Questions by go_editor / GO Mechanical

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GATE2020-ME-1: 21
A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of $10\:\text{grams}$, attached to four points on the $100\: mm$ radius circle shown in the figure. The rotor is driven bt a motor at uniform angular speed of ... gets detached then the magnitude of the resultant unbalance force on the rotor is ________$N$ (rounded off to $2$ decimal places).

A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of $10\:\text{grams}$, attached to four points on the $100\: mm$ radius circle shown ...

asked Feb 19, 2020

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GATE2020-ME-1: 22
A sheet metal with a stock hardness of $250\: HRC$ has to be sheared using a punch and a die having a clearance of $\text{1 mm}$ between them. If the stock hardness of the sheet metal increases to $400\: HRC$, the clearance between the punch and the die should be _________ $mm.$

A sheet metal with a stock hardness of $250\: HRC$ has to be sheared using a punch and a die having a clearance of $\text{1 mm}$ between them. If the stock hardness of th...

asked Feb 19, 2020

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GATE2020-ME-1: 23
A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one woman will be selected is _______(round off to $2$ decimal places).

A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability...

asked Feb 19, 2020

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GATE2020-ME-1: 24
The compressor of a gas turbine plant, operating on an ideal intercooled Brayton cycle, accomplishes an overall compression ratio of $6$ in a two-stage compression process. Intercooling is used to cool the air coming out from the first stage to the ... gas are constant, the intercooling pressure for minimum compressor work is __________ $kPa$ (rounded off to $2$ decimal places).

The compressor of a gas turbine plant, operating on an ideal intercooled Brayton cycle, accomplishes an overall compression ratio of $6$ in a two-stage compression proces...

asked Feb 19, 2020

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GATE2020-ME-1: 25
In a concentric tube counter-flow heat exchanger, hot oil enters at $102^{\circ}C$ and leaves at $65^{\circ}C$. Cold water enters at $25^{\circ}C$ and leaves at $42^{\circ}C$. The log mean temperature difference $(LMTD)$ is ________ $^{\circ}C$ (round off to one decimal place).

In a concentric tube counter-flow heat exchanger, hot oil enters at $102^{\circ}C$ and leaves at $65^{\circ}C$. Cold water enters at $25^{\circ}C$ and leaves at $42^{\cir...

asked Feb 19, 2020

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GATE2020-ME-1: 26
The evaluation of the definite integral $\int ^{1.4}_{ – 1}x \mid x \mid dx$ by using Simpson’s $1/3^{rd}$ (one - third) rule with step size $h=0.6$ yields $0.914$ $1.248$ $0.581$ $0.592$

The evaluation of the definite integral $\int ^{1.4}_{ – 1}x \mid x \mid dx$ by using Simpson’s $1/3^{rd}$ (one - third) rule with step size $h=0.6$ yields$0.914$$1.2...

asked Feb 19, 2020

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GATE2020-ME-1: 27
A vector field is defined as ... shell formed by two concentric spheres with origin as the center, and internal and external radii of $1$ and $2$, respectively, is $0$ $2\pi$ $4\pi$ $8\pi$

A vector field is defined as $$\overrightarrow{f}\left ( x,y,z \right )=\dfrac{x}{\left [ x^{2}+y^{2}+z^{2} \right ]^{\frac{3}{2}}}\widehat{i}\:+\:\dfrac{y}{\left [ x^{2}...

asked Feb 19, 2020

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GATE2020-ME-1: 28
Bars of square and circular cross-section with $0.5\: m$ length are made of a material with shear strength of $20\: MPa$. The square bar cross-section dimension is $4\:cm \times$ $4\:cm$ and the cylindrical bar cross- ... the applied load as per maximum shear stress theory? Tensile and compressive load specimens Torsional load specimen Bending load specimen None of the specimens

Bars of square and circular cross-section with $0.5\: m$ length are made of a material with shear strength of $20\: MPa$. The square bar cross-section dimension is $4\:cm...

