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Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test)


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65 Questions MCQ Test GATE Mechanical (ME) 2023 Mock Test Series | Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test)

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) for GATE 2022 is part of GATE Mechanical (ME) 2023 Mock Test Series preparation. The Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) questions and answers have been prepared according to the GATE exam syllabus.The Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) MCQs are made for GATE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) below.
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Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 1

Directions:

Q. No. 1 - 5 Carry One Mark Each

Q.

If you choose plan P, you will have to _______ plan Q, as these two are mutually _________.

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 2

P looks at Q while Q looks at R. P is married, R is not. The number of people in which a married person is looking at an unmarried person is

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 3

If a and b are integers and a – b is even, which of the following must always be even?

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 3

According to the given relation of a–b = even, there is a possibility of odd-odd (or) even-even is equal to even. From the options, Option (D) is correct. Since, odd x odd–odd (or) even x even–even → is always even number.

Alternate Method: Let a – b =2K ⇒ a = b + 2K
ab-b = (b + 2K) b-b = b2 + 2Kb -b = b2 -b + 2Kb = b b -1)+ 2Kb

Even; since 2Kb always even & b (b-1) also even, if with b is odd or even. 

 

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 4

The property of a material which enables it to resist fracture due to high impact loads is known as

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 5

The ways in which this game can be played __________ potentially infinite.

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 6

Directions:

Q. No. 6- 10 Carry Two Marks Each

Q.

“If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters.”

Which of the following closest in meaning to „cleaving‟?

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 7

There are 4 women P, Q, R, S, and 5 men V, W, X, Y, Z in a group. We are required to form pairs each consisting of one woman and one man. P is not to be paired with Z, and Y must necessarily be paired with someone. In how many ways can 4 such pairs be formed?

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 7

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 8

In the graph below, the concentration of a particular pollutant in a lake is plotted over (alternate) days of a month in winter (average temperature 10°C) and a month in summer (average temperature 30°C).

Consider the following statements based on the data shown above:

(i) Over the given months, the difference between the maximum and the minimum pollutant concentrations is the same in both winter and summer.

(ii) There are at last four days in the summer month such that the pollutant concentrations on those days are within 1 ppm of the pollutant concentrations on the corresponding days in the winter month.Which one of the following options is correct?

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 8

The difference between the maximum and the minimum pollutant concentrations

(i) in winter = 8-0=8 ppm,

(ii) in summer = 10.5-1.5=9 ppm

∴ (i) is false & (ii) is correct from the graph.

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 9

All people in a certain island are either 'Knights' or 'Knaves' and each person knows every other person‟s identity. Knights NEVER lie, and knaves ALWAYS lie.P says “Both of us are knights”. Q says “None of us are knaves”.Which one of the following can be logically inferred from the above?

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 10

X bullocks and Y tractors take 8 days to plough a field. If we halve the number of bullocks and double the number of tractors, it takes 5days to plough the same field. How many days will it take X bullocks alone to plough the field?

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 10

Given Number of days required that X bullocks and Y tractors to plough a field = 8 days → (1) ( i.e, X + Y → 8D ⇒8X + 8Y → 1day )  

Number of days required that X/2 bullocks and 2 y tractors to plough field = 5→(2)

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 11

Directions:

Q. No. 11 to 35 Carry One Mark Each

Q.

A mass m of a perfect gas at pressure p1 and volume V1 undergoes an isothermal process. The final pressure is p2 and volume is V2. The work done on the system is considered positive. If R is the gas constant and T is the temperature, then the work done in the process is 

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 11

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 12

Which one of the following statements is TRUE for the ultrasonic machining (USM) process?

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 13

The standard deviation of linear dimensions P and Q are 3 mm and 4 mm, respectively. When assembled, the standard deviation (in mm ) of the resulting linear dimension (P+Q) is ________


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 13

Given that Standard deviate of P is 3 μm ⇒ Variance of P is 9 μm

Standard deviation of Q is 4 μm ⇒ Variance of Q is 16 μm

Variance of P + Q = Var (P+Q) = Variance P + Variance Q

= 9 + 16= 25

∴standard deviation of P + Q =

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 14

The emissive power of a blackbody is P. If its absolute temperature is doubled, the emissive power becomes.

