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GATE Mechanical 2022 Set 2 | Question: 31
Parts $P1 - P7$ are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total completion time required tor carrying out both the operations for all $7$ ... $31$ $33$ $30$ $32$

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GATE Mechanical 2022 Set 2 | Question: 32
A manufacturing unit produces two products $P1$ and $P2$. For each piece of $P1$ and $P2$, the table below provides quantities of materials $\text{M1, M2}$ and $M3$ ... $5000$ $4000$ $3000$ $6000$

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GATE Mechanical 2022 Set 2 | Question: 33
A tube of uniform diameter $D$ is immersed in a steady flowing inviscid liquid stream of velocity $V$, as shown in the figure. Gravitational acceleration is represented by $g$. The volume flow rate through the tube is __________________. $\dfrac{\pi}{4}D^{2}V$ ... $\dfrac{\pi}{4}D^{2}\sqrt{V^{2} - 2gh_{2}}$

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GATE Mechanical 2022 Set 2 | Question: 34
The steady velocity field in an inviscid fluid of density $1.5$ is given to be $\vec{V} = \left ( y^{2}-x^{2} \right )\hat{i} + \left ( 2xy \right )\hat{j}.$ Neglecting body forces, the pressure gradient at $(x = 1, y = 1)$ is _________________. $10\hat{j}$ $20\hat{i}$ $-6\hat{i} - 6\hat{j}$ $-4\hat{i} - 4\hat{j}$

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GATE Mechanical 2022 Set 2 | Question: 35
In a vapour compression refrigeration cycle, the refrigerant enters the compressor in saturated vapour state at evaporator pressure, with specific enthalpy equal to $250$ $\text{kJ/kg}$. The exit of the compressor is superheated at condenser pressure with specific ... of the refrigerant at entry to evaporator is _______________. $0.2$ $0.25$ $0.3$ $0.35$

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GATE Mechanical 2022 Set 2 | Question: 36
$A$ is a $3 \times 5$ real matrix of rank $2$. For the set ot homogeneous equations $Ax = 0$, where $0$ is a zero vector and $x$ is a vector of unknown variables, which of the following is/are true? The given ... size. The given set of equations will have infinitely many solutions. The given set of equations will have many but a finite number of solutions.

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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)? $\text{AB}$ $\text{CD}$ $\text{EF}$ $\text{GH}$

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GATE Mechanical 2022 Set 2 | Question: 38
If the sum and product of eigenvalues of a $2 \times 2$ real matrix $\begin{bmatrix} 3 & p\\ p & q \end{bmatrix}$ are $4$ and $-1$ respectively, then $\left | p \right |$ is ______________ (in integer).

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GATE Mechanical 2022 Set 2 | Question: 39
Given $z = x + iy, i = \sqrt{-1}$. $C$ is a circle of radius $2$ with the centre at the origin. If the contour $C$ is traversed anticlockwise, then the value of the integral $\dfrac{1}{2\pi}\int _{C}\dfrac{1}{\left ( z-i \right )\left ( z+4i \right )}dz$ is __________________ (round off to one decimal place).

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GATE Mechanical 2022 Set 2 | Question: 40
A shaft of length $L$ is made of two materials, one in the inner core and the other in the outer rim, and the two are perfectly joined together (no slip at the interface) along the entire length of the shaft. The diameter of the inner ... strain relations are linear. Then the ratio $\tau_{i}/ \tau_{o}$ is ______________ (round off to $2$ decimal places).

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GATE Mechanical 2022 Set 2 | Question: 41
A rigid beam $\text{AD}$ of length $3a = 6\:m$ is hinged at frictionless pin joint $A$ and supported by two strings as shown in the figure. String $\text{BC}$ passes over two small frictionless pulleys of negligible radius. All the ... deflections, the tension developed in the string at $C$ is _______________ $\text{kN}$ (round off to $2$ decimal places).

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GATE Mechanical 2022 Set 2 | Question: 42
In the configuration of the planar four-bar mechanism at a certain instant as shown in the figure, the angular velocity of the $2$ $\text{cm}$ long link is $w_{2} = 5$ $\text{rad/s}$. Given the dimensions as shown, the magnitude of the angular ... of the $4$ $\text{cm}$ long link is given by ______________ $\text{rad/s}$ (round off to $2$ decimal places).

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GATE Mechanical 2022 Set 2 | Question: 43
A shaft $\text{AC}$ rotating at a constant speed carries a thin pulley of radius $r= 0.4\:m$ at the end $C$ which drives a belt. A motor is coupled at the end $A$ ... and assuming maximum shear stress theory, the minimum required shaft diameter is _____________ $\text{mm}$ (round off to $2$ decimal places).

