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GATE Mechanical 2021 Set 2 | Question: 16
The controlling force curves $\text{P, Q,}$ and $\text{R}$ for a spring controlled governor are shown in the figure, where $r_{1}$ and $r_{2}$ are any two radii of rotation. The characteristics shown by the curves are $\text{P}$ ... $\text{R}$ - Unstable $\text{P}$ - Stable; $\text{Q}$ - Unstable; $\text{R}$ - Isochronous

The controlling force curves $\text{P, Q,}$ and $\text{R}$ for a spring controlled governor are shown in the figure, where $r_{1}$ and $r_{2}$ are any two radii of rotati...

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GATE Mechanical 2021 Set 2 | Question: 17
The von Mises stress at a point in a body subjected to forces is proportional to the square root of the total strain energy per unit volume plastic strain energy per unit volume dilatational strain energy per unit volume distortional strain energy per unit volume

The von Mises stress at a point in a body subjected to forces is proportional to the square root of thetotal strain energy per unit volumeplastic strain energy per unit v...

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GATE Mechanical 2021 Set 2 | Question: 18
Value of $\int_{4}^{5.2} \ln x\: dx$ using Simpson’s one-third rule with interval size $0.3$ is $1.83$ $1.60$ $1.51$ $1.06$

Value of $\int_{4}^{5.2} \ln x\: dx$ using Simpson’s one-third rule with interval size $0.3$ is$1.83$$1.60$$1.51$$1.06$

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GATE Mechanical 2021 Set 2 | Question: 19
Value of $\left ( 1+i \right )^{8}$, where $i=\sqrt{-1}$, is equal to $4$ $16$ $4i$ $16i$

Value of $\left ( 1+i \right )^{8}$, where $i=\sqrt{-1}$, is equal to$4$$16$$4i$$16i$

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GATE Mechanical 2021 Set 2 | Question: 20
Consider adiabatic flow of air through a duct. At a given point in the duct, velocity of air is $\text{300 m/s}$, temperature is $\text{330 K}$ and pressure is $\text{180 kPa}$. Assume that the air behaves as a perfect gas with constant ... $\text{K} (\textit{round off to two decimal places}$).

Consider adiabatic flow of air through a duct. At a given point in the duct, velocity of air is $\text{300 m/s}$, temperature is $\text{330 K}$ and pressure is $\text{180...

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GATE Mechanical 2021 Set 2 | Question: 21
Consider an ideal vapour compression refrigeration cycle working on $\text{R-134a}$ refrigerant. The $\text{COP}$ of the cycle is $10$ and the refrigeration capacity is $\text{150 kJ/kg}$. The heat rejected by the refrigerant in the condenser is __________ $\text{kJ/kg} (\textit{round off to the nearest integer}$).

Consider an ideal vapour compression refrigeration cycle working on $\text{R-134a}$ refrigerant. The $\text{COP}$ of the cycle is $10$ and the refrigeration capacity is $...

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GATE Mechanical 2021 Set 2 | Question: 22
A rigid tank of volume $50 \text{ m}^{3}$ contains a pure substance as a saturated liquid vapour mixture at $\text{400 kPa}$. Of the total mass of the mixture, $20\%$ mass is liquid and $80\%$ ... $\text{kg } (\textit{round off to the nearest integer}$).

A rigid tank of volume $50 \text{ m}^{3}$ contains a pure substance as a saturated liquid vapour mixture at $\text{400 kPa}$. Of the total mass of the mixture, $20\%$ mas...

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GATE Mechanical 2021 Set 2 | Question: 23
An object is moving with a Mach number of $0.6$ in an ideal gas environment, which is at a temperature of $\text{350 K}$. The gas constant is $\text{320 J/kg.K}$ and ratio of specific heats is $1.3$. The speed of object is _________ $\text{m/s} (\textit{round off to the nearest integer}$).

An object is moving with a Mach number of $0.6$ in an ideal gas environment, which is at a temperature of $\text{350 K}$. The gas constant is $\text{320 J/kg.K}$ and rati...

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GATE Mechanical 2021 Set 2 | Question: 24
A column with one end fixed and one end free has a critical buckling load of $\text{100 N}$. For the same column, if the free end is replaced with a pinned end then the critical buckling load will be _______ $\text{N}\; (\textit{round off to the nearest integer}$).

A column with one end fixed and one end free has a critical buckling load of $\text{100 N}$. For the same column, if the free end is replaced with a pinned end then the c...

