integer)
Consider the second-order linear ordinary differential equation$$x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}-y=0, \quad x \geq 1$$with the initial conditions$$y(x=1)=6,\lef...
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GATE Mechanical 2023 | Question: 40
The initial value problem $ \frac{d y}{d t}+2 y=0, \quad y(0)=1 $ is solved numerically using the forward Euler's method with a constant and positive time step of $\Delta t$. Let $y_n$ represent the numerical solution obtained after $n$ ... $\Delta t$ does not exceed _________. (Answer in integer)
The initial value problem$$\frac{d y}{d t}+2 y=0, \quad y(0)=1$$is solved numerically using the forward Euler's method with a constant and positive time step of $\Delta t...
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GATE Mechanical 2023 | Question: 41
The atomic radius of a hypothetical face-centered cubic (FCC) metal is $(\sqrt{2} / 10) \; \mathrm{nm}$. The atomic weight of the metal is $24.092 \mathrm{~g} /$ mol. Taking Avogadro's number to be $6.023 \times 10^{23} \; \mathrm{atom/mol}$, the density of the metal is _________ $\mathrm{kg} / \mathrm{m}^3$. (Answer in integer)
The atomic radius of a hypothetical face-centered cubic (FCC) metal is $(\sqrt{2} / 10) \; \mathrm{nm}$. The atomic weight of the metal is $24.092 \mathrm{~g} /$ mol. Tak...
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GATE Mechanical 2023 | Question: 42
A steel sample with $1.5 \; \mathrm{wt}. \%$ carbon (no other alloying elements present) is slowly cooled from $1100^{\circ} \mathrm{C}$ ... the total cementite content in the microstructure that develops just below the eutectoid temperature is ___________. (Rounded off to two decimal places)
A steel sample with $1.5 \; \mathrm{wt}. \%$ carbon (no other alloying elements present) is slowly cooled from $1100^{\circ} \mathrm{C}$ to just below the eutectoid tempe...
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GATE Mechanical 2023 | Question: 43
A part, produced in high volumes, is dimensioned as shown. The machining process making this part is known to be statistically in control based on sampling data. The sampling data shows that $\text{D1}$ follows a normal distribution with a mean of ... upper limit of dimension $\mathrm{C}$ should be _____________ $\mathrm{mm}$. (Rounded off to one decimal place)
A part, produced in high volumes, is dimensioned as shown. The machining process making this part is known to be statistically in control based on sampling data. The samp...
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GATE Mechanical 2023 | Question: 44
A coordinate measuring machine (CMM) is used to determine the distance between Surface $\text{SP}$ and Surface $\text{SQ}$ of an approximately cuboidal shaped part. Surface $\text{SP}$ is declared as the datum as per the engineering ... to fit the necessary planes. The distance between the two fitted planes is ____________ $\mathrm{mm}$. (Answer in integer)
A coordinate measuring machine (CMM) is used to determine the distance between Surface $\text{SP}$ and Surface $\text{SQ}$ of an approximately cuboidal shaped part. Surfa...
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GATE Mechanical 2023 | Question: 45
A solid part (see figure) of polymer material is to be fabricated by additive manufacturing $\text{(AM)}$ in square-shaped layers starting from the bottom of the part working upwards. The nozzle diameter of the $\text{(AM)}$ ... delays between layers or the serpentine scan lines. The time taken to fabricate this part is ____________ minutes. (Answer in integer)
A solid part (see figure) of polymer material is to be fabricated by additive manufacturing $\text{(AM)}$ in square-shaped layers starting from the bottom of the part wor...
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GATE Mechanical 2023 | Question: 46
An optical flat is used to measure the height difference between a reference slip gauge $\text{A}$ and a slip gauge $\text{B}$. Upon viewing via the optical flat using a monochromatic light of wavelength $0.5 \mu \mathrm{m}, 12$ fringes were ... $45 \mathrm{~mm}$ apart, the height difference of the gauges is ____________ $\mu \mathrm{m}$. (Answer in integer)
An optical flat is used to measure the height difference between a reference slip gauge $\text{A}$ and a slip gauge $\text{B}$. Upon viewing via the optical flat using a ...
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GATE Mechanical 2023 | Question: 47
Ignoring the small elastic region, the true stress $(\sigma)-\operatorname{true}$ strain $(\varepsilon)$ variation of a material beyond yielding follows the equation $\sigma=400 \varepsilon^{0.3} \mathrm{MPa}$. The engineering ultimate tensile strength value of this material is ____________ $\text{MPa}$. (Rounded off to one decimal place)
Ignoring the small elastic region, the true stress $(\sigma)-\operatorname{true}$ strain $(\varepsilon)$ variation of a material beyond yielding follows the equation $\si...
