Recent questions tagged numerical-answers / GO Mechanical

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GATE2017 ME-2: 1
Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _______.

Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _______.

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GATE2017 ME-2: 8
For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is $M(x)=5x^{2}+10x$, where $x$ is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at $x=10$ mm is __________.

For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is $M(x)=5x^{2}+10x$, where $x$ is the distance (in mm) measured from...

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GATE2017 ME-2: 7
The state of stress at a point is $\sigma _{x}=\sigma _{y}=\sigma _{z}=\tau _{xz}=\tau _{zx}=\tau _{yz}=\tau _{zy}=0$ and $\tau _{xy}=\tau _{yx}=50$ MPa. The maximum normal stress (in MPa) at that point is ________.

The state of stress at a point is $\sigma _{x}=\sigma _{y}=\sigma _{z}=\tau _{xz}=\tau _{zx}=\tau _{yz}=\tau _{zy}=0$ and $\tau _{xy}=\tau _{yx}=50$ MPa. The maximum norm...

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GATE2017 ME-1: 55
Two cutting tools with tool life equations given below are being compared: Tool $1$: $VT^{0.1}=150$ Tool $2$: $VT^{0.3}=300$ where $V$ is cutting speed in m/minute and $T$ is tool life in minutes. The breakeven cutting speed beyond which Tool $2$ will have a higher tool life is ________ m/minute.

Two cutting tools with tool life equations given below are being compared:Tool $1$: $VT^{0.1}=150$Tool $2$: $VT^{0.3}=300$where $V$ is cutting speed in m/minute and $T$ i...

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GATE2017 ME-1: 54
A sprue in a sand mould has a top diameter of $20 \: mm$ and height of $200$ mm. The velocity of the molten metal at the entry of the sprue is $0.5 \: m/s$. Assume acceleration due to gravity as $9.8 \: m/s^{2}$ and neglect all losses. If the mould is well ventilated, the velocity (upto $3$ decimal points accuracy) of the molten metal at the bottom of the sprue is _________ $m/s$

A sprue in a sand mould has a top diameter of $20 \: mm$ and height of $200$ mm. The velocity of the molten metal at the entry of the sprue is $0.5 \: m/s$. Assume accele...

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GATE2017 ME-1: 53
A block of length $200$ mm is machined by a slab milling cutter $34$ mm in diameter. The depth of cut and table feed are set at $2$ mm and $18$ mm/minute, respectively. Considering the approach and the over travel of the cutter to be same, the minimum estimated machining time per pass is ________ minutes.

A block of length $200$ mm is machined by a slab milling cutter $34$ mm in diameter. The depth of cut and table feed are set at $2$ mm and $18$ mm/minute, respectively. C...

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GATE2017 ME-1: 52
Following data refers to the jobs $(P, Q, R, S)$ which have arrived at a machine for scheduling. The shortest possible average flow time is __________ days. $\begin{array}{|l|l|} \hline \text{Job} & \text{Processing Time (days)} \\ \hline P & 15 \\ \hline Q & 9 \\ \hline R & 22 \\ \hline S & 12 \\ \hline \end{array}$

Following data refers to the jobs $(P, Q, R, S)$ which have arrived at a machine for scheduling. The shortest possible average flow time is __________ days.$$\begin{array...

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GATE2017 ME-1: 51
Two models, $P$ and $Q$, of a product, earn profits of Rs.$100$ and Rs. $80$ per piece, respectively. Production times for $P$ and $Q$ are $5$ hours and $3$ hours, respectively, while the total production time available is $150$ hours. For a total batch size of $40$, to maximise profit, the number of units of $P$ to be produced is ________.

Two models, $P$ and $Q$, of a product, earn profits of Rs.$100$ and Rs. $80$ per piece, respectively. Production times for $P$ and $Q$ are $5$ hours and $3$ hours, respec...

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GATE2017 ME-1: 48
A $10$ mm deep cylindrical cup with diameter of $15$ mm is drawn from a circular blank. Neglecting the variation in the sheet thickness, the diameter (upto $2$ decimal points accuracy) of the blank is _________ mm.

A $10$ mm deep cylindrical cup with diameter of $15$ mm is drawn from a circular blank. Neglecting the variation in the sheet thickness, the diameter (upto $2$ decimal po...

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GATE2017 ME-1: 47
For an inline slider-crank mechanism, the lengths of the crank and connecting rod are $3$ m and $4$ m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is $1$ m/s, the magnitude of angular velocity (upto $3$ decimal points accuracy) of the crank is ________ radian/s

For an inline slider-crank mechanism, the lengths of the crank and connecting rod are $3$ m and $4$ m, respectively. At the instant when the connecting rod is perpendicul...