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GATE Mechanical 2021 Set 2 | Question: 25
A steel cubic block of side $\text{200 mm}$ is subjected to hydrostatic pressure of $\text{250 N/mm}^{2}$. The elastic modulus is $2 \times 10^{5}\:\text{N/mm}^{2}$ and Poisson ratio is $0.3$ for steel. The side of the block is reduced by _________ $\text{mm}\: (\textit{round off to two decimal places}$).

A steel cubic block of side $\text{200 mm}$ is subjected to hydrostatic pressure of $\text{250 N/mm}^{2}$. The elastic modulus is $2 \times 10^{5}\:\text{N/mm}^{2}$ and P...

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GATE Mechanical 2021 Set 2 | Question: 26
The value of $\int_{0}^{^{\pi }/_{2}}\int_{0}^{\cos\theta }r\sin\theta \:dr\:d\theta$ is $0$ $\frac{1}{6}$ $\frac{4}{3}$ $\pi$

The value of $\int_{0}^{^{\pi }/_{2}}\int_{0}^{\cos\theta }r\sin\theta \:dr\:d\theta$ is $0$$\frac{1}{6}$$\frac{4}{3}$$\pi$

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GATE Mechanical 2021 Set 2 | Question: 27
Let the superscript $\text{T}$ represent the transpose operation. Consider the function $f(x)=\frac{1}{2}x^TQx-r^Tx$, where $x$ and $r$ are $n \times 1$ vectors and $\text{Q}$ is a symmetric $n \times n$ matrix. The stationary point of $f(x)$ is $Q^{T}r$ $Q^{-1}r$ $\frac{r}{r^{T}r}$ $r$

Let the superscript $\text{T}$ represent the transpose operation. Consider the function $f(x)=\frac{1}{2}x^TQx-r^Tx$, where $x$ and $r$ are $n \times 1$ vectors and $\tex...

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GATE Mechanical 2021 Set 2 | Question: 28
Consider the following differential equation $\left ( 1+y \right )\frac{dy}{dx}=y.$ The solution of the equation that satisfies condition $y(1)=1$ is $2ye^{y}=e^{x}+e$ $y^{2}e^{y}=e^{x}$ $ye^{y}=e^{x}$ $\left ( 1+y \right )e^{y}=2e^{x}$

Consider the following differential equation$$\left ( 1+y \right )\frac{dy}{dx}=y.$$The solution of the equation that satisfies condition $y(1)=1$ is$2ye^{y}=e^{x}+e$$y^{...

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GATE Mechanical 2021 Set 2 | Question: 29
A factory produces $m (i= 1,2,\cdots, m)$ products, each of which requires processing on $n(j = 1,2,\cdots, n)$ workstations. Let $a_{ij}$ be the amount of processing time that one unit of the $i^{th}$ product requires on the $j^{th}$ workstation. Let the revenue ... $I_{it}=I_{i,t-1}+S_{it}-X_{it}\:\forall \:i,t$

A factory produces $m (i= 1,2,\cdots, m)$ products, each of which requires processing on $n(j = 1,2,\cdots, n)$ workstations. Let $a_{ij}$ be the amount of processing ti...

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GATE Mechanical 2021 Set 2 | Question: 30
Ambient pressure, temperature, and relative humidity at a location are $\text{101 kPa}$, $\text{300 K}$, and $60\%$, respectively. The saturation pressure of the water at $\text{300 K}$ is $\text{3.6 kPa}$. The specific humidity of ambient air is ____________________ $\text{g/kg}$ of dry air. $21.4$ $35.1$ $21.9$ $13.6$

Ambient pressure, temperature, and relative humidity at a location are $\text{101 kPa}$, $\text{300 K}$, and $60\%$, respectively. The saturation pressure of the water at...

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GATE Mechanical 2021 Set 2 | Question: 31
A plane frame $\text{PQR}$ (fixed at $\text{P}$ and free at $\text{R}$) is shown in the figure. Both members ($\text{PQ}$ and $\text{QR}$) have length, $\text{L}$, and flexural rigidity, $\text{EI}$. Neglecting the effect of axial stress and transverse shear, the ... , is $\frac{5FL^{3}}{3EI}$ $\frac{4FL^{3}}{3EI}$ $\frac{2FL^{3}}{3EI}$ $\frac{FL^{3}}{3EI}$

A plane frame $\text{PQR}$ (fixed at $\text{P}$ and free at $\text{R}$) is shown in the figure. Both members ($\text{PQ}$ and $\text{QR}$) have length, $\text{L}$, and fl...