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GATE Mechanical 2023 | Question: 48
The area moment of inertia about the $y$-axis of a linearly tapered section shown in the figure is __________ $\mathrm{m}^4$. (Answer in integer)
The area moment of inertia about the $y$-axis of a linearly tapered section shown in the figure is __________ $\mathrm{m}^4$.(Answer in integer)
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GATE Mechanical 2023 | Question: 49
A cylindrical bar has a length $L=5 \mathrm{~m}$ and cross section area $S=10 \mathrm{~m}^{2}$. The bar is made of a linear elastic material with a density $\rho=2700 \mathrm{~kg} / \mathrm{m}^{3}$ ... J. (Rounded off to two decimal places) Take the acceleration due to gravity as $g=9.8 \mathrm{~m} / \mathrm{s}^{2}$.
A cylindrical bar has a length $L=5 \mathrm{~m}$ and cross section area $S=10 \mathrm{~m}^{2}$. The bar is made of a linear elastic material with a density $\rho=2700 \ma...
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GATE Mechanical 2023 | Question: 50
A cylindrical transmission shaft of length $1.5 \mathrm{~m}$ and diameter $100 \mathrm{~mm}$ is made of a linear elastic material with a shear modulus of $80 \mathrm{GPa}$. While operating at $500 \mathrm{rpm}$, the angle of twist across ... transmitted by the shaft at this speed is ____________ $\mathrm{kW}$. (Rounded off to two decimal places) Take $\pi=3.14$
A cylindrical transmission shaft of length $1.5 \mathrm{~m}$ and diameter $100 \mathrm{~mm}$ is made of a linear elastic material with a shear modulus of $80 \mathrm{GPa}...
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GATE Mechanical 2023 | Question: 51
Consider a mixture of two ideal gases, $\mathrm{X}$ and $\mathrm{Y}$, with molar masses $\bar{M}_{\mathrm{X}}=10 \mathrm{~kg} / \mathrm{kmol}$ and $\bar{M}_{\mathrm{Y}}=20 \mathrm{~kg} / \mathrm{kmol}$, respectively, in a container. The ... off to one decimal place) Assume that the universal gas constant is $8314 \mathrm{~J} \mathrm{kmol}^{-1} \mathrm{~K}^{-1}$.
Consider a mixture of two ideal gases, $\mathrm{X}$ and $\mathrm{Y}$, with molar masses $\bar{M}_{\mathrm{X}}=10 \mathrm{~kg} / \mathrm{kmol}$ and $\bar{M}_{\mathrm{Y}}=2...
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GATE Mechanical 2023 | Question: 52
The velocity field of a certain two-dimensional flow is given by $\boldsymbol{V}(x, y)=k(x \hat{\imath}-y \hat{\jmath})$ where $k=2 \mathrm{~s}^{-1}$. The coordinates $x$ and $y$ are in meters. Assume gravitational effects to be negligible. If ... $(2 \mathrm{~m}, 2 \mathrm{~m})$ is __________ $\mathrm{kPa}$. (Answer in integer)
The velocity field of a certain two-dimensional flow is given by$\boldsymbol{V}(x, y)=k(x \hat{\imath}-y \hat{\jmath})$where $k=2 \mathrm{~s}^{-1}$. The coordinates $x$ a...
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GATE Mechanical 2023 | Question: 53
Consider a unidirectional fluid flow with the velocity field given by $ V(x, y, z, t)=u(x, t) \hat{\imath} $ where $u(0, t)=1$. If the spatially homogeneous density field varies with time $t$ as $ \rho(t)=1+0.2 e^{-t} $ the value of $u(2,1)$ is ______________. (Rounded off to two decimal places) Assume all quantities to be dimensionless.
Consider a unidirectional fluid flow with the velocity field given by$$V(x, y, z, t)=u(x, t) \hat{\imath}$$where $u(0, t)=1$. If the spatially homogeneous density field v...
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GATE Mechanical 2023 | Question: 54
The figure shows two fluids held by a hinged gate. The atmospheric pressure is $P_a=100 \mathrm{kPa}$. The moment per unit width about the base of the hinge is ____________ $\mathrm{kNm} / \mathrm{m}$. (Rounded off to one decimal place) Take the acceleration due to gravity to be $\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2$.
The figure shows two fluids held by a hinged gate. The atmospheric pressure is $P_a=100 \mathrm{kPa}$. The moment per unit width about the base of the hinge is __________...
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GATE Mechanical 2023 | Question: 55
An explosion at time $t=0$ releases energy $\text{E}$ 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 $\text{R}$ denote the ... where $k$ is a dimensionless constant. The value of exponent $\text{a}$ is _____________. (Rounded off to one decimal place)
An explosion at time $t=0$ releases energy $\text{E}$ at the origin in a space filled with a gas of density $\rho$. Subsequently, a hemispherical blast wave propagates ra...
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