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GATE2017 ME-1: 45
In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at $100$ rpm. Let the number of teeth on the sun, planet and outer gears to be $50, 25$ and $100$, respectively. The ratio of magnitudes of angular velocity of the planet gear to the angular velocity of the carrier arm is ________.

In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at $100$ rpm. Let the number of teeth on the su...

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GATE2017 ME-1: 44
A horizontal bar, fixed at one end $(x=0)$, has a length of $1$ m, and cross-sectional area of $100 mm^{2}$. Its elastic modulus varies along its length as given by $E(x)=100 e^{-x}$ GPa, where $x$ is the length coordinate (in m) along the axis of the bar. An axial tensile load of $10$ kN is applied at the free end $(x=1)$. The axial displacement of the free end is _________ mm

A horizontal bar, fixed at one end $(x=0)$, has a length of $1$ m, and cross-sectional area of $100 mm^{2}$. Its elastic modulus varies along its length as given by $E(x)...

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GATE2017 ME-1: 43
A machine element has an ultimate strength $(\sigma _{u})$ of $600 N/mm^{2}$, and endurance limit $(\sigma _{en})$ of $250 N/mm^{2}$. The fatigue curve for the element on a $\log-\log$ plot is shown below. If the element is to be designed for a finite life of $10000$ cycles, the maximum amplitude of a completely reversed operating stress is _________ $N/mm^{2}$.

A machine element has an ultimate strength $(\sigma _{u})$ of $600 N/mm^{2}$, and endurance limit $(\sigma _{en})$ of $250 N/mm^{2}$. The fatigue curve for the element on...

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GATE2017 ME-1: 42
A rectangular region in a solid is in a state of plane strain. The $(x, y)$ coordinates of the corners of the undeformed rectangle are given by $P(0, 0), Q(4, 0), R(4, 3), S(0, 3)$ ... . The deformed length of the elongated diagonal, up to three decimal places is _______ units.

A rectangular region in a solid is in a state of plane strain. The $(x, y)$ coordinates of the corners of the undeformed rectangle are given by $P(0, 0), Q(4, 0), R(4, 3)...

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GATE2017 ME-1: 40
A point mass of $100$ kg is dropped onto a massless elastic bar (cross-sectional area $= 100 mm^{2}$, length $= 1$ m, Young's modulus$=100$ GPa) from a height $H$ of $10$ mm as shown (Figure is not to scale). If $g= 10 m/s^{2}$, the maximum compression of the elastic bar is _______ mm

A point mass of $100$ kg is dropped onto a massless elastic bar (cross-sectional area $= 100 mm^{2}$, length $= 1$ m, Young's modulus$=100$ GPa) from a height $H$ of $10$...

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GATE2017 ME-1: 38
Heat is generated uniformly in a long solid cylindrical rod (diameter$=10$ mm) at the rate of $4 \times 10^{7} W/m^{3}$. The thermal conductivity of the rod material is $25 W/m.K$. Under steady state conditions, the temperature difference between the centre and the surface of the rod is ______ $^{\circ} C$.

Heat is generated uniformly in a long solid cylindrical rod (diameter$=10$ mm) at the rate of $4 \times 10^{7} W/m^{3}$. The thermal conductivity of the rod material is $...

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GATE2017 ME-1: 37
Two black surfaces, AB and BC, of lengths $5$ m and $6$ m, respectively, are oriented as shown. Both surfaces extend infinitely into the third dimension. Given that view factor $F_{12}=0.5, T_{1}=800 K, T_{2}=600 K, T_{\text{surrounding}}=300 K$ and Stefan- ... $2$ to the surrounding environment is _______ kW.

Two black surfaces, AB and BC, of lengths $5$ m and $6$ m, respectively, are oriented as shown. Both surfaces extend infinitely into the third dimension. Given that view ...

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GATE2017 ME-1: 36
Air contains $79\%$ $N_{2}$ and $21\%$ $O_{2}$ on a molar basis. Methane $(CH_{4})$ is burned with $50\%$ excess air than required stoichiometrically. Assuming complete combustion of methane, the molar percentage of $N_{2}$ in the products is _______.

Air contains $79\%$ $N_{2}$ and $21\%$ $O_{2}$ on a molar basis. Methane $(CH_{4})$ is burned with $50\%$ excess air than required stoichiometrically. Assuming complete c...

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GATE2017 ME-1: 35
Moist air is treated as an ideal gas mixture of water vapour and dry air (molecular weight of air$= 28.84$ and molecular weight of water $=18$). At a location, the total pressure is $100$ kPa, the temperature is $30^{\circ}$ C and the relative humidity is ... saturation pressure of water at $30^{\circ} C$ is $4246$ Pa, the mass of water vapour per kg of dry air is _________ grams.

Moist air is treated as an ideal gas mixture of water vapour and dry air (molecular weight of air$= 28.84$ and molecular weight of water $=18$). At a location, the total ...