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 14

Emissive power of black body (Eb) =σT4

Given (Eb)1=P =σT4

now T → 2T

(Eb)2 =(σ2T)4 = 16σT4 ⇒ (Eb)2 =16P

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 15

The state of stress at a point is σxy =σz = τxz = τzxzy = τyz and τxy = τyx =50MPa.

The maximum normal stress (in MPa) at that point is _________


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 15

It is a pure torsion case in 2D

   

so maximum Normal stress σ1 = 50MPa

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 16

The determinant of a 2×2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigenvalue is ___________ 


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 16

Given that det of 2×2 Matrix is 50 and are Eigen Value is 10.

⇒ Other Eigen value is 5 (∴  det= product of eigenvalues )

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 17

Which one of the following statement is TRUE?

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 18

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


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 18

Total No of outcomes when two coins are tossed is 4 and sample space

S = { HH, HT, TH, TT }

Favorable out comes for existence of at least one head are HH, HT, TH. 

Required probability = 3/4 = 0.75

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 19

A cantilever beam of length L and flexural modulus EI is subjected to a point load P at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) 

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 19

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 20

It is desired to make a product having T-shaped cross-section from a rectangular aluminium block. Which one of the following processes is expected to provide the highest strength of the product?

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 21

The heat loss from a fin is 6W. The effectiveness and efficiency of the fin are 3 and 0.75, respectively. The heat loss (in W) from the fin, keeping the entire fin surface at base temperature, is __________.


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 21

Given Qloss = 6W

ε = 3, η = 0.75

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 22

For a single server with Poisson arrival and exponential service time, the arrival rate is 12 per hour. Which one of the following service rates will provide a steady state finite queue length?

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 22

λ = 12/ hour

For steady state finite queue length

μ > λ

So, μ = 24/hour

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 23

For the stability of a floating body the

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 23

Stability of floating body is measure with the help of Meta center.
Floating body to be stable, Meta center must be above C.G

For stability MG > 0

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 24

The divergence of the vector -yi+ xj __________


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 24

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 25

For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is M(x) = 5x2+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 ________.


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 25

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 26

A sample of 15 data is a follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of the data is

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 26

We know that mode is the value of the data which occurred most of 

∴ 17 is mode

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 27

If a mass of moist air contained in a closed metallic vessel is heated, then its 

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 27

Given that mass of moist air contained in a closed metallic vessel is heated, means its specific humidity (ω) is constant.
So, from the psychometric chart

We can say that at constant specific humidity, as temperature increases relative humidity decreases i.e.,

Ø2 < Ø1 So, Answer is (A)

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 28

In a slider-crank mechanism, the lengths of the crank and the connecting rod are 100mm and 160mm, respectively. The crank is rotating with an angular velocity of 10 radian/s counterclockwise. The magnitude of linear velocity (in m/s) of the piston at the instant corresponding to the configuration shown in the figure is ___________

 

 


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 28

 

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 29

A machine component made of a ductile material is subjected to a variable loading with 
σmin = -50 MPa and σmax = 50 MPa. If the corrected endurance limit and the yield strength for the material are σe= 100 MPa and σy = 300MPa, the factor of safety is __________


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 29

σmax = 50MPa

σmin = -50MPa

σ = 300MPa

σe = 100MPa

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 30

The crystal structure of aluminium is

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 31

Uniformly distributed load of 5 kN acts on a simply supported beam of length 10 m. What are the reactions at end points of the beam?

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 32

The Laplace transform of tet is

 

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 32

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 33

Consider a laminar flow at zero incidence over a flat plate. The shear stress at the wall is denoted by τw . The axial positions x1 and x2 on the plate are measured from the leading edge in the direction of flow. If x2 > x1, then 

 

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 33

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 34

A mass m is attached to two identical springs having spring constant k as shown in the figure. The natural frequency w of this single degree of freedom system is

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 34

Equivalent stiffness keq = k+k = 2k

Natural frequency =

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 35

Given the atomic weight of Fe is 56 and that of C is 12, the weight percentage of carbon in cementite (Fe3C) is _________.


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 35

Percentage of carbon by weight in cementite =

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 36

Directions:

Q. No. 36 to 65 Carry Two Marks Each

Q.

