Recent questions tagged numerical-answers / GO Mechanical

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GATE2019 ME-2: 48
An idealized centrifugal pump (blade outer radius of $50 \: mm$) consumes $2 \: kW$ power while running at $3000 \: rpm$. The entry of the liquid into the pump is axial and exit from the pump is radial with respect to impeller. If the losses are neglected, then the mass flow rate of the liquid through the pump is ___________ $kg/s$ (round off to two decimal places)

An idealized centrifugal pump (blade outer radius of $50 \: mm$) consumes $2 \: kW$ power while running at $3000 \: rpm$. The entry of the liquid into the pump is axial a...

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GATE2019 ME-2: 49
An air standard Otto cycle has thermal efficiency of $0.5$ and the mean effective pressure of the cycle is $1000 \: kPa$. For air, assume specific heat ratio $\gamma=1.4$ and specific gas constant $R=0.287 \: kJ/kg \cdot K$. If the pressure and ... $300 \: K$, respectively, then the specific net work output of the cycle is _____ $kJ/kg $ (round off to two decimal places).

An air standard Otto cycle has thermal efficiency of $0.5$ and the mean effective pressure of the cycle is $1000 \: kPa$. For air, assume specific heat ratio $\gamma=1.4$...

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GATE2019 ME-2: 50
The figure shows a pouring arrangement for casting of a metal block. Frictional losses are negligible. The acceleration due to gravity is $9.81 \: m/s^2$ .The time (in $s$, round off to two decimal places) to fill up the mold cavity (of size $40 \: cm \times 30 \: cm \times 15 \: cm$) is _____

The figure shows a pouring arrangement for casting of a metal block. Frictional losses are negligible. The acceleration due to gravity is $9.81 \: m/s^2$ .The time (in $s...

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GATE2019 ME-2: 51
A gas tungsten arc welding operation is performed using a current of $250 \: A$ and an arc voltage of $20 \: V$ at a welding speed of $5 \: mm/s$. Assuming that the arc efficiency is $70 \%$, the net heat input per unit length of the weld will be _________$kJ/mm$ (round off to one decimal place)

A gas tungsten arc welding operation is performed using a current of $250 \: A$ and an arc voltage of $20 \: V$ at a welding speed of $5 \: mm/s$. Assuming that the arc e...

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GATE2019 ME-2: 52
The thickness of a sheet is reduced by rolling (without any change in width) using $600 \: mm$ diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is $0.05$. The sheet enters ... final thickness that can be produced by this process in a single pass is __________ $mm$ (round off to two decimal places).

The thickness of a sheet is reduced by rolling (without any change in width) using $600 \: mm$ diameter rolls. Neglect elastic deflection of the rolls and assume that the...

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GATE2019 ME-2: 53
A through hole is drilled in an aluminium alloy plate of $15 \: mm$ thickness with a drill bit of diameter $10$ mm, at a feed of $0.25$ mm/rev and a spindle speed of $1200$ rpm. If the specific energy required for cutting this material is $0.7 \: N \cdot m/mm^3$, the power required for drilling is ____________$W$ (round off to two decimal places)

A through hole is drilled in an aluminium alloy plate of $15 \: mm$ thickness with a drill bit of diameter $10$ mm, at a feed of $0.25$ mm/rev and a spindle speed of $120...

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GATE2019 ME-2: 54
In an orthogonal machining with a single point cutting tool of rake angle $10^{\circ}$, the uncut chip thickness and the chip thickness are $0.125$ mm and $0.22$ mm, respectively. Using Merchant’s first solution for the condition of minimum cutting force, the coefficient of friction at the chip-tool interface is _______ (round off to two decimal places).

In an orthogonal machining with a single point cutting tool of rake angle $10^{\circ}$, the uncut chip thickness and the chip thickness are $0.125$ mm and $0.22$ mm, resp...

