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MECHANICAL ENGINEERING GATE : 2008

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Read t he fol l ow ing i nst r uct i ons car efu l l y.

1. This quest ion paper contains al l object ive quest i ons. Q. 1 to Q. 20 car r y on e mar k each andQ. 21 to Q. 85 car ry t w o marks each.

2. Answer al l the quest ions.

3. Quest ions must be answered on Object ive Response Sheet (ORS) by darkening the appropr iate bubble(marked A, B, C, D) using HB pencil against the quest ion number on the left hand side of the ORS. Eachquest i on has on l y one cor r ect answ er . I n case you wish to change an answer, erase the old answercompletely.

4. Wrong answers wil l car ry NEGATIVE marks. In Q.1 to Q.20, 0.25 mark wil l be deducted for each wronganswer. In Q.21 to Q.76, Q.78, Q.80, Q.82 and in Q.84 0.5 mark wil l be deducted for each wrong answer.However, there is no negat ive marking in Q.77, Q.79, Q.81, Q.83. More than one answer bubbled anainsta quest ion wil l be taken as an incor rect response.

5. Write your registration number, your name and name of the examinat ion centre at the specified locationson the r ight half of the ORS.

6. Using HB pencil , darken the appropr iate bubble under each digit of your registrat ion number and thelet ters cor responding to your paper code.

7. Calculator is al lowed in the examinat ion hall .

8. Char ts, graph sheets or tables are NOT al lowed in the examinat ion hall .

9. Rough work can be done on the quest ion paper i tself. Addit ionally, blank pages are given at the end of thequest ion paper for rough work.

10. This quest ion paper contains 20 pr inted pages including pages for rough work. Please check al l pages andrepor t , i f there is any discrepancy.

GATE 2008 MECHANICAL ENGINEERING

Time Al l ow ed : 3 Hou r s M ax imum M ar k s : 150

GATE : 2008 MECHANICAL ENGINEERING

2

Q.1 – Q.20 car r y one mar k each .

1. I n the Taylor ser ies expansion of ex about x = 2,the coefficient of (x – 2)4 is

(a)14!

(b)42

4!

(c)2

4!e

(d)4

4!e

2. Given that x + 3x = 0, and x(0) = 1, x (0) = 0, whatis x(1)?

(a) – 0.99 (b) – 0.16

(c) 0.16 (d) 0.99

3. The value of

13 2lim

8 8x

x x

is

(a)1

16(b)

112

(c)18

(d)14

4. A coin is tossed 4 t imes. What is the probabil i ty ofget t ing heads exact ly 3 t imes?

(a)14

(b)38

(c)12

(d)34

5. The matr ix

1 2 4

3 0 6

1 1 p

L

NMMM

O

QPPP

has one eigenvalue equal

to 3. The sum of the other two eigenvalues is

(a) p (b) p – 1

(c) p – 2 (d) p – 3

6. The divergence of the vector field

(x – y) i + (y – x) j + (x + y + z) k is

(a) 0 (b) 1

(c) 2 (d) 3

7. The t ransverse shear st ress act ing in a beam ofr ect angu l ar cr oss-sect i on , subject ed t o atransverse shear load, is(a) variable with maximum at the bottom of the beam(b) var iable with maximum at the top of the beam(c) uniform(d) var iable with maximum of the neutral axis

8. A rod of length L and diameter D is subjected to atensi le load P. Which of the fol lowing is sufficientto calculate the result ing change in diameter?