In an orthogonal machining with a tool of 9° orthogonal rake angle, the uncut chip thickness is 0.2mm. The chip thickness fluctuates between 0.25 mm and 0.4 mm. The ratio of the maximum shear angle to the minimum shear angle during machining is ___________


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 36

α = 9o

t1 = 0.2mm

tc = 0.25mm to 0.4mm

if tc = 0.25mm, r = 0.8 and Ø = 42.08o

if tc = 0.4mm, r = 0.5 and Ø = 28.18o

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 37

A cylindrical pin of diameter is electroplated. Plating thickness is 2.0+0.005 mm. Neglecting the gauge tolerance, the diameter (in mm, up to 3 decimal points accuracy) of the GO ring gauge to inspect the plated pin is _________.

 


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 37

Diameter of GO end of ring gauge = 25.02 + 2(2.005) = 29.030mm

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 38

A helical compression spring made of wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is _____.


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 38

P1=P2 , d2 = 2d1 , D2 =2D1 

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 39

In a counter-flow heat exchanger, water is heated at the rate of 1.5kg/s from 40°C to 80°C by an oil entering at 120°C and leaving at 60°C. The specific heats of water and oil are 4.2kJ/kg.K and 2kJ/kg.K respectively. The overall heat transfer coefficient is 400 W/m2.K. The required heat transfer surface area (in m2) is

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 39

Given counter flow Heat Exchanger

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 40

The rod PQ of length L = √2 m, and uniformly distributed mass of M = 10 kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces OP and OQ. Assume acceleration due to gravity, g = 10 m/s2. The mass moment of inertia of the rod about its centre of mass and an axis perpendicular to the plane of the figure is (ML2/12). At this instant, the magnitude of angular acceleration (in radian/s2) of the rod is ____________


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 40

M = 10kg, g=10m/sec

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 41

A steel plate, connected to a fixed channel using three identical bolts A, B and C, carries a load of 6kN as shown in the figure. Considering the effect of direct load and moment, the magnitude of resultant shear force (in kN) on bolt C is.

 

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 41

Resultant shear at ' C ' =2+15=17 kN.
Resultant shear=15+2=17 kN.

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 42

The volume and temperature of air (assumed to be an ideal gas) in a closed vessel is 2.87 m3 and 300K, respectively. The gauge pressure indicated by a manometer fitted to the wall of the vessel is 0.5bar. If the gas constant of air is R = 287 J/kg. K and the atmospheric pressure is 1 bar, the mass of air (in kg) in the vessel is

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 42

V = 2.87m3 , T = 300K

Pgauge = 0.5bar

R = 287 J/kg.K

Patm = 1 bar

Pabs = Pg + Patm = 1.5 bar

PV = mRT

 

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 43

For the laminar flow of water over a sphere, the drag coefficient CF is defined as 
CF = F /(ρU2 D2) , where F is the drag force, r is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m3. When the diameter of the sphere is 100mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200mm under dynamically similar conditions, the drag force (in N) on this sphere is _____________


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 43

Given that the condition is dynamic similarity, and in the given condition, Inertia and viscous force plays major role, hence Reynold‟s number should be same for both model and prototype.
(Re)1 = (Re)2 

In the first case: 
U1 = 2m/sec, D1 = 100 mm, ρ = 1000 kg/m3

In the second case: U2 = 2m/s , D2= 200mm, ρ = 1000kg/m3

Since same water is flowing over both sphere

μ1 = μ2 , ρ1 = ρ2

U1D1 = U2D2

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 44

A rod of length 20mm is stretched to make a rod of length 40 mm. Subsequently, it is compressed to make a rod of final length 10mm. Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 44

1 = 20mm      ℓf =10mm

∴ true strain,

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 45

A gear train shown in the figure consists of gears P, Q, R and S. Gear Q and gear R are mounted on the same shaft. All the gears are mounted on parallel shafts and the number of teeth of P, Q, R and S are 24, 45, 30 and 80, respectively. Gear P is rotating at 400 rpm. The speed (in rpm) of the gear S is _________.

