Recent questions tagged gateme-2020-set1 / GO Mechanical

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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 ...

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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 ...

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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...

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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 $28^{\circ}C$ ...

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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...

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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...

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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...

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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...

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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...

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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 $1000\:kg/m^{3}$ ...

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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).

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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...

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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 ...

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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...

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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...

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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...

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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 ...

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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...

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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...

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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 $...

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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...

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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\: ...

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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...

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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...

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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 ...

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