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GATE Mechanical 2021 Set 1 | Question: 24
The figure shows an arrangement of a heavy propeller shaft in a ship. The combined polar mass moment of inertia of the propeller and the shaft is $\text{100 kg.m}^{2}$. The propeller rotates at $\omega =12$ $\text{rad/s}$. The ... moment generated on the shaft due to the motion described is ________ $\text{N.m}(\textit{round off to the nearest integer}$).

The figure shows an arrangement of a heavy propeller shaft in a ship. The combined polar mass moment of inertia of the propeller and the shaft is $\text{100 kg.m}^{2}$. T...

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GATE Mechanical 2021 Set 1 | Question: 25
Consider a single degree of freedom system comprising a mass $\text{M}$, supported on a spring and a dashpot as shown in the figure. If the amplitude of the free vibration response reduces from $\text{8 mm}$ to $\text{1.5 mm}$ in $3$ cycles, the damping ratio of the system is ______________ ($\textit{round off to three decimal places}$).

Consider a single degree of freedom system comprising a mass $\text{M}$, supported on a spring and a dashpot as shown in the figure.If the amplitude of the free vibration...

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GATE Mechanical 2021 Set 1 | Question: 28
A set of jobs $\text{A, B, C, D, E, F, G, H}$ arrive at time $t= 0$ for processing on turning and grinding machines. Each job needs to be processed in sequence first on the turning machine and second on the grinding machine, and the grinding must occur immediately after turning. The ... $\text{G-E-D-F-H-C-A-B}$ $\text{B-G-C-H-F-D-E-A}$

A set of jobs $\text{A, B, C, D, E, F, G, H}$ arrive at time $t= 0$ for processing on turning and grinding machines. Each job needs to be processed in sequence first on ...

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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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GATE Mechanical 2021 Set 1 | Question: 30
Consider a two degree of freedom system as shown in the figure, where $\text{PQ}$ is a rigid uniform rod of length, $\text{b}$ and mass, $\text{m}$. Assume that the spring deflects only horizontally and force $\text{F}$ is applied horizontally at $\text{Q}$. For ...

Consider a two degree of freedom system as shown in the figure, where $\text{PQ}$ is a rigid uniform rod of length, $\text{b}$ and mass, $\text{m}$.Assume that the spring...

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GATE Mechanical 2021 Set 1 | Question: 31
A right solid circular cone standing on its base on a horizontal surface is of height $\text{H}$ and base radius $\text{R}$. The cone is made of a material with specific weight $\text{w}$ and elastic modulus $\text{E}$. The vertical deflection at the mid-height ... $\frac{\text{wH}^{2}}{6E}$ $\frac{\text{wRH}}{8E}$ $\frac{\text{wRH}}{6E}$

A right solid circular cone standing on its base on a horizontal surface is of height $\text{H}$ and base radius $\text{R}$. The cone is made of a mater...

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GATE Mechanical 2021 Set 1 | Question: 32
A tappet valve mechanism in an $\text{IC}$ engine comprises a rocker arm $\text{ABC}$ that is hinged at $\text{B}$ as shown in the figure. The rocker is assumed rigid and it oscillates about the hinge $\text{B}$. The mass moment of inertia of ... at a speed of ____________ $\text{rpm} (\textit{round off to the nearest integer}$). $496$ $4739$ $790$ $2369$

A tappet valve mechanism in an $\text{IC}$ engine comprises a rocker arm $\text{ABC}$ that is hinged at $\text{B}$ as shown in the figure. The rocker is assumed rigid and...

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GATE Mechanical 2021 Set 1 | Question: 35
Activities $\text{A, B, C}$ and $\text{D}$ form the critical path for a project with a $\text{PERT}$ network. The means and variances of the activity duration for each activity are given below. All activity durations follow the Gaussian (normal) ... $\text{Note}$: Probability is a number between $0$ and $1$).

Activities $\text{A, B, C}$ and $\text{D}$ form the critical path for a project with a $\text{PERT}$ network. The means and variances of the activity duration for each ac...