 


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 45

Tp = 24 , TQ = 45 , TR = 30, TS= 80

N= 400rpm

Np.Tp = NQ.TQ

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 46

In the Rankine cycle for a steam power plant the turbine entry and exit enthalpies are 2803 kJ/kg and 1800 kJ/kg, respectively. The enthalpies of water at pump entry and exit are 121 kJ/kg and 124 kJ/kg, respectively. The specific steam consumption (in kg/k W.h) of the cycle is ______

 


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 46

Given that 

h1 = 2803kJ/kg , h2 = 1800kJ/kg

h3 = 121kJ/kg ,   h4 = 124kJ/kg

WT = h- h2

= 2803 - 1800 = 1003kJ / kg

Wp = h4 - h3 

= 124 -121 = 3kJ/kg

Wnet = WT - W= 1000Kj/kg

Specific Steam consumption =

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 47

A calorically perfect gas (specific heat at constant pressure 1000 J/kg.K) enters and leaves a gas turbine with the same velocity. The temperatures of the gas at turbine entry and exit are 1100 K and 400 K. respectively. The power produced is 4.6 MW and heat escapes at the rate of 300 kJ/s through the turbine casing. The mass flow rate of the gas (in kg/s) through the turbine is.

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 47

Given that

Cp = 1000J/kgK

T1 = 1100K       P=4.6MW

T2 = 400K        QL = 300kJ/s

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 48

Three masses are connected to a rotating shaft supported on bearings A and B as shown in the figure. The system is in a space where the gravitational effect is absent. Neglect the mass of shaft and rods connecting the masses. For m1 = 10kg, m2 = 5kg and m3 = 2.5 kg and for a shaft angular speed of 1000 radian/s, the magnitude of the bearing reaction (in N) at location B is _________.

 


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 48

m1 = 10kg    r1 = 0.1m

m2 = 5kg,    r2 = 0.2m

m3 = 2.5,     r3 = 0.4m

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 49

A strip of 120 mm width and 8mm thickness is rolled between two 300 mm-diameter rolls to get a strip of 120 mm width and 7.2 mm thickness. The speed of the strip at the exit is 30 m/min. There is no front or back tension. Assuming uniform roll pressure of 200 MPa in the roll bite and 100% mechanical efficiency, the minimum total power (in kW) required to drive the two rolls is _________.


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 49

Width = 120mm

Initial thickness to = 8mm

Diameter of Roller = 300mm

Radius of Roller = 150mm

Final thickness = 7.2mm

Δh = ti - tf = 8 - 7.2= 0.8

Power require to drive one roller

So, power require to drive 2 roller = 2P = 2 x 4.8 kW = 9.6 kW

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 50

A product made in two factories p and Q, is transported to two destinations, R and S. The per unit costs of transportation (in Rupees) from factories to destinations are as per the following matrix:

Factory P produces 7 units and factory Q produces 9 units of the product. Each destination requires 8 units. If the north-west corner method provides the total transportation cost as X (in Rupees) and the optimized (the minimum) total transportation cost Y (in Rupees), then (X-Y), in Rupees, is

 

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 50

Total minimum Cost,

y = 3×8+4×1+7×7=Rs.77

So, x–y = Rs.28

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 51

One kg of an ideal gas (gas constant R = 287 J/kg.K) undergoes an irreversible process from state-1 (1 bar, 300 K) to state -2 (2 bar, 300 K). The change in specific entropy (s2 – s1) of the gas (in J/kg. K) in the process is ___________

 


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 51

 Given 
m =1kg,     R = 287J/kg.K

P1=1bar,    P2= 2bar

T1= 300K,  T2= 300K

∴Same Temperature

 

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 52

A 60 mm-diameter water jet strikes a plate containing a hole of 40mm diameter as shown in the figure. Part of the jet passes through the hole horizontally, and the remaining is deflected vertically. The density of water is 1000 kg/m3. If velocities are as indicated in the figure, the magnitude of horizontal force (in N) required to hold the plate is _________

 

 


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 52

Force in X–direction = Rate of change of momentum =

(Pi - Pf )x-direction

= (m1V1 - m2V2)x-direction

= V(ρA1V1 - ρA2V2) (∵ V1 = V2 )

 

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 53

The arrangement shown in the figure measures the velocity V of a gas of density 1 kg/m flowing through a pipe. The acceleration due to gravity is 9.81 m/s2. If the manometric fluid is water (density 1000 kg/m3) and the velocity V is 20 m/s, the differential head h (in mm) between the two arms of the manometer is ____________

 

 


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 53

Given 

ρg = 1kg/m3 ,    g = 9.81m/s2

ρm = 1000kg/m,  V=20m/s

h= 0.0204m = 2.04cm  ∴h = 20.4mm

 

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 54

A metal ball of diameter 60mm is initially at 220 °C. The ball is suddenly cooled by an air jet of 20°C. The heat transfer coefficient is 200 W/m2.K and 9000kg/m3, respectively. The ball temperature (in °C) after 90 seconds will be approximately.