(a) Young’s modulus

(b) Shear modulus

(c) Poisson’s rat io

(d) Both Young’s modulus and shear modulus

9. A straight rod of length L(t ), hinged at one endand freely extensible at the other end, rotatesthrough an angle (t ) about the hinge. At t ime t ,

L (t ) = 1 m, L (t ) = 1 m/s, (t ) = 4

r ad and

(t) = 1 rad/s. The magnitude of the velocity at theother end of the rod is

(a) 1 m/s (b) 2 m/s

(c) 3 m/s (d) 2 m/s

10. A cant i lever type gate hinged at Q is shown in thefigure. P and R are the centers of gravity of thecantilever part and the counterweight respectively.The mass of the cant ilever par t is 75 kg. The massof the counterweight , for stat ic balance, is

R Q P

0.5 m 2.0 m

(a) 75 kg (b) 150 kg

(c) 225 kg (d) 300 kg

11. A planar mechanism has 8 l inks and 10 rotaryjoints. The number of degrees of freedom of themechanism, using Gruebler ’s cr i ter ion, is

(a) 0 (b) 1

(c) 2 (d) 3

12. An axial residual compr essive str ess due to amanufactur ing process is present on the outersur face of a rotat ing shaft subjected to bending.Under a given bending load, the fat igue li fe of theshaft in the presence of the residual compressivestress is

(a) decreased

(b) increased or decreased, depending on theexternal bending load

(c) neither decreased nor increased

(d) increased


3

13. 2 moles of oxygen are mixed adiabat ical ly withanother 2 moles of oxygen in mixing chamber, sothat the final total pressure and temperature ofthe mixture become same as those of the individualconst ituents at their init ial states. The universalgas constant is given as R. The chang in entropydue to mixing, per mole of oxygen, is given by

(a) – R ln2 (b) 0

(c) R ln2 (d) R ln4

14. For flow of fluid over a heated plate, the followingfluid proper t ies are known

viscosity = 0.001 Pa.s ; specific heat at constantpressure = 1kj/kg.K ;

thermal conduct ivity = 1 W/m.k.

The hydrodynamic boundary layer thickness at aspeci fied locat ion on the plate is 1 mm. Thethermal boundary layer thickness at the samelocat ion is

(a) 0.001 mm (b) 0.01 mm

(c) 1 mm (d) 1000 mm

15. For the cont inuity equat ion given by V = 0 to

be val id, where V is the velocity vector, which

one of the fol lowing is a necessary condit ion?

(a) steady flow (b) ir rotat ional flow

(c) inviscid flow (d) incompressible flow

16. Which one of the fol lowing is NOT a necessaryassumpt ion for the air -standard Otto cycle?

(a) Al l processes are both internally as well asexternally reversible.

(b) Intake and exhaust pr ocesses are constantvolume heat reject ion processes.

(c) The combust ion process is a constant volumeheat addit ion process.

(d) The working fluid is an ideal gas with constantspecific heats.

17. I n an M /M/1 queuing system, the number ofar r ivals in an interval of length T is a Poissonrandom var iable (i.e. the probability of there beingn ar r i val s i n an i n t er val of l engt h T i s

e– T T n

n!

( )). The probability density function f(t)

of the inter -ar r ival t ime is given by

(a) 2 e–2

tFHG

IKJ (b) e–

2t

2

(c) e– t (d) e–

t

18. A set of 5 jobs is to be pr ocessed on a singlemachine. The processing t ime (in days) is givenin the table below. The holding cost for each job isRs. K per day.

Job Pr ocessing t ime

P 5

Q 2

R 3

S 2

T 1

A schedule that minimizes the total inventory costis

(a) T-S-Q-R-P (b) P-R-S-Q-T

(c) T-R-S-Q-P (d) P-Q-R-S-T

19. For generat ing a Coon’s sur face we require

(a) a set of gr id points on the sur face

(b) a set of gr id control points

(c) four bounding curves defining the sur face

(d) two bounding curves and a set of gr id controlpoints

20. I nternal gear cut t ing operat ion can be per formedby

(a) milling

(b) shaping with rack cut ter

(c) shaping with pinion cutter

(d) hobbing

Q.21 t o Q.75 car r y t w o mar k s each .

21. Consider the shaded t r iangular region P shown

in the figure. What is xydxdyPzz ?