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GATE Mechanical 2021 Set 2 | Question: 32
A power transmission mechanism consists of a belt drive and a gear train as shown in the figure. Diameters of pulleys of belt drive and number of teeth $\text{(T)}$ on the gears $2$ to $7$ are indicated in the figure. The speed and ... $\text{255.68 rpm}$; anticlockwise $\text{575.28 rpm}$; clockwise $\text{575.28 rpm}$; anticlockwise

A power transmission mechanism consists of a belt drive and a gear train as shown in the figure.Diameters of pulleys of belt drive and number of teeth $\text{(T)}$ on the...

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GATE Mechanical 2021 Set 2 | Question: 33
A machine of mass $\text{100 kg}$ is subjected to an external harmonic force with a frequency of $\text{40 rad/s}$. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination ... the force transmitted to the foundation. $1-3-4-2$ $1-3-2-4$ $4-3-1-2$ $3-1-2-4$

A machine of mass $\text{100 kg}$ is subjected to an external harmonic force with a frequency of $\text{40 rad/s}$. The designer decides to mount the machine on an isolat...

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GATE Mechanical 2021 Set 2 | Question: 34
Consider the system shown in the figure. A rope goes over a pulley. A mass, $\text{m}$, is hanging from the rope. A spring of stiffness, $\text{k}$, is attached at one end of the rope. Assume rope is inextensible, massless and there is no slip between pulley and rope. The ... $\sqrt{\frac{kr^{2}}{J + mr^{2}}}$ $\sqrt{k/m}$ $\sqrt{\frac{kr^{2}}{J}}$

Consider the system shown in the figure. A rope goes over a pulley. A mass, $\text{m}$, is hanging from the rope. A spring of stiffness, $\text{k}$, is attached at one en...

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GATE Mechanical 2021 Set 2 | Question: 35
Find the positive real root of $x^3-x-3=0$ using Newton-Raphson method. lf the starting guess $(x_{0})$ is $2,$ the numerical value of the root after two iterations $(x_{2})$ is ______ ($\textit{round off to two decimal places}$).

Find the positive real root of $x^3-x-3=0$ using Newton-Raphson method. lf the starting guess $(x_{0})$ is $2,$ the numerical value of the root after two iterations $(x_{...

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GATE Mechanical 2021 Set 2 | Question: 36
Daily production capacity of a bearing manufacturing company is $30000$ bearings. The daily demand of the bearing is $15000$. The holding cost per year of keeping a bearing in the inventory is $₹20$. The setup cost for the production of a ... $\textit{in integer}$).

Daily production capacity of a bearing manufacturing company is $30000$ bearings. The daily demand of the bearing is $15000$. The holding cost per year of keeping a beari...

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GATE Mechanical 2021 Set 2 | Question: 37
A cast product of a particular material has dimensions $75\: \text{mm} \times 125\: \text{mm} \times 20 \:\text{mm}$. The total solidification time for the cast product is found to be $2.0$ minutes as calculated using Chvorinov's ... = $\text{50 mm}$, the total solidification time will be ______ minutes ($\textit{round off to two decimal places}$).

A cast product of a particular material has dimensions $75\: \text{mm} \times 125\: \text{mm} \times 20 \:\text{mm}$. The total solidification time for the cast product i...

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GATE Mechanical 2021 Set 2 | Question: 38
A spot welding operation performed on two pieces of steel yielded a nugget with a diameter of $\text{5 mm}$ and a thickness of $\text{1 mm}$. The welding time was $\text{0.1 s}$ ... $\text{kW} (\textit{round off to two decimal places}$).

A spot welding operation performed on two pieces of steel yielded a nugget with a diameter of $\text{5 mm}$ and a thickness of $\text{1 mm}$. The welding time was $\text{...

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GATE Mechanical 2021 Set 2 | Question: 39
A surface grinding operation has been performed on a Cast Iron plate having dimensions $\text{300 mm} (\textit{length}) \times \text{10 mm} (\textit{width})\times\text{50 mm}({height}$). The grinding was performed using an alumina wheel ... energy under the aforesaid grinding conditions is ______ $\text{J/mm}^{3} (\textit{round off to one decimal place}$).

A surface grinding operation has been performed on a Cast Iron plate having dimensions $\text{300 mm} (\textit{length}) \times \text{10 mm} (\textit{width})\times\text{50...

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GATE Mechanical 2021 Set 2 | Question: 40
In a pure orthogonal turning by a zero rake angle single point carbide cutting tool, the shear force has been computed to be $\text{400 N}$. The cutting velocity, $V_{c}=100$ $\text{m/min}$, depth of cut, $\text{t= 2.0 mm}$ ... , the shear strength, $\tau_{s}$, of the material will be ______ $\text{MPa} (\textit{round off to two decimal places}$).