asked Feb 19, 2020

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GATE2020-ME-1: 29
The $2$ kg block shown in the figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness $5\: N/m$. The cord hinged at $\text{O}$ is initially unstretched and always remains elastic. The block is given a velocity $v$ ... $0.4\: m$ is $0.83$ $1.07$ $1.36$ $1.50$

The $2$ kg block shown in the figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness $5\: N/m$. ...

asked Feb 19, 2020

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GATE2020-ME-1: 30
The truss shown in the figure has four members of length $\text{l}$ and flexural rigidity $\text{EI}$, and one member of length $l\sqrt{2}$ and flexural rigidity $\text{4EI}$. The truss is loaded by a pair of forces of magnitude $\text{P}$ ... $\dfrac{2\pi ^{2}EI}{l^{2}} \\$ $\dfrac{\pi ^{2}EI}{2l^{2}}$

The truss shown in the figure has four members of length $\text{l}$ and flexural rigidity $\text{EI}$, and one member of length $l\sqrt{2}$ and flexural rigidity $\text{4...

asked Feb 19, 2020

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GATE2020-ME-1: 31
A rigid mass-less rod of length $L$ is connected to a disc (pulley) of mass $m$ and radius $r = L/4$ through a friction-less revolute joint. The other end of that rod is attached to a wall through a friction-less hinge. A spring of stiffness $2k$ is attached to the rod at its mid-span ... $\sqrt{3}\sqrt{\dfrac{k}{m}} \\$ $\sqrt{\dfrac{k}{m}}$

A rigid mass-less rod of length $L$ is connected to a disc (pulley) of mass $m$ and radius $r = L/4$ through a friction-less revolute joint. The other end of that rod is ...

asked Feb 19, 2020

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GATE2020-ME-1: 32
A strip of thickness $40\:mm$ is to be rolled to a thickness of $20\:mm$ using a two-high mill having rolls of diameter $200\:mm$. Coefficient of friction and arc length in $mm$, respectively are $0.45\:\text{and}\:38.84$ $0.39\:\text{and}\:38.84$ $0.39\:\text{and}\:44.72$ $0.45\:\text{and}\:44.72$

A strip of thickness $40\:mm$ is to be rolled to a thickness of $20\:mm$ using a two-high mill having rolls of diameter $200\:mm$. Coefficient of friction and arc length ...

asked Feb 19, 2020

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GATE2020-ME-1: 33
For an assembly line, the production rate was $4$ pieces per hour and the average processing time was $60$ minutes. The $\text{WIP}$ inventory was calculated. Now, the production rate is kept the same, and the average processing time is brought down by $30$ percent. As ... , the $\text{WIP}$ inventory decreases by $25\%$ increases by $25\%$ decreases by $30\%$ increases by $30\%$

For an assembly line, the production rate was $4$ pieces per hour and the average processing time was $60$ minutes. The $\text{WIP}$ inventory was calculated. Now, the pr...

asked Feb 19, 2020

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GATE2020-ME-1: 34
A small metal bead $(\text{radius}\: 0.5\: mm)$, initially at $100^{\circ}C$ , when placed in a stream of fluid at $20^{\circ}C$ , attains a temperature of $28^{\circ}C$ in $4.35$ ... heat transfer coefficient $(in\:W/m^{2}.K)$ between the metal bead and the fluid stream is $283.3$ $299.8$ $149.9$ $449.7$

A small metal bead $(\text{radius}\: 0.5\: mm)$, initially at $100^{\circ}C$ , when placed in a stream of fluid at $20^{\circ}C$ , attains a temperature of $28^{\circ}C$ ...

asked Feb 19, 2020

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GATE2020-ME-1: 35
Consider two exponentially distributed random variables $\text{X and Y}$, both having a mean of $0.50$. Let $Z=X+Y$ and $r$ be the correlation between $\text{X and Y}$.If the variance of $Z$ equals $0$, then the value of $r$ is __________ (roundoff to $2$ decimal places).