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GATE2017 ME-1: 27
For the vector $\vec{V}=2yz\hat{i}+3xz \hat{j}+4xy \hat{k}$, the value of $\bigtriangledown$. $(\bigtriangledown \times \vec{V})$ is ________.

For the vector $\vec{V}=2yz\hat{i}+3xz \hat{j}+4xy \hat{k}$, the value of $\bigtriangledown$. $(\bigtriangledown \times \vec{V})$ is ________.

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GATE2017 ME-1: 34
The pressure ratio across a gas turbine (for air, specific heat at constant pressure, $c_{p}=1040 J/kg.K$ and ratio of specific heats, $\gamma=1.4$) is $10$. If the inlet temperature to the turbine is $1200$ K and the isentropic efficiency is $0.9$, the gas temperature at turbine exit is ________ $K$

The pressure ratio across a gas turbine (for air, specific heat at constant pressure, $c_{p}=1040 J/kg.K$ and ratio of specific heats, $\gamma=1.4$) is $10$. If the inlet...

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GATE2017 ME-1: 33
One kg of an ideal gas (gas constant, $R= 400 J/kg.K$; specific heat at constant volume, $c_{v}=1000 J/kg.K$) at $1$ bar, and $300$ K is contained in a sealed rigid cylinder. During an adiabatic process, $100$ kJ of work is done on the system by a stirrer. The increase in entropy of the system is _______ $J/K$.

One kg of an ideal gas (gas constant, $R= 400 J/kg.K$; specific heat at constant volume, $c_{v}=1000 J/kg.K$) at $1$ bar, and $300$ K is contained in a sealed rigid cylin...

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GATE2017 ME-1: 24
Metric thread of $0.8$ mm pitch is to be cut on a lathe. Pitch of the lead screw is $1.5$ mm. If the spindle rotates at $1500$ rpm, the speed of rotation of the lead screw (rpm) will be ________.

Metric thread of $0.8$ mm pitch is to be cut on a lathe. Pitch of the lead screw is $1.5$ mm. If the spindle rotates at $1500$ rpm, the speed of rotation of the lead scre...

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GATE2017 ME-1: 21
In a metal forming operation when the material has just started yielding. the principal stresses are $\sigma_{1}=+180 MPa, \sigma_{2}=-100 MPa, \sigma_{3}=0$. Following von Mises' criterion, the yield stress is _________ MPa.

In a metal forming operation when the material has just started yielding. the principal stresses are $\sigma_{1}=+180 MPa, \sigma_{2}=-100 MPa, \sigma_{3}=0$. Following v...

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GATE2017 ME-1: 17
The following figure shows the velocity-time plot for a particle travelling along a straight line. The distance covered by the particle from $t=0$ to $t=5$s is __________ m.

The following figure shows the velocity-time plot for a particle travelling along a straight line. The distance covered by the particle from $t=0$ to $t=5$s is __________...

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GATE2017 ME-1: 15
A motor driving a solid circular steel shaft transmits $40$ kW of power at $500$ rpm. If the diameter of the shaft is $40$ mm, the maximum shear stress in the shaft is _____________MPa.

A motor driving a solid circular steel shaft transmits $40$ kW of power at $500$ rpm. If the diameter of the shaft is $40$ mm, the maximum shear stress in the shaft is __...

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GATE2017 ME-1: 12
A heat pump absorbs $10$kW of heat from outside environment at $250$ K while absorbing $15$ kW of work. It delivers the heat to a room that must be kept warm at $300$ K. The Coefficient of Performance (COP) of the heat pump is ________.

A heat pump absorbs $10$kW of heat from outside environment at $250$ K while absorbing $15$ kW of work. It delivers the heat to a room that must be kept warm at $300$ K. ...

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GATE2017 ME-1: 11
The molar specific heat at constant volume of an ideal gas is equal to $2.5$ times the universal gas constant ($8.314$ J/mol.K). When the temperature increases by $100$K, the change in molar specific enthalpy is __________ J/mol.

The molar specific heat at constant volume of an ideal gas is equal to $2.5$ times the universal gas constant ($8.314$ J/mol.K). When the temperature increases by $100$K,...

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GATE2017 ME-1: 5
A six-face fair dice is rolled a large number of times. The mean value of the outcomes is ________.

A six-face fair dice is rolled a large number of times. The mean value of the outcomes is ________.

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GATE2017 ME-1: 10
Saturated steam at $100^{\circ} C$ condenses on the outside of a tube. Cold fluid enters the tube at $20^{\circ} C$ and exits at $50^{\circ} C$. The value of the Log mean Temperature Difference (LMTD) is ________ $^{\circ}$ C.

Saturated steam at $100^{\circ} C$ condenses on the outside of a tube. Cold fluid enters the tube at $20^{\circ} C$ and exits at $50^{\circ} C$. The value of the Log mean...