In a pure orthogonal turning by a zero rake angle single point carbide cutting tool, the shear force has been computed to be $\text{400 N}$. The cutting velocity, $V_{c}=...

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GATE Mechanical 2021 Set 2 | Question: 41
The thickness, width and length of a metal slab are $\text{50 mm}$, $\text{250 mm}$ and $\text{3600 mm}$, respectively. A rolling operation on this slab reduces the thickness by $10\%$ and increases the width by $3\%$. The length of the rolled slab is ________ $\text{mm} \:(\textit{round off to one decimal place}$).

The thickness, width and length of a metal slab are $\text{50 mm}$, $\text{250 mm}$ and $\text{3600 mm}$, respectively. A rolling operation on this slab reduces the thick...

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GATE Mechanical 2021 Set 2 | Question: 42
A $\text{76.2 mm}$ gauge block is used under one end of a $\text{254 mm}$ sine bar with roll diameter of $\text{25.4 mm}$. The height of gauge blocks required at the other end of the sine bar to measure an angle of $30^{\circ}$ is ______ $\text{mm} (\textit{round off to two decimal places}$).

A $\text{76.2 mm}$ gauge block is used under one end of a $\text{254 mm}$ sine bar with roll diameter of $\text{25.4 mm}$. The height of gauge blocks required at the othe...

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GATE Mechanical 2021 Set 2 | Question: 43
The demand and forecast of an item for five months are given in the table. ... Mean Absolute Percent Error $\text{(MAPE)}$ in the forecast is __________________ $\% (\textit{round off to two decimal places}$)

The demand and forecast of an item for five months are given in the table.$$\begin{array}{|cl|cI|cI|}\hline&\textbf{Month} & \textbf{Demand} & \textbf{Forecast} \\ \hline...

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GATE Mechanical 2021 Set 2 | Question: 44
A shell and tube heat exchanger is used as a steam condenser. Coolant water enters the tube at $300 \text{ K}$ at a rate of $100 \text{ kg/s}$ ... temperature of the coolant water coming out of the condenser is __________________ $\text{K} (\textit{round off to the nearest integer}$).

A shell and tube heat exchanger is used as a steam condenser. Coolant water enters the tube at $300 \text{ K}$ at a rate of $100 \text{ kg/s}$. The overall heat transfer ...

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GATE Mechanical 2021 Set 2 | Question: 45
Ambient air flows over a heated slab having flat, top surface at $y = 0$. The local temperature (in Kelvin) profile within the thermal boundary layer is given by $\text{T(y)} = 300 + 200 \exp (-5y)$, where $\text{y}$ is the distance ... $y=0$ is ____________________ $\text{K/m} (\textit{round off to the nearest integer}$).

Ambient air flows over a heated slab having flat, top surface at $y = 0$. The local temperature (in Kelvin) profile within the thermal boundary layer is given by $\text{T...

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GATE Mechanical 2021 Set 2 | Question: 46
Water flows out from a large tank of cross-sectional area $A_{t}=1 \text{ m}^{2}$ through a small rounded orifice of cross-sectional area $A_{o} = 1 \text{ cm}^2$, located at $y= 0$ ... in the tank to reach a level of $\text{y = H/4}$ is __________________ seconds ($\textit{round off to one decimal places}$).

Water flows out from a large tank of cross-sectional area $A_{t}=1 \text{ m}^{2}$ through a small rounded orifice of cross-sectional area $A_{o} = 1 \text{ cm}^2$, locat...

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GATE Mechanical 2021 Set 2 | Question: 47
Consider the open feed water heater $\text{(FWH)}$ shown in the figure given below: Specific enthalpy of steam at location $2$ is $\text{2624 kJ/kg}$, specific enthalpy of water at location $5$ is $\text{226.7 kJ/kg}$ and specific enthalpy ... then the mass flow rate of steam at location $2$ will be ________ $\text{kg/s}$ (round off to one decimal place).

Consider the open feed water heater $\text{(FWH)}$ shown in the figure given below:Specific enthalpy of steam at location $2$ is $\text{2624 kJ/kg}$, specific enthalpy of...

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GATE Mechanical 2021 Set 2 | Question: 48
A high velocity water jet of cross section area = $0.01 \text{ m}^{2}$ and velocity $\text{35 m/s}$ enters a pipe filled with stagnant water. The diameter of the pipe is $\text{0.32 m}$. This high velocity water jet entrains ... the figure. The flow rate of entrained water is _______________ liters/$\text{s}\: (\textit{round off to two decimal places}$).