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GATE2019 ME-2: 55
The annual demand of valves per year in a company is $10,000$ units. The current order quantity is $400$ valves per order. The holding cost is Rs. $24$ per valve per year and the ordering cost is Rs. $400$ per order. If the current order ... Economic Order Quantity, then the saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal places).

The annual demand of valves per year in a company is $10,000$ units. The current order quantity is $400$ valves per order. The holding cost is Rs. $24$ per valve per year...

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GATE2019 ME-1: 18
Evaluation of $\int_2^4 x^3 dx$ using a $2$-equal-segment trapezoidal rule gives a value of _______

Evaluation of $\int_2^4 x^3 dx$ using a $2$-equal-segment trapezoidal rule gives a value of _______

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GATE2019 ME-1: 19
A block of mass $10$ kg rests on a horizontal floor. The acceleration due to gravity is $9.81 \: m/s^2$. The coefficient of static friction between the floor and the block is $0.2$. A horizontal force of $10$ N is applied on the block as shown in the figure. The magnitude of force of friction (in N) on the block is _____

A block of mass $10$ kg rests on a horizontal floor. The acceleration due to gravity is $9.81 \: m/s^2$. The coefficient of static friction between the floor and the bloc...

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GATE2019 ME-1: 20
A cylindrical rod of diameter $10$ mm and length $0.1$m fixed at one end. The other end is twisted by an angle of $10^{\circ}$ by applying a torque. If the maximum shear strain in the rod is $p \times 10^{-3}$, then $p$ is equal to ____ (round off to two decimal places).

A cylindrical rod of diameter $10$ mm and length $0.1$m fixed at one end. The other end is twisted by an angle of $10^{\circ}$ by applying a torque. If the maximum shear ...

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GATE2019 ME-1: 21
A solid cube of side $1$ m is kept at a room temperature of $32^{\circ} C$. The coefficient of linear thermal expansion of the cube material is $1 \times 10^{-5} / ^{\circ}C$ and the bulk modulus is $200$ GPa. If the cube is constrained all around and heated uniformly to $42^{\circ}C$, then the magnitude of volumetric (mean) stress (in MPa) included due to heating is _______

A solid cube of side $1$ m is kept at a room temperature of $32^{\circ} C$. The coefficient of linear thermal expansion of the cube material is $1 \times 10^{-5} / ^{\cir...

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GATE2019 ME-1: 22
During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of $+140$ MPa, and a minimum stress of $-70$ MPa. The $R$-ratio (minimum stress to maximum stress) for this cyclic loading is _____ (round off to one decimal place)

During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of $+140$ MPa, and a minimum stress of $-70$ MPa. The $R$-ratio (m...

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GATE2019 ME-1: 23
Water flows through a pipe with a velocity given by $\overrightarrow{V}= \bigg( \dfrac{4}{t}+x+y \bigg) \hat{j} \: m/s$, where $\hat{j}$ is the unit vector in the $y$ direction, $t(>0)$ is in seconds, and $x$ and $y$ are in meters. The magnitude of total acceleration at the point $(x,y)=(1,1)$ at $t=2\: s$ is ______$m/s^2$

Water flows through a pipe with a velocity given by $\overrightarrow{V}= \bigg( \dfrac{4}{t}+x+y \bigg) \hat{j} \: m/s$, where $\hat{j}$ is the unit vector in the $y$ dir...

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GATE2019 ME-1: 24
Air of mass $1$ kg, initially at $300$ K and $10$ bar, is allowed to expand isothermally till it reaches a pressure of $1$ bar. Assuming air as an ideal gas with gas constant of $0.287 \: kJ/kg.K$, the change in entropy of air (in $kJ/kg.K$, round off to two decimal places) is ______

Air of mass $1$ kg, initially at $300$ K and $10$ bar, is allowed to expand isothermally till it reaches a pressure of $1$ bar. Assuming air as an ideal gas with gas cons...