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GATE Mechanical 2021 Set 1 | Question: 36
A true centrifugal casting operation needs to be performed horizontally to make copper tube sections with outer diameter of $\text{250 mm}$ and inner diameter of $\text{230 mm}$ ... the tube, the rotational speed required is _________ $\text{rpm}$ ($\textit{round off to the nearest integer}$).

A true centrifugal casting operation needs to be performed horizontally to make copper tube sections with outer diameter of $\text{250 mm}$ and inner diameter of $\text{2...

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GATE Mechanical 2021 Set 1 | Question: 37
The resistance spot welding of two $\text{1.55 mm}$ thick metal sheets is performed using welding current of $\text{10000 A}$ for $\text{0.25 s}$. The contact resistance at the interface of the metal sheets is $0.0001\; \Omega$ . The ... $\%$ ($\textit{round off to one decimal place}$).

The resistance spot welding of two $\text{1.55 mm}$ thick metal sheets is performed using welding current of $\text{10000 A}$ for $\text{0.25 s}$. The contact resistance ...

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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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GATE Mechanical 2021 Set 1 | Question: 39
In a grinding operation of a metal, specific energy consumption is $15 \text{ J/mm}^{3}$. If a grinding wheel with a diameter of $\text{200 mm}$ is rotating at $\text{3000 rpm}$ to obtain a material removal rate of $6000\text{ mm$^{3}$/min}$, then the tangential force on the wheel is _______ $\text{N}$ ($\textit{round off to two decimal places}$).

In a grinding operation of a metal, specific energy consumption is $15 \text{ J/mm}^{3}$. If a grinding wheel with a diameter of $\text{200 mm}$ is rotating at $\text{300...

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GATE Mechanical 2021 Set 1 | Question: 40
A $\text{200 mm}$ wide plate having a thickness of $\text{20 mm}$ is fed through a rolling mill with two rolls. The radius of each roll is $\text{300 mm}$. The plate thickness is to be reduced to $\text{18 mm}$ in one pass ... to permit the rolling operation then the roll force will be _________ $\text{kN}$ ($\textit{round off to the nearest integer}$).

A $\text{200 mm}$ wide plate having a thickness of $\text{20 mm}$ is fed through a rolling mill with two rolls. The radius of each roll is $\text{300 mm}$. The plate thic...

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GATE Mechanical 2021 Set 1 | Question: 41
The $\text{XY}$ table of a $\text{NC}$ machine tool is to move from $P(1,1)$ to $Q(51,1)$; all coordinates are in $\text{mm}$. The pitch of the $\text{NC}$ drive leadscrew is $\text{1 mm}$. If the backlash between the leadscrew and the ... of the table on moving from $\text{P}$ to $\text{Q}$ is ______ $\text{mm}$ ($\textit{round off to two decimal places}$)

The $\text{XY}$ table of a $\text{NC}$ machine tool is to move from $P(1,1)$ to $Q(51,1)$; all coordinates are in $\text{mm}$. The pitch of the $\text{NC}$ drive leadscre...

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GATE Mechanical 2021 Set 1 | Question: 42
Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of $12$ jobs/hour. The process time of the workstation is exponentially distributed with a mean of $4$ minutes. The expected ... at the workstation at any given point of time is _______ ($\textit{round off to the nearest integer}$).

Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of $12$ jobs/hour. The process time of the worksta...

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GATE Mechanical 2021 Set 1 | Question: 43
An uninsulated cylindrical wire of radius $\text{1.0 mm}$ produces electric heating at the rate of $\text{5.0 W/m}$. The temperature of the surface of the wire is $75\;^{\circ}C$ when placed in air at $25\;^{\circ}C$. When the wire is ... Wire. The thermal conductivity of $\text{PVC}$ is ______ $\text{W/m.K}$ ($\textit{round off to two decimal places}$).