A high velocity water jet of cross section area = $0.01 \text{ m}^{2}$ and velocity $\text{35 m/s}$ enters a pipe filled with stagnant water. The diameter of the pipe is ...

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GATE Mechanical 2021 Set 2 | Question: 49
A vertical shaft Francis turbine rotates at $\text{300 rpm}$. The available head at the inlet to the turbine is $\text{200 m}$. The tip speed of the rotor is $\text{40 m/s}$. Water leaves the runner of the turbine without whirl. Velocity at ... $\% (\textit{round off to one decimal place}$).

A vertical shaft Francis turbine rotates at $\text{300 rpm}$. The available head at the inlet to the turbine is $\text{200 m}$. The tip speed of the rotor is $\text{40 m/...

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GATE Mechanical 2021 Set 2 | Question: 50
An adiabatic vortex tube, shown in the figure given below is supplied with $\text{5 kg/s}$ of air (inlet $1$) at $\text{500 kPa}$ and $\text{300 K}$. Two separate streams of air are leaving the device from outlets $2$ and $3$. ... the boundary of this device. The rate of entropy generation is _______ $\text{kW/K}\:(\textit{round off to one decimal place}$).

An adiabatic vortex tube, shown in the figure given below is supplied with $\text{5 kg/s}$ of air (inlet $1$) at $\text{500 kPa}$ and $\text{300 K}$. Two separate streams...

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GATE Mechanical 2021 Set 2 | Question: 51
A block of negligible mass rests on a surface that is inclined at $30^{\circ}$ to the horizontal plane as shown in the figure. When a vertical force of $\text{900 N}$ and a horizontal force of $\text{750 N}$ are applied, ... to slide. The coefficient of static friction between the block and surface is _______ ($\textit{round off to two decimal places}$).

A block of negligible mass rests on a surface that is inclined at $30^{\circ}$ to the horizontal plane as shown in the figure. When a vertical force of $\text{900 N}$ and...

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GATE Mechanical 2021 Set 2 | Question: 52
The wheels and axle system lying on a rough surface is shown in the figure. Each wheel has diameter $\text{0.8 m}$ and mass $\text{1 kg}$. Assume that the mass of the wheel is concentrated at rim and neglect the mass of the spokes. The ... of the wheel axle system in horizontal direction is ______ $\text{m/s}^{2} (\textit{round off to one decimal place}$).

The wheels and axle system lying on a rough surface is shown in the figure.Each wheel has diameter $\text{0.8 m}$ and mass $\text{1 kg}$. Assume that the mass of the whe...

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GATE Mechanical 2021 Set 2 | Question: 53
A cantilever beam with a uniform flexural rigidity ($\text{EI} = 200 \times 10^{6} \text{N.m}^{2}$ ) is loaded with a concentrated force at its free end. The area of the bending moment diagram corresponding to the full length of the ... magnitude of the slope of the beam at its free end is ______ micro radian ($\textit{round off to the nearest integer}$).

A cantilever beam with a uniform flexural rigidity ($\text{EI} = 200 \times 10^{6} \text{N.m}^{2}$ ) is loaded with a concentrated force at its free end. The area of the ...

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GATE Mechanical 2021 Set 2 | Question: 54
The torque provided by an engine is given by $T(\theta) =12000+ 2500 \sin(2 \theta) \text{N.m}$, where $\theta$ is the angle turned by the crank from inner dead center. The mean speed of the engine is $\text{200 rpm}$ and it ... minimum mass moment of inertia of the flywheel should be _______ $\text{kg.m}^{2} (\textit{round off to the nearest integer}$).

The torque provided by an engine is given by $T(\theta) =12000+ 2500 \sin(2 \theta) \text{N.m}$, where $\theta$ is the angle turned by the crank from inner dead center. T...

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GATE Mechanical 2021 Set 2 | Question: 55
The figure shows the relationship between fatigue strength $\text{(S)}$ and fatigue life $\text{(N)}$ of a material. The fatigue strength of the material for a life of $1000$ cycles is $\text{450 MPa}$, while its fatigue strength for a ... to an alternating stress of $\text{200 MPa}$ will then be _______ cycles ($\textit{round off to the nearest integer}$).

The figure shows the relationship between fatigue strength $\text{(S)}$ and fatigue life $\text{(N)}$ of a material. The fatigue strength of the material for a life of $1...

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