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GATE2019 ME-1: 25
Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from $O$. Upon loading, the stress-strain curve passes through initial yield point at $P$, and then ... specimen is reloaded in tension from point $R$, the value of stress at which the material yields again is _______ MPa.

Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from $O$. U...

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GATE2019 ME-1: 38
A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of $10 \: kN$ is applied at point D. The magnitude of force (in kN) in the member BC is __________

A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of $10 \: kN$ is applied at point D. The magnitude of force (in kN) in the m...

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GATE2019 ME-1: 39
Consider an elastic straight beam of length $L= 10 \pi \: m$, with square cross-section of side $a=5 \: mm$, and Young's modulus $E=200 \: GPa$. This straight beam was bent in such a way that the two ends meets, to form a ... $MPa$.

Consider an elastic straight beam of length $L= 10 \pi \: m$, with square cross-section of side $a=5 \: mm$, and Young’s modulus $E=200 \: GPa$. This straight beam was ...

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GATE2019 ME-1: 40
Consider a prismatic straight beam of length $L=\pi \: m$, pinned at the two ends as shown in the figure. The beam has a square cross-section of side $p=6 \: mm$. The Young’s modulus $E=200 \: GPa$, and the coefficient of thermal expansion $\alpha = 3 \times 10^{-6} K^{-1}$. The minimum temperature rise required to cause Euler buckling of the beam is _______$K$.

Consider a prismatic straight beam of length $L=\pi \: m$, pinned at the two ends as shown in the figure. The beam has a square cross-section of side $p=6 \: mm$. The You...

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GATE2019 ME-1: 41
In a UTM experiment, a sample of length $100 \: mm$, was loaded in tension until failure. The failure load was $40 \: kN$. The displacement, measured using the cross-head motion, at failure, was $15 \: mm$. The compliance of the UTM is constant and is given $5 \times 10^{-8} \: m/N$. The strain at failure in the sample is ______$\%$

In a UTM experiment, a sample of length $100 \: mm$, was loaded in tension until failure. The failure load was $40 \: kN$. The displacement, measured using the cross-head...

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GATE2019 ME-1: 42
At a critical point in a component, the state of stress is given as $\sigma_{xx}=100 \: MPa, \: \sigma_{yy}=220 \: MPa, \: \sigma_{xy}= \sigma_{yx} = 80 \: MPa$ and all other stress components are zero. The yield strength of the material is $468 \: MPa$ The factor of safety on the basis of maximum shear stress theory is ___________ (round off to one decimal place)

At a critical point in a component, the state of stress is given as $\sigma_{xx}=100 \: MPa, \: \sigma_{yy}=220 \: MPa, \: \sigma_{xy}= \sigma_{yx} = 80 \: MPa$ and all o...

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GATE2019 ME-1: 43
A uniform thin disk of mass $1 \: kg$ and radius $0.1 \: m$ is kept on a surface as shown in the figure. A spring of stiffness $k_1=400 \: N/m$ is connected to the disk center $A$ ... disk. For small disturbance from the equilibrium, the natural frequency of vibration of the system is _________ $rad/s$ (round off to oe decimal place).

A uniform thin disk of mass $1 \: kg$ and radius $0.1 \: m$ is kept on a surface as shown in the figure. A spring of stiffness $k_1=400 \: N/m$ is connected to the disk c...

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GATE2019 ME-1: 44
A single block brake with a short shoe and torque capacity of $250 \: N \cdot m$ is shown. The cylindrical brake drum rotates anticlockwise at $100 \: rpm$ and the coefficient of friction is $0.25$. The value of $a$ in mm (round off to one decimal place), such that the minimum actuating force $P$ is $2000 \: N$, is ___________

A single block brake with a short shoe and torque capacity of $250 \: N \cdot m$ is shown. The cylindrical brake drum rotates anticlockwise at $100 \: rpm$ and the coeffi...