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GATE2017 ME-1: 8
Water (density $= 1000 kg/m^{3}$) at ambient temperature flows through a horizontal pipe of uniform cross section at the rate of $1 kg/s$. If the pressure drop across the pipe is $100$ KPa, the minimum power required to pump the water across the pipe, in watts, is ______.

Water (density $= 1000 kg/m^{3}$) at ambient temperature flows through a horizontal pipe of uniform cross section at the rate of $1 kg/s$. If the pressure drop across the...

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GATE2016-3-55
A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the maximum machining time available on each machine. The profit per unit on parts $I$ and $II$ are $Rs. 40$ ... minutes) I II Turning machine $12$ $6$ $6000$ Milling center $4$ $10$ $4000$ Grinding Machine $2$ $3$ $1800$

A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the max...

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GATE2016-3-52
Two optically flat plates of glass are kept at a small angle $\theta$ as shown in the figure. Monochromatic light is incident vertically. If the wavelength of light used to get a fringe spacing of $1$ $mm$ is $450$ $nm$, the wavelength of light (in $nm$) to get a fringe spacing of $1.5$ $mm$ is _________

Two optically flat plates of glass are kept at a small angle $\theta$ as shown in the figure. Monochromatic light is incident vertically.If the wavelength of light used t...

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GATE2016-3-51
In a single point turning operation with cemented carbide tool and steel work piece, it is found that the Taylor’s exponent is $0.25$. If the cutting speed is reduced by $50 \%$ then the tool life changes by ______ times.

In a single point turning operation with cemented carbide tool and steel work piece, it is found that the Taylor’s exponent is $0.25$. If the cutting speed is reduced b...

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GATE2016-3-50
In a sheet metal of $2$ $mm$ thickness a hole of $10$ $mm$ diameter needs to be punched. The yield strength in tension of the sheet material is $100$ $MPa$ and its ultimate shear strength is $80$ $MPa$. The force required to punch the hole (in $kN$) is __________

In a sheet metal of $2$ $mm$ thickness a hole of $10$ $mm$ diameter needs to be punched. The yield strength in tension of the sheet material is $100$ $MPa$ and its ultima...

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GATE2016-3-48
Spot welding of two steel sheets each $2 \: mm$ thick is carried out successfully by passing $4 \: kA$ of current for $0.2$ seconds through the electrodes. The resulting weld nugget formed between the sheets is $5 \: mm$ in diameter. Assuming cylindrical shape for the nugget, the ...

Spot welding of two steel sheets each $2 \: mm$ thick is carried out successfully by passing $4 \: kA$ of current for $0.2$ seconds through the electrodes. The resulting ...

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GATE2016-3-47
In the vapour compression cycle shown in the figure, the evaporating and condensing temperatures are $260 \: K$ and $310 \: K$, respectively. The compressor takes in liquid-vapour mixture (state $1$) and isentropically compresses it to a dry saturated vapour condition (state ... $1$ and $0$ (in $kJ/kg$) is ____________

In the vapour compression cycle shown in the figure, the evaporating and condensing temperatures are $260 \: K$ and $310 \: K$, respectively. The compressor takes in liqu...

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GATE2016-3-46
In a $3$-stage air compressor, the inlet pressure is $p_1$, discharge pressure is $p_4$.and the intermediate pressures are $p_2$ and $p_3 ( p_2 < p_3)$. The total pressure ratio of the compressor is $10$ and the pressure ratios of the stages are equal. If $p_1 = 100$ $kPa$, the value of the pressure $p_3$ (in $kPa$) is __________

In a $3$-stage air compressor, the inlet pressure is $p_1$, discharge pressure is $p_4$.and the intermediate pressures are $p_2$ and $p_3 ( p_2 < p_3)$. The total pressur...

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GATE2016-3-45
In a mixture of dry air and water vapor at a total pressure of $750$ $mm$ of $Hg$, the partial pressure of water vapor is $20$ $mm$ of $Hg$. The humidity ratio of the air in grams of water vapor per $kg$ of dry air ($g_w/kg_{da}$) is __________

In a mixture of dry air and water vapor at a total pressure of $750$ $mm$ of $Hg$, the partial pressure of water vapor is $20$ $mm$ of $Hg$. The humidity ratio of the air...

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GATE2016-3-44
Steam at an initial enthalpy of $100$ $kJ/kg$ and inlet velocity of $100$ $m/s$, enters an insulated horizontal nozzle. It leaves the nozzle at $200$ $m/s$. The exit enthalpy (in $kJ/kg$) is __________

Steam at an initial enthalpy of $100$ $kJ/kg$ and inlet velocity of $100$ $m/s$, enters an insulated horizontal nozzle. It leaves the nozzle at $200$ $m/s$. The exit enth...

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Arjun asked Feb 24, 2017