Consider two exponentially distributed random variables $\text{X and Y}$, both having a mean of $0.50$. Let $Z=X+Y$ and $r$ be the correlation between $\text{X and Y}$.If...

asked Feb 19, 2020

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GATE2020-ME-1: 36
An analytic function of a complex variable $z=x + iy \left ( i=\sqrt{-1} \right )$ is defined as $f\left ( z \right )=x^{2}-y^{2}+i\psi \left ( x,y \right ),$ where $\psi \left ( x,y \right )$ is a real function. The value of the imaginary part of $f(z)$ at $z=\left ( 1+i \right )$ is __________ (round off to $2$ decimal places).

An analytic function of a complex variable $z=x + iy \left ( i=\sqrt{-1} \right )$ is defined as$$f\left ( z \right )=x^{2}-y^{2}+i\psi \left ( x,y \right ),$$where $\psi...

asked Feb 19, 2020

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GATE2020-ME-1: 37
In a disc-type axial clutch, the frictional contact takes place within an annular region with outer and inner diameters $250\:mm$ and $50\:mm$, respectively. An axial force $F_{1}$ is needed to transmit a torque by a new clutch. However, to transmit the same ... coefficient of friction does not change, then the ratio $F_{1}/F_{2}$ is _________ (round off to $2$ decimal places).

In a disc-type axial clutch, the frictional contact takes place within an annular region with outer and inner diameters $250\:mm$ and $50\:mm$, respectively. An axial for...

asked Feb 19, 2020

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GATE2020-ME-1: 38
A cam with a translating flat-face follower is desired to have the follower motion $y\left ( \theta \right )=4\left [ 2\pi \theta -\theta ^{2} \right ],\:\:\:0\leq \theta \leq 2\pi .$ Contact stress considerations dictate that the radius ... should not be less than $40\:mm$ anywhere. The minimum permissible base circle radius is _________$mm$ (round off to one decimal place).

A cam with a translating flat-face follower is desired to have the follower motion$$y\left ( \theta \right )=4\left [ 2\pi \theta -\theta ^{2} \right ],\:\:\:0\leq \thet...

asked Feb 19, 2020

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GATE2020-ME-1: 39
A rectangular steel bar of length $500\: mm$, width $100\: mm$, and thickness $15\: mm$ is cantilevered to a $200\: mm$ steel channel using $4$ bolts, as shown For an external load of $10\: kN$ applied at the tip of the steel bar, the resultant shear load on the bolt at $B$, is _______$kN$ (round off to one decimal place).

A rectangular steel bar of length $500\: mm$, width $100\: mm$, and thickness $15\: mm$ is cantilevered to a $200\: mm$ steel channel using $4$ bolts, as shownFor an exte...

asked Feb 19, 2020

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GATE2020-ME-1: 40
The barrier shown between two water tanks of unit width $(1\: m)$ into the plane of the screen in modeled as a cantilever. Taking the density of water as $1000\:kg/m^{3}$ , and the acceleration due to gravity as $10\:m/s^{2}$ , the maximum absolute bending moment developed in the cantilever is _________$kN\cdot m$ (round off to the nearest integer).

The barrier shown between two water tanks of unit width $(1\: m)$ into the plane of the screen in modeled as a cantilever.Taking the density of water as $1000\:kg/m^{3}$ ...

asked Feb 19, 2020

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GATE2020-ME-1: 41
The magnitude of reaction force at joint $C$ of the hinge-beam shown in the figure is __________$kN$ (round off to $2$ decimal places).

The magnitude of reaction force at joint $C$ of the hinge-beam shown in the figure is __________$kN$ (round off to $2$ decimal places).

asked Feb 19, 2020

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GATE2020-ME-1: 42
A slot of $25\:mm\times 25\:mm$ is to be milled in a workpiece of $300\: mm$ length using a side and face milling cutter of diameter $100\: mm$, width $25\: mm$ and having $20$ teeth.For a depth of cut $5\: mm$ ... and approach and over travel distance of $5\: mm$ each, the time required for milling the slot is ________ minutes (round off to one decimal place).