0 2 x

P

y

1

(a)16

(b)29

(c)1

16(d) 1


4

22. The direct ional der ivat ive of the scalar funct ionf(x, y, z) = x2 + 2y2 + z at the point P = (1, 1, 2) inthe direct ion of the vector

a = 3i – 4j is

(a) – 4 (b) – 2

(c) – 1 (d) 1

23. For what value of a, if any, will the following systemof equat ions in x, y and z have a solut ion?

2x + 3y = 4

x + y + x = 4

x + 2y – z = a

(a) Any real number (b) 0

(c) 1 (d) There is no such value

24. Which of the fol lowing integrals is unbounded?

(a) t an x dx0

4

z (b)1

xdx

20

z 1

(c) xe dx– x

0

z (d)1

1

1

– xdx

0z

25. The integral f(z)dzz evaluated around the unit

circle on the complex plane for f(z) = cos z

z is

(a) 2 i (b) 4 i

(c) – 2 i (d) 0

26. The length of the curve y = 23

x3

2 between x = 0

and x = 1 is

(a) 0.27 (b) 0.67

(c) 1 (d) 1.22

27. The eigenvectors of the matr ix 1

0

2

2LNM

OQP are written

in the form 1

aLNMOQP

and 1

bLNMOQP

. What is a + b ?

(a) 0 (b)12

(c) 1 (d) 2

28. Let f = yx. What is 2 fx y

at x = 2, y = 1 ?

(a) 0 (b) In 2

(c) 1 (d)1

In 2

29. I t is given that y + 2y + y = 0, y(0) = 0, y(1) = 0.What is y(0.5) ?

(a) 0 (b) 0.37

(c) 0.62 (d) 1.13

30. The strain energy stored in the beam with flexuralr igidity FL and loaded as shown in the figure is

(a)P L3EI

2 3

(b)2P L

3EI

2 3

(c)4P L

3EI

2 3

(d)8P L

3EI

2 3

31. For the component loaded with a force F as shownin the figure, the axial st ress at the corner pointP is

P F

L–b

L

L

2b

2b

(a) F(3L – b)

b34(b) F(3L + b)

b34

(c) F(3L + b)

b3

4

4(d) F(3L + b)

b3

2

4

32. A sol id ci r cular shaft of diameter 100 mm issubjected to an axial st ress of 50 MPa. I t is fur thersubjected to a torque of 10 kNm. The maximumprincipal stress experienced on the shaft is closest to

(a) 41 MPa (b) 82 MPa

(c) 164 MPa (d) 204 MPa

33. A circular disk of radius R rol ls without sl ippingat a velocity v. The magnitude of the velocity atpoint P (see figure) is

(a) 3 v (b) 3 v/2

(c) v/2 (d) 2v/ 3


5

34. Consider a t russ PQR loaded at P with a force Fas shown in the figure.

The tension in the member QR is

45° 30°

PF

Q R

(a) 0.5 F (b) 0.63 F

(c) 0.73 F (d) 0.87 F

35. The natural frequency of the spr ing mass systemshown in the figure is closest to

(a) 8 Hz (b) 10 Hz

(c) 12 Hz (d) 14 Hz

36. The rod PQ of length L and with flexural r igidityEI is hinged at both ends. For what minimum forceF is i t expected to buckle?

(a)2EI

L2 (b)2 2 EI

L2

(c)2

2

EI

L2 (d)2

2

EI

L2

37. I n a cam design, the r ise mot ion is given by a

simple harmonic motion (SHM) s = h2

cos1 –

FHG

IKJ

where h is total r ise, is camshaft angle, is thetotal angle of the r ise interval. The jerk is given by

(a)h2

cos1 –

FHG

IKJ (b)

hsin

2FHG

IKJ

(c)

2

2 2h

cosFHG

IKJ (d) –

3

3 2h

sinFHG

IKJ

38. A uniform r igid rod of mass m = 1 kg and lengthL = 1 m is hinged at i t s cent re and lateral lysupported at one end by a spr ing of spr ing constantk = 300 N/m. The natural frequency n in rad/s is