An uninsulated cylindrical wire of radius $\text{1.0 mm}$ produces electric heating at the rate of $\text{5.0 W/m}$. The temperature of the surface of the wire is $75\;^{...

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GATE Mechanical 2021 Set 1 | Question: 44
A solid sphere of radius $\text{10 mm}$ is placed at the centroid of a hollow cubical enclosure of side length $\text{30 mm}$. The outer surface of the sphere is denoted by $1$ and the inner surface of the cube is denoted by $2$. The view factor $F_{22}$ for radiation heat transfer is ______ ($\textit{rounded off to two decimal places}$).

A solid sphere of radius $\text{10 mm}$ is placed at the centroid of a hollow cubical enclosure of side length $\text{30 mm}$. The outer surface of the sphere is denoted ...

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GATE Mechanical 2021 Set 1 | Question: 45
Consider a steam power plant operating on an ideal reheat Rankine cycle. The work input to the pump is $\text{20 kJ/kg}$. The work output from the high pressure turbine is $\text{750 kJ/kg}$. The work output from the low pressure turbine is ... of steam at the exit of the low pressure turbine is ______ $\%$ ($\textit{round off to the nearest integer}$).

Consider a steam power plant operating on an ideal reheat Rankine cycle. The work input to the pump is $\text{20 kJ/kg}$. The work output from the high pressure turbine i...

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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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GATE Mechanical 2021 Set 1 | Question: 47
A cylindrical jet of water (density = $1000 \text{ kg/m}^{3}$ ... jet, then the velocity of the incoming jet is ___________________ $\text{m/s} (\textit{round off to one decimal place}$).

A cylindrical jet of water (density = $1000 \text{ kg/m}^{3}$) impinges at the center of a flat, circular plate and spreads radially outwards, as shown in the figure. The...

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GATE Mechanical 2021 Set 1 | Question: 48
A single jet Pelton wheel operates at $\text{300 rpm}$. The mean diameter of the wheel is $\text{2 m}$. Operating head and dimensions of jet are such that water comes out of the jet with a velocity of $\text{40 m/s}$ and flow rate ... all losses, the power developed by the Pelton wheel is _______ $\text{MW}$ ($\textit{round off to two decimal places}$).

A single jet Pelton wheel operates at $\text{300 rpm}$. The mean diameter of the wheel is $\text{2 m}$. Operating head and dimensions of jet are such that water comes out...

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GATE Mechanical 2021 Set 1 | Question: 49
An air-conditioning system provides a continuous flow of air to a room using an intake duct and an exit duct, as shown in the figure. To maintain the quality of the indoor air, the intake duct supplies a mixture of fresh air with a cold air ... of heat gain by the air from the room is _________________ $\text{kW}(\textit{round off to two decimal places}$).

An air-conditioning system provides a continuous flow of air to a room using an intake duct and an exit duct, as shown in the figure. To maintain the quality of the indoo...

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GATE Mechanical 2021 Set 1 | Question: 50
Two smooth identical spheres each of radius $\text{125 mm}$ and weight $\text{100 N}$ rest in a horizontal channel having vertical walls. The distance between vertical walls of the channel is $\text{400 mm}$. The reaction at the point of contact between two spheres is ___________________ $\text{N} (\textit{round off to one decimal place}$).

Two smooth identical spheres each of radius $\text{125 mm}$ and weight $\text{100 N}$ rest in a horizontal channel having vertical walls. The distance between vertical wa...

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GATE Mechanical 2021 Set 1 | Question: 51
An overhanging beam $\text{PQR}$ is subjected to uniformly distributed load $\text{20 kN/m}$ as shown in the figure. The maximum bending stree developed in the beam is ___________________ $\text{MPa} (\textit{round off to one decimal place}$).

An overhanging beam $\text{PQR}$ is subjected to uniformly distributed load $\text{20 kN/m}$ as shown in the figure.The maximum bending stree developed in the beam is ___...