A slot of $25\:mm\times 25\:mm$ is to be milled in a workpiece of $300\: mm$ length using a side and face milling cutter of diameter $100\: mm$, width $25\: mm$ and havin...

asked Feb 19, 2020

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GATE2020-ME-1: 43
The following data applies to basic shaft system: tolerance for hole$ = 0.002\: mm$, tolerance for shaft$ = 0.001\: mm$, allowance $= 0.003\: mm$, basic size $= 50\: mm$. The maximum hole size is _______ $mm$ (round off to $3$ decimal places).

The following data applies to basic shaft system:tolerance for hole$ = 0.002\: mm$,tolerance for shaft$ = 0.001\: mm$,allowance $= 0.003\: mm$,basic size $= 50\: mm$.The ...

asked Feb 19, 2020

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GATE2020-ME-1: 44
A steel part with surface area of $125\:cm^{2}$ is to be chrome coated through an electroplating process using chromium acid sulphate as an electrolyte. An increasing current is applied to the part according to the following current time relation: $I=12+0.2t$ ... $\mu m$ (round off to one decimal place).

A steel part with surface area of $125\:cm^{2}$ is to be chrome coated through an electroplating process using chromium acid sulphate as an electrolyte. An increasing cur...

asked Feb 19, 2020

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GATE2020-ME-1: 45
In a turning process using orthogonal tool geometry, a chip length of $100\: mm$ is obtained for an uncut chip length of $250\: mm$. The cutting conditions are: cutting speed $= 30\: m/min$, rake angle $ = 20^{\circ}$. The shear plane angle is _______ degrees (round off to one decimal place).

In a turning process using orthogonal tool geometry, a chip length of $100\: mm$ is obtained for an uncut chip length of $250\: mm$. The cutting conditions are: cutting s...

asked Feb 19, 2020

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GATE2020-ME-1: 46
The thickness of a steel plate with material strength coefficient of $210\: MPa$, has to be reduced from $20\: mm$ to $15\: mm$ in a single pass in a two-high rolling mill with a roll radius of $450\: mm$ and rolling velocity of $28\: m/min$. If the ... ). Note: $\text{Average Flow Stress = Material Strength Coefficient}\times \dfrac{\left (\text{True Strain} \right )^{n}}{(1+n)}$

The thickness of a steel plate with material strength coefficient of $210\: MPa$, has to be reduced from $20\: mm$ to $15\: mm$ in a single pass in a two-high rolling mil...

asked Feb 19, 2020

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GATE2020-ME-1: 47
Two business owners Shveta and Ashok run their business in two different states. Each of them, independent of the other, produces two products $A$ and $B$, sells them at $Rs.\:2,000$ per kg and $Rs.\:3,000$ per kg, respectively, and uses ... value of the difference in daily (optimal) revenue of Shveta and Ashok is _________ thousand Rupees (round off to $2$ decimal places).

Two business owners Shveta and Ashok run their business in two different states. Each of them, independent of the other, produces two products $A$ and $B$, sells them at ...

asked Feb 19, 2020

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GATE2020-ME-1: 48
$\textbf{Consider two cases as below.}$ $\textbf{Case 1:}$ A company buys $1000$ pieces per year of a certain part from vendor $'X'.$ The changeover time is $2$ hours and the price is $Rs.\: 10$ per piece. The holding cost rate per part is $10\%$ ... reduction in the annual cost of $\text{Case 2}$, as compared to $\text{Case 1}$ is __________ (round off to $2$ decimal places).