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 54

D = 60mm = 0.06m

Ti = 220C,  h = 200W/m2

 ρ = 9000Kg/m3

T =  20oC  , Cp = 400J/Kgk

K= 400W/mK    , t = 90sec 

T= ?

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 55

A single – plate clutch has a friction disc with inner and outer radii of 20mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction m varies radially as μ = 0.01r, where r is in mm. The clutch needs to transmit a friction torque of 18.85kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is -


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 55

ri = 20mm , ro = 40mm , μ = 0.01r

T = 18.85kN-mm

p = ?

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 56

The surface integral  over the surface S of the sphere x2 + y2 + z2 = 9, where F=(x+y) i+ (x+z) j+(y+z) k and n is the unit outward surface normal, yields ______.


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 56

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 57

Block 2 slides outward on link 1 at a uniform velocity of 6 m/s as shown in the figure. Link 1 is rotating at a constant angular velocity of 20 radian/s counterclockwise. The magnitude of the total acceleration (in m/s2) of point P of the block with respect to fixed point O is ----


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 57

Acceleration of the block,

v = 6m / sec, ω = 20rad / sec

r = OP,

acr = 2vω = 2 x 6 x 20 = 240m/s2

ar = ω2r = (20)2 x 0.1 = 40

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 58

During the turning of a 20mm-diameter steel bar at a spindle speed of 400 rpm, a tool life of 20 minute is obtained. When the same bar is turned at 200 rpm, the tool life becomes 60 minute. Assume that Taylor‟s tool life equation is valid. When the bar is turned at 300 rpm, the tool life (in minute) is approximately.

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 58

Taylors Tool life equation,

VTn = C

∴ V1T1 = V2T2n

T3 =31.57 minutes  

T3 =32 minutes

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 59

Consider the matrix A =    whose eigenvectors corresponding to eigenvalues λand λ2 are x1 =    and x2 =  respectively. The value of x1Tx2   is -----

 


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 59

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 60

The radius of gyration of a compound pendulum about the point of suspension is 100mm. The distance between the point of suspension and the centre of mass is 250mm. Considering the acceleration due to gravity as 9.81 m/s2, the natural frequency (in radian/s) of the compound pendulum is _________.


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 60

k = 100mm = 0.1m

L = 250mm = 0.250m

g = 9.81m/sec

I= mK2 = m(0.1)2

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 61

Consider the differential equation 3y"( x ) + 27 y ( x )= 0 with initial conditions y(0) = 0 and y '(0) = 2000. The value of y at x = 1 is ________.


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 61

3y"(x)+27y(x) = 0 , y(0) = 0 , y'(0) = 2000

Auxillary equation, 3m2 + 27 = 0

⇒m2+ 9 = 0 ⇒m = 0 +3i

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 62

If f(z) = (x2+ay2) + ibxy is a complex analytic function of z = x + iy, where , then 

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 62

Given f ( z ) = ( x2 + ay2 ) + i bxy is analytic

value u= x2 + ay , v = bxy

Clearly for b = 2 and a= –1 above Cauchy-Riemann equations holds

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 63

A project starts with activity A and ends with activity F. The precedence relation and durations of the activities are as per the following table:

The minimum project completion time (in days) is ______


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 63

∴ Minimum project completion Time = Length of longest path = 4+3+14+9=30 Days.

*Answer can only contain numeric values
Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 64

Maximize Z = 5x1+3x

Subject to

x1 + 2x2 ≤ 10,

x1 - x≤ 8,

x1 , x2 ≥ 0.

In the starting Simplex tableau, x1 and x2 are non-basic variables and the value of Z is zero. The value of Z in the next Simplex tableau is _________.


Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 64

1st Table at (0,0) → Z = 0

2nd Table at (8,0)→ Z = 40 

Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 65

The principal stresses at a point in a critical section of a machine component are σ1= 60MPa, σ2= 5MPa and σ3  = -40 MPa. For the material of the component, the tensile yield strength is σy = 200 MPa. According to the maximum shear stress theory, the factor of safety is

Detailed Solution for Mechanical Engineering (Set-2) - ME 2017 GATE Paper (Practice Test) - Question 65

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