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GATE Mechanical 2021 Set 1 | Question: 52
The Whitworth quick return mechanism is shown in the figure with link lengths as follows: $\text{OP = 300 mm, OA = 150 mm, AR = 160 mm, RS = 450 mm}$. The quick return ratio for the mechanism is ____________________ ($\textit{round off to one decimal place}$).

The Whitworth quick return mechanism is shown in the figure with link lengths as follows: $\text{OP = 300 mm, OA = 150 mm, AR = 160 mm, RS = 450 mm}$.The quick return rat...

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GATE Mechanical 2021 Set 1 | Question: 53
A short shoe drum (radius $\text{260 mm}$) brake is shown in the figure. A force of $\text{1 kN}$ is applied to the lever. The coefficient of friction is $0.4$. The magnitude of the torque applied by the brake is ____________________ $\text{N.m}(\textit{round off to one decimal place}$).

A short shoe drum (radius $\text{260 mm}$) brake is shown in the figure. A force of $\text{1 kN}$ is applied to the lever. The coefficient of friction is $0.4$.The magnit...

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GATE Mechanical 2021 Set 1 | Question: 54
A machine part in the form of cantilever beam is subjected to fluctuating load as shown in the figure The load varies from $\text{800 N}$ to $\text{1600 N}$. The modified endurance. yield and ultimate strengths of the ... factor of safety of the beam using modified Goodman criterion is ____________________ ($\textit{round off to one decimal place}$).

A machine part in the form of cantilever beam is subjected to fluctuating load as shown in the figure The load varies from $\text{800 N}$ to $\text{1600 N}$. The modified...

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GATE Mechanical 2021 Set 1 | Question: 55
A cantilever beam of rectangular cross-section is welded to a support by means of two filled welds as shown in figure. A vertical load of $\text{2 kN}$ acts at free end of the beam. Considering that the allowable shear stress in weld ... minimum size (leg) of the weld required is _____________________ $\text{mm} (\textit{round off to one decimal place}$).

A cantilever beam of rectangular cross-section is welded to a support by means of two filled welds as shown in figure. A vertical load of $\text{2 kN}$ acts at free end o...

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GATE2020-ME-2: 11
Which one of the following statements about a phase diagram is INCORRECT? It indicates the temperature at which different phases start to melt Relative amount of different phases can be found under given equillibrium conditions It gives information on transformation rates Solid solubility limits are depicted by it

Which one of the following statements about a phase diagram is INCORRECT?It indicates the temperature at which different phases start to meltRelative amount of different ...

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GATE2020-ME-2: 12
The figure below shows a symbolic representation of the surface texture in a perpendicular lay orientation with indicative values (I through VI) marking the various specifications whose definitions are listed below. P: Maximum waviness Height (mm); Q: Maximum Roughness Height (mm); R: Minimum Roughness Height (mm) ... II-S, III-Q, IV-T, V-R, VI-P I-Q, II-U, III-R, IV-T, V-S, VI-P

The figure below shows a symbolic representation of the surface texture in a perpendicular lay orientation with indicative values (I through VI) marking the various speci...

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GATE2020-ME-2: 13
In Materials Requirement Planning, if the inventory holding cost is very high and the set up cost is zero, which one of the following lot sizing approaches should be used? Economic Order Quantity Lot-for-Lot Base Stock Level Fixed Period Quantity, for $2$ periods

In Materials Requirement Planning, if the inventory holding cost is very high and the set up cost is zero, which one of the following lot sizing approaches should be used...

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GATE2020-ME-2: 15
In the space above the mercury column in a barometer tube, the gauge pressure of the vapour is positive, but more than one atmosphere negative zero positive, but less than one atmosphere

In the space above the mercury column in a barometer tube, the gauge pressure of the vapour ispositive, but more than one atmospherenegativezeropositive, but less than on...