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GATE Mechanical 2022 Set 2 | Question: 44
A straight-teeth horizontal slab milling cutter is shown in the figure. It has $4$ teeth and diameter $(D)$ of $200$ $\text{mm}$. The rotational speed of the cutter is $100$ $\text{rpm}$ and the linear feed given to the workpiece ... $\text{kN}$ (round off to one decimal place).

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GATE Mechanical 2022 Set 2 | Question: 45
ln an orthogonal machining operation, the cutting and thrust forces are equal in magnitude. The uncut chip thickness is $0.5$ $\text{mm}$ and the shear angle is $15^{\circ}$. The orthogonal rake angle of the tool is $0^{\circ}$ and ... strength is $500$ $\text{MPa}$. The cutting force is ___________________ $\text{N}$ (round off to the nearest integer).

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GATE Mechanical 2022 Set 2 | Question: 46
The best size wire is fitted in a groove of a metric screw such that the wire touches the flanks of the thread on the pitch line as shown in the figure. The pitch $(p)$ and included angle of the thread are $4$ $\text{mm}$ and $60^{\circ}$, respectively. The diameter of the best size wire is _______________ $\text{mm}$ (round off to $2$ decimal places).

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GATE Mechanical 2022 Set 2 | Question: 47
In a direct current arc welding process, the power source has an open circuit voltage of $100\: V$ and short circuit current of $1000 \:A$. Assume a linear relationship between voltage and current. The arc voltage $(V)$ varies with the ... is in $\text{mm}$. The maximum available arc power during the process is ________________ $\text{kVA}$ (in integer).

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GATE Mechanical 2022 Set 2 | Question: 48
A cylindrical billet of $100$ $\text{mm}$ diameter and $100$ $\text{mm}$ length is extruded by a direct extrusion process to produce a bar of $L$-section. The cross sectional dimensions of this $L$-section bar are shown in the ... $\text{kN}$ (round off to one decimal place).

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GATE Mechanical 2022 Set 2 | Question: 49
A project consists of five activities $\text{(A, B, C, D and E)}$. The duration of each activity follows beta distribution. The three time estimates (in weeks) of each activity and immediate predecessor$(s)$ are listed in the table. The expected time of the project completion is ... Pessimistic time A 4 5 6 None B 1 3 5 A C 1 2 3 A D 2 4 6 C E 3 4 5 B, D

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GATE Mechanical 2022 Set 2 | Question: 50
A rigid tank of volume of $8 \:m^{3}$ is being filled up with air from a pipeline connected through a valve. Initially the valve is closed and the tank is assumed to be completely evacuated. The air pressure and temperature ... temperature of the tank after the completion of the filling process is _______________ $K$ (round off to the nearest integer).

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GATE Mechanical 2022 Set 2 | Question: 51
At steady state, $500$ $\text{kg/s}$ of steam enters a turbine with specific enthalpy equal to $3500$ $\text{kJ/kg}$ and specific entropy equal to $6.5$ ${kJ \cdot kg^{-1} \cdot K^{-1}}$. It expands reversibly in the turbine to the ... $\text{MW}$ (in integer).

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GATE Mechanical 2022 Set 2 | Question: 52
A uniform wooden rod (specific gravity = $0.6$, diameter = $4$ $\text{cm}$ and length = $8\:m$) is immersed in the water and is hinged without friction at point $A$ on the waterline as shown in the figure. A solid spherical ball made of lead ( ... $\pi = 3.14$. Radius of the ball is _____________ $\text{cm}$ (round off to $2$ decimal places).

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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).

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GATE Mechanical 2022 Set 2 | Question: 54
Saturated vapor at $200\: ^{\circ}C$ condenses to saturated liquid at the rate of $150$ $\text{kg/s}$ on the shell side of a heat exchanger (enthalpy of condensation $h_{fg} = 2400$ $\text{kJ/kg}$ ... heat exchanger is $0.9$, then the mass flow rate of the fluid in the tube side is ____________ $\text{kg/s}$ (in integer).

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GATE Mechanical 2022 Set 2 | Question: 55
Consider a hydrodynamically and thermally fully-developed, steady fluid flow of $1$ $\text{kg/s}$ in a uniformly heated pipe with diameter of $0.1\: m$ and length of $40 \:m$ ... of the pipe diameter. The pipe surface temperature at the exit is _______________ $^{\circ}C$ (round off to the nearest integer).

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