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GATE2019 ME-1: 45
Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, $2 \: m$ apart as shown below. The bottom plate is fixed and the upper plate moves to the right with a constant ... fluid, $\mu_1$, then the velocity at the interface (round off to two decimal places) is _______ $m/s$.

Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, $2 \: m$ apa...

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GATE2019 ME-1: 46
A cube of side $100 \: mm$ is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is $800 \: kg/m^3$. Liquid of density $1000 \: kg/m^3$ is now poured into the container. The minimum height to which the liquid needs to be poured into the container for the cube to just lift up is __________$mm$.

A cube of side $100 \: mm$ is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is $800 \: kg/m^3$. Liquid of densit...

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GATE2019 ME-1: 47
Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a non-uniform internal heat generation with an average value equal to $10000 \: Wm^{-3}$, while the left and right slabs have no ... $T_1$ is measured to be $100^{\circ} C$, the right extreme face temperature $T_2$ is ______$^{\circ} C$.

Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a non-uniform internal heat ...

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GATE2019 ME-1: 48
If one mole of $H_2$ has occupies a rigid container with a capacity of $1000$ litres and the temperature is raised from $27^{\circ} C$ to $37^{\circ} C$, the change in pressure of the contained gas (round off to two decimal places), assuming ideal gas behaviour, is _______ Pa. $(R=8.314 \: J/mol \cdot K)$

If one mole of $H_2$ has occupies a rigid container with a capacity of $1000$ litres and the temperature is raised from $27^{\circ} C$ to $37^{\circ} C$, the change in pr...

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GATE2019 ME-1: 49
A steam power cycle with regeneration as shown below on the $T-s$ diagram employs a single open feedwater heater for efficiency improvement. The fluid mix with each other in an open feedwater heater. The turbine is isentropic and the input (bleed) to the feedwater ... from the turbine as a percentage of the total mass flow rate at the inlet to the turbine at state $1$ is _______

A steam power cycle with regeneration as shown below on the $T-s$ diagram employs a single open feedwater heater for efficiency improvement. The fluid mix with each other...

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GATE2019 ME-1: 50
A gas turbine with air as the working fluid has an isentropic efficiency of $0.70$ when operating at a pressure ratio of $3$. Now, the pressure ratio of the turbine is increased to $5$, while maintaining the same inlet conditions. Assume air as a ... the cases, the isentropic efficiency of the turbine at the pressure ratio of $5$ is ___________ (round off to two decimal places)

A gas turbine with air as the working fluid has an isentropic efficiency of $0.70$ when operating at a pressure ratio of $3$. Now, the pressure ratio of the turbine is in...

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GATE2019 ME-1: 51
The value of the following definite integral is __________ (round off to three decimal places) $\int_1^e (x \: \ln \: x) dx$

The value of the following definite integral is __________ (round off to three decimal places)$$\int_1^e (x \: \ln \: x) dx$$

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GATE2019 ME-1: 52
In ASA system, the side cutting and end cutting edge angles of a sharp turning tool are $45^{\circ}$ and $10^{\circ}$, respectively. The feed during cylindrical turning is $0.1 \: mm/rev$. The center line average surface roughness (in $\mu m$, round off to one decimal place) of the generated surface is __________

In ASA system, the side cutting and end cutting edge angles of a sharp turning tool are $45^{\circ}$ and $10^{\circ}$, respectively. The feed during cylindrical turning i...

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GATE2019 ME-1: 53
Taylor’s tool life equation is given by $VT^n=C$, where $V$ is in $m/min$ and $T$ is in $min$. In a turning operation, two tools $X$ and $Y$ are used. For tool $X$, $n=0.3$ and $C=60$ and for tool $Y$, $n=0.6$ and $C=90$. Both the tools will have the same tool life for the cutting speed (in $m/min$, round off to one decimal place) of ____________

Taylor’s tool life equation is given by $VT^n=C$, where $V$ is in $m/min$ and $T$ is in $min$. In a turning operation, two tools $X$ and $Y$ are used. For tool $X$, $n=...