$\textbf{Consider two cases as below.}$$\textbf{Case 1:}$ A company buys $1000$ pieces per year of a certain part from vendor $’X’.$The changeover time is $2$ hours a...

asked Feb 19, 2020

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GATE2020-ME-1: 49
Consider steady, viscous, fully developed flow of a fluid through a circular pipe of internal diameter $\text{D}$. We know that the velocity profile forms a paraboloid about the pipe centre line, given by: $V=-C\left(r^{2}-\dfrac{D^{2}}{4}\right) m/s$ ... the control surface $\text{A-B}$, as shown in the figure, is proportional to $D^{n}$. The value of $n$ is ________.

Consider steady, viscous, fully developed flow of a fluid through a circular pipe of internal diameter $\text{D}$. We know that the velocity profile forms a paraboloid ab...

asked Feb 19, 2020

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GATE2020-ME-1: 50
Air discharges steadily through a horizontal nozzle and impinges on a stationary vertical plate as shown in figure. The inlet and outlet areas of the nozzle are $0.1\:m^{2}\:\text{and}\:0.02\:m^{2}$ ... is $0.36\:kPa$, the gauge pressure at point $O$ on the plate is __________ $kPa$ (round off to two decimal places).

Air discharges steadily through a horizontal nozzle and impinges on a stationary vertical plate as shown in figure. The inlet and outlet areas of the nozzle are $...

asked Feb 19, 2020

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GATE2020-ME-1: 51
Air (ideal gas) enters a perfectly insulated compressor at a temperature of $310\: K$. The pressure ratio of the compressor is $6$. Specific heat at constant pressure for air is $1005\: J/kg . K$ and ratio of specific heats at constant pressure ... difference in enthalpies of air between the exit and the inlet of the compressor is _________ $kJ/kg$ (round off to nearest integer).

Air (ideal gas) enters a perfectly insulated compressor at a temperature of $310\: K$. The pressure ratio of the compressor is $6$. Specific heat at constant pressure for...

asked Feb 19, 2020

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GATE2020-ME-1: 52
One kg of air, initially at a temperature of $127^{\circ}C$ , expands reversibly at a constant pressure until the volume is doubled. If the gas constant of air is $287\: J/kg.K$, the magnitude of work transfer is ________ $kJ$ (round off to $2$ decimal places).

One kg of air, initially at a temperature of $127^{\circ}C$ , expands reversibly at a constant pressure until the volume is doubled. If the gas constant of air is $287\: ...

asked Feb 19, 2020

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GATE2020-ME-1: 53
For an ideal Rankine cycle operating between pressures of $30$ bar and $0.04$ bar,the work output from the turbine is $903\: kJ/kg$ and the work input to the feed pump is $3\: kJ/kg$. The specific steam consumption is _________ $kg/kW.h$ round off to $2$ decimal places).

For an ideal Rankine cycle operating between pressures of $30$ bar and $0.04$ bar,the work output from the turbine is $903\: kJ/kg$ and the work input to the feed pump is...

asked Feb 19, 2020

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GATE2020-ME-1: 54
For a Kaplan (axial flow) turbine, the outlet blade velocity diagram at a section is shown in the figure. The diameter at this section is $3\:m$.The hub and tip diameters of the blade are $2\:m$ and $4\:m$, respectively. The water volume flow ... rotational speed of the turbine is $300\:rpm$. The blade outlet angle $\beta$ is ________ degrees (round off to one decimal place).

For a Kaplan (axial flow) turbine, the outlet blade velocity diagram at a section is shown in the figure. The diameter at this section is $3\:m$.The hub and tip diam...

asked Feb 19, 2020

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GATE2020-ME-1: 55
The indicated power developed by an engine with compression ratio of $8$, is calculated using an air-standard Otto cycle (constant properties). The rate of heat addition is $10\: kW$ ... of the engine is $80$ percent. The brake power output of the engine is _________$kW$ (round off to one decimal place).

The indicated power developed by an engine with compression ratio of $8$, is calculated using an air-standard Otto cycle (constant properties). The rate of heat addition ...

asked Feb 19, 2020