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GATE2020-ME-2: 18
The values of enthalpies at the stator inlet and rotor outlet of a hydraulic turbomachine stage are $h_1$ and $h_3$ respectively. The enthalpy at the stator outlet (or, rotor inlet) is $h_2$. The condition $(h_2-h_1)=(h_3-h_2)$ indicates that the degree of reaction of this stage is $\text{zero}$ $50 \%$ $75 \%$ $100 \%$

The values of enthalpies at the stator inlet and rotor outlet of a hydraulic turbomachine stage are $h_1$ and $h_3$ respectively. The enthalpy at the stator outlet (or, r...

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GATE2020-ME-2: 20
A beam of negligible mass is hinged at support $P$ and has a roller support $Q$ as shown in the figure. A point load of $1200 \: N$ is applied at point $R$. The magnitude of the reaction force at support $Q$ is _________ $N$.

A beam of negligible mass is hinged at support $P$ and has a roller support $Q$ as shown in the figure.A point load of $1200 \: N$ is applied at point $R$. The magnitude ...

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GATE2020-ME-2: 21
A machine member is subjected to fluctuating stress $\sigma = \sigma_0 \cos (8 \pi t)$. The endurance limit of the material is $350$ MPa. If the factor of safety used in the design is $3.5$ then the maximum allowable value of $\sigma_0$ is _______ MPa. (round off to $2$ decimal places)

A machine member is subjected to fluctuating stress $\sigma = \sigma_0 \cos (8 \pi t)$. The endurance limit of the material is $350$ MPa. If the factor of safety used in ...

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GATE2020-ME-2: 22
A bolt head has to be made at the end of a rod of diameter $d=12$ mm by localized forging (upsetting) operation. The length of the unsupported portion of the rod is $40$ mm. To avoid buckling of the rod, a closed forging operation has to be performed with a maximum die diameter of _______ mm.

A bolt head has to be made at the end of a rod of diameter $d=12$ mm by localized forging (upsetting) operation. The length of the unsupported portion of the rod is $40$ ...

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GATE2020-ME-2: 23
Consider the following network of activities, with each activity named $\textbf{A – L}$, illustrated in the nodes of the network. The number of hours required for each activity is shown alongside the nodes. The slack on the activity $\textbf{L}$, is _______ hours.

Consider the following network of activities, with each activity named $\textbf{A – L}$, illustrated in the nodes of the network.The number of hours required for each a...

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GATE2020-ME-2: 24
In a furnace, the inner and outer sides of the brick wall $(k_1=2.5 \: \text{W/m.k})$ are maintained at $1100 ^\circ C$ and $700 ^\circ C$, respectively as shown in figure. The brick wall is covered by an insulating material of thermal conductivity $k_2$. The ... composite walls is $2500 \: W/m^2$. The value of $k_2$ is _______ $\text{W/m.K}$ (round off to one decimal place)

In a furnace, the inner and outer sides of the brick wall $(k_1=2.5 \: \text{W/m.k})$ are maintained at $1100 ^\circ C$ and $700 ^\circ C$, respectively as shown in figur...

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GATE2020-ME-2: 25
If a reversed Carnot cycle operates between the temperature limits of $27^\circ C$ and $-3^\circ C$, then the ratio of the COP of a refrigerator to that of a heat pump (COP of refrigerator / COP of heat pump) based on the cycle is __________ (round off to $2$ decimal places).

If a reversed Carnot cycle operates between the temperature limits of $27^\circ C$ and $-3^\circ C$, then the ratio of the COP of a refrigerator to that of a heat pump (C...

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GATE2020-ME-2: 28
A cantilever of length $l$, and flexural rigidity $EI$, stiffened by a spring of stiffness $k$, is loaded by a transverse force $P$, as shown. The transverse deflection under the load is $\dfrac{Pl^3}{3EI} \begin{bmatrix} \dfrac{3EI}{3EI+2kl^3} \end{bmatrix}$ ... $\dfrac{Pl^3}{3EI} \begin{bmatrix} \dfrac{3EI}{3EI+kl^3} \end{bmatrix}$

A cantilever of length $l$, and flexural rigidity $EI$, stiffened by a spring of stiffness $k$, is loaded by a transverse force $P$, as shown.The transverse deflection un...

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