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GATE2019 ME-1: 54
Five jobs $(J1, J2, J3, J4$ and $J5)$ need to be processes in a factory. Each job can be assigned to any of the five different machines $(M1, M2, M3, M4$ and $M5)$. The time durations taken (in minutes) by the machines for each of the jobs, are given in the table. ...

Five jobs $(J1, J2, J3, J4$ and $J5)$ need to be processes in a factory. Each job can be assigned to any of the five different machines $(M1, M2, M3, M4$ and $M5)$. The t...

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GATE2019 ME-1: 55
A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below: ... amount of time, the maximum duration (in weeks) of the activity $S$ without delaying the completion of the project is ________

A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below:$\begin{array}{|c|c|c|} \h...

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GATE2018-2-55
A vehicle powered by a spark ignition engine follows air standard Otto cycle ($\gamma =1.4$). The engine generates $70$ kW while consuming $10.3$ kg/hr of fuel. The calorific value of the fuel is $44,000 \: kJ/kg$. The compression ratio is _________ (correct to two decimal places.

A vehicle powered by a spark ignition engine follows air standard Otto cycle ($\gamma =1.4$). The engine generates $70$ kW while consuming $10.3$ kg/hr of fuel. The calor...

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GATE2018-2-54
Steam in the condenser of a thermal power plant is to be condensed at a temperature of $30^{\circ}C$ with cooling water which enters the tubes of the condenser at $14^{\circ}C$ and exists at $22^{\circ}C$ ... coefficient is $2000 \: W/m^2 \: K$. The heat transfer (in $MW$) to the condenser is _________ (correct to two decimal places).

Steam in the condenser of a thermal power plant is to be condensed at a temperature of $30^{\circ}C$ with cooling water which enters the tubes of the condenser at $14^{\c...

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GATE2018-2-53
A welding operation is being performed with voltage $= 30 \: V$ and current =$100 \: A$. The cross-sectional area of the weld bead is $20 \: mm^2$. The work-piece and filler are titanium for which the specific energy of melting is $14 \: J/mm^3$. Assuming a thermal efficiency of the welding process $70 \%$, the welding speed (in $mm/s$) is __________ (correct to two decimal places).

A welding operation is being performed with voltage $= 30 \: V$ and current =$100 \: A$. The cross-sectional area of the weld bead is $20 \: mm^2$. The work-piece and fil...

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GATE2018-2-52
A circular hole of $25 \: mm$ diameter and depth of $20 \: mm$ is machined by EDM process. The material removal rate (in $mm^3/min$) is expressed as $ 4 \times 10^4 \: IT^{-1.23}$ where $I=300 \: A $ and the melting point of the material, $T=1600^{\circ}C$. The time ( in minutes) for machining this hole is _________ (correct to two decimal places)

A circular hole of $25 \: mm$ diameter and depth of $20 \: mm$ is machined by EDM process. The material removal rate (in $mm^3/min$) is expressed as $$ 4 \times 10^4 \: I...

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GATE2018-2-51
The arc lengths of a directed graph of a project are as shown in the figure. The shortest path length from node $1$ to node $6$ is __________

The arc lengths of a directed graph of a project are as shown in the figure. The shortest path length from node $1$ to node $6$ is __________

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GATE2018-2-50
For sand-casting a steel rectangular plate with dimensions $80 \: mm \times 120 \: mm \times 20 \: mm$, a cylindrical riser has to be designed. The height of the riser is equal to its diameter. The total solidification time for the casting in $2$ ... a solidification time for $3$ minutes in the riser, the diameter (in mm) of the riser is ________ (correct to two decimal places)

For sand-casting a steel rectangular plate with dimensions $80 \: mm \times 120 \: mm \times 20 \: mm$, a cylindrical riser has to be designed. The height of the riser is...

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