(a) 10 (b) 20

(c) 30 (d) 40

39. A compression spr ing is made of music wire of2 mm diameter having a shear st rength and shearmodulus of 800 MPa and 80 GPa respectively. Themean coi l diameter is 20 mm, fr ee length is40 mm and the number of act ive coi ls is 10. I f themean coi l diameter is reduced to 10 mm, thest i ffness of the spr ing is approximately

(a) decreased by 8 t imes

(b) decreased by 2 t imes

(c) increased by 2 t imes

(d) increased by 8 t imes

40. A journal bear ing has shaft diameter of 40 mmand a length of 40 mm. The shaft is rotat ing at20 r ad/s and the viscosi ty of the lubr icant is20 mPa.s. The clearance is 0.020 mm. The loss oftorque due to the viscosity of the lubr icant isapproximately

(a) 0.040 Nm

(b) 0.252 Nm

(c) 0.400 Nm

(d) 0.652 Nm

41. A clutch has outer and inner diameters 100 mmand 40 mm respect ively. Assuming a uni formpressure of 2 MPa and coefficient of fr ict ion ofl iner mater ial 0.4, the torque car rying capacity ofthe clutch is

(a) 148 Nm

(b) 196 Nm

(c) 372 Nm

(d) 490 Nm

42. A spur gear has a module of 3 mm, number ofteeth 16, a face width of 36 mm and a pressureangle of 20. I t is t ransmit t ing a power of 3 kW at20 rev/s. Taking a velocity factor of 1.5, and a formfactor of 0.3, the stress in the gear tooth is about

(a) 32 MPa

(b) 46 MPa

(c) 58 MPa

(d) 70 MPa


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43. M at ch t he t ype of gear s w i t h t hei r mostappropr iate descr iption.

Type of gear

P. Helical

Q. Spiral Bevel

R. Hypoid

S. Rack and pinion

Descr i p t ion

1. Axes non paral lel and non intersect in

2. Axes paral lel and teeth are incl ined to the axis

3. Axes paral lel and teeth are parallel to the axis

4. Axes are perpendicular and intersect ing, andteeth are incl ined to the axis

5. Axes are perpendicular and used for large speedreduct ion

6. Axes paral lel and one of the gears has infiniteradius

(a) P-2, Q-4, R-1, S-6

(b) P-1, Q-4, R-5, S-6

(c) P-2, Q-6, R-4, S-2

(d) P-6, Q-3, R-1, S-5

44. A gas expands in a fr ict ionless piston-cyl inderarrangement. The expansion process is very slow,and is resisted by an ambient pressure of 100 kPa.Dur ing the expansion process, the pressure of thesystem (gas) remains constant at 300 kPa. Thechange in volume of the gas is 0.01 m3. Themaximum amount of work that could be ut i l izedfrom the above process is

(a) 0 kJ (b) 1 kJ

(c) 2 kJ (d) 3 kJ

45. The logar i thmic mean temperatur e differ ence(LMTD) of a counter flow heat exchanger is 20C.The cold fluid enters at 20C and the hot fluidenters at 100C. Mass flow rate of the cold fluid istwice that of the hot fluid. Specific heat at constantpressure of the hot fluid is twice that of the coldfluid. The exit temperature of the cold fluid

(a) is 40C

(b) is 60C

(c) is 80C

(d) cannot be determined

46. A two dimensional fluid element rotates like a r igidbody. At a point within the element, the pressure is1 unit. Radius of the Mohr’s circle, characterizingthe state of stress at that point, is(a) 0.5 unit

(b) 0 unit

(c) 1 unit

(d) 2 unit

47. A cycl ic device operates between three thermalr eser voi r s, as shown i n t he f igur e. Heat i stransferred to/form the cyclic device. I t is assumedthat heat transfer between each thermal reservoirand the cyclic device takes place across negligibletemperature difference. Interact ions between thecyclic device and the respective thermal reservoirsthat are shown in the figure are al l in the form ofheat t ransfer.

The cycl ic device can be

(a) a reversible hear engine

(b) a reversible heat pump or a reversible refrigerator

(c) an ir reversible heat engine

(d) an ir reversible heat pump or an ir reversiblerefr igerator

48. A balloon containing an ideal gas is init ial ly keptin an evacuated and insulated room. The balloonruptures and the gas fi l ls up the ent ire room.Which one of the fol lowing statements is TRUEat the end of above process?

(a) The internal energy of the gas decreases fromits init ial value, but the enthalpy remainsconstant

(b) The internal energy of the gas increases fromits init ial value, but the enthalpy remainsconstant

(c) Both internal energy and enthalpy of the gasremain constant

(d) Both internal energy and enthalpy of the gasincrease


7

49. A r igid, insulated tank is init ial ly evacuated. Thetank is connected with a supply line through whichair (assumed to be ideal gas with constant specificheats) passes at 1 MPa, 350C. A valve connectedwith the supply l ine is opened and the tank ischarged with air unt i l the final pressure insidethe tank reaches 1 MPa. The final temperatureinside the tank

(a) is greater than 350C

(b) is less than 350C

(c) is equal to 350C

(d) may be greater than, less than, or equal to350C, depending on the volume of the tank

50. For the three-dimensional object shown in thefigure below, five faces are insulated. The sixthface (PQRS), which is not insulated, interactsthermally with the ambient , with a convect iveheat transfer coefficient of 10 W/m2.K. The ambienttemperature is 30C. Heat is uniformly generatedinside the object at the rate of 100 W/m3. Assumingthe face PQRS to be at uniform temperature, i tssteady state temperature is

(a) 10C (b) 20C

(c) 30C (d) 40C

51. Water, having a density of 1000 kg/m3, issues froma nozzle with a velocity of 10 m/s and the jet str ikesa bucket mounted on a Pelton wheel. The wheelrotates at 10 rad/s. The mean diameter of thewheel is 1 m. The jet is spl it into two equal st reamsby the bucket , such that each stream is deflected

by 120, as shown in the figure. Fr ict ion in thebucket may be neglected. Magnitude of the torqueexer ted by the water on the wheel, per unit massflow rate of the incoming jet , is

(a) 0 (N.m)/(kg/s)

(b) 1.25 (N.m)/(kg/s)

(c) 2.5 (N.m)/(kg/s)

(d) 3.75 (N.m)/(kg/s)

52. A thermal power plant operates on a regenerat ivecycle wi th a single open feedwater heater, asshown in the figure. For the state points shown,the specific enthalpies are: h1 = 2800 kJ/kg andh2 = 200 kJ/kg. The bleed to the feedwater heateris 20% of the boiler steam generat ion rate. Thespecific enthalpy at state 3 is

(a) 720 kJ/kg

(b) 2280 kJ/kg

(c) 1500 kJ/kg

(d) 3000 kJ/kg

53. Moist air at a pressure of 100 kPa is compressed to500 kPa and then cooled to 35C in an aftercooler.The ai r at t he en t r y t o t he af t er cool er i sunsaturated and becomes just saturated at the exitof the aftercooler. The saturation pressure of waterat 35C is 5.628 kPa. The par tial pressure of watervapour (in kPa) in the moist air enter ing thecompressor is closest to

(a) 0.57

(b) 1.13

(c) 2.26

(d) 4.52


8

54. A hollow enclosure is formed between two infinitelylong concentr ic cyl inders of radi i 1 m and 2 m,respect ively. Radiat ive heat exchange takes placebetween the inner sur face of the larger cyl inder(sur face-2) and the outer sur face of the smallercyl inder (sur face-1). The radiat ing sur faces arediffuse and the medium in the enclosure is non-participating. The fraction of the thermal radiationleaving the larger sur face and str ik ing i tself is

(a) 0.25 (b) 0.5

(c) 0.75 (d) 1

55. Ai r (at atmospher ic pr essur e) at a dr y bu lbtemperature of 40C and wet bulb temperature of20C is humidified in an air washer operating withcont inuous water r ecir culat ion. The wet bulbdepression (i .e. the difference between the dry andwet bulb temperatures) at the exit is 25% of thatat the inlet . The dry bulb temperature at the exitof the air washer is closest to

(a) 10C (b) 20C

(c) 25C (d) 30C

56. Steady two-dimensional heat conduct ion takesplace in the body shown in the figure below. Thenormal temperature gradients over surfaces P andQ can be consi der ed t o be un i for m. The

temperature gradient Tx

at sur face Q is equal to

10 K /m. Sur faces P and Q ar e maintained atconstant temperatures as shown in the figure,while the r emaining par t of the boundary isinsulated. The body has a constant ther mal

conduct ivity of 0.1 W/m.K. The values of Tx

and

Ty

at sur face P are

(a)Tx

= 20 K/m, Ty

= 0 K /m

(b)Tx

= 0 K /m, Ty

= 10 K/m

(c)Tx

= 10 K/m, Ty

= 10 K/m

(d) Tx

= 0 K /m, Ty

= 20 K/m

57. I n a steady state steady flow process taking placein a device with a single inlet and a single out let ,the work done per unit mass flow rate is given by

w = – vdpi nlet

out letz , where v is the specific volume and

p is the pressure. The expression for w given above

(a) is val id only i f the process is both reversibleand adiabat ic

(b) is val id only i f the process is both reversibleand isothermal

(c) is val id for any reversible process

(d) is incor rect ; i t must be w = pdvinlet

out letz58. For the standard t ransportation linear programme

with m sources and n dest inations and total supplyequaling total demand, an opt imal solution (lowestcost ) with the smallest number of non-zer o x i j

values (amounts from source i to dest inat ion j) isdesired. The best upper bound for this number is

(a) mn (b) 2 (m + n)

(c) m + n (d) m + n – 1

59. A moving average system is used for forecast ingweekly demand. F1(t ) and F2(t ) are sequences offorecasts with parameters m1 and m2, respect ively,where m1 and m2 (m1 > m2) denote the numbers ofweeks over which the moving averages are taken.The actual demand shows a step increase from d1

to d2 at a cer tain t ime. Subsequent ly,

(a) neither F1(t ) nor F2(t ) wil l catch up with thevalue d2

(b) both sequences F1(t ) and F2(t ) wil l reach d2 inthe same per iod

(c) F1(t ) wil l at tain the value d2 before F2(t )

(d) F2(t ) wil l at tain the value d2 before F1(t )


9

60. For the network below, the object ive is to find thelength of the shor test path from node P to nodeG. Let di j be the length of directed are from nodei to node j.Let sj be the length of the shor test path from P tonode j. Which of the fol lowing equat ions can beused to find sG?

Q

G

R

P

(a) sG = Min{sQ, sR}

(b) sG = Min{sQ – dQG, sR – dRG}

(c) sG = Min{sQ + dQG, sR + dRG}

(d) sG = Min{dQG, dRG}

61. The product st ructure of an assembly P is shownin the figure.Estimated demand for end product P is as fol lows

Week 1 2 3 4 5 6

Demand 1000 1000 1000 1000 1200 1200

ignore lead t imes for assembly and sub-assembly.Product ion capacity (per week) for component Ris the bot t leneck operat ion. Star t ing with zeroinventory, the smallest capacity that wil l ensurea feasible product ion plan up to week 6 is

(a) 1000 (b) 1200(c) 2200 (d) 2400

62. One tooth of a gear having 4 module and 32 teethis shown in the figure. Assume that the gear toothand the cor responding tooth space make equali n ter cepts on the pi t ch ci r cumfer ence. Thedimensions ‘a’ and ‘b’, respect ively, are closest to

(a) 6.08 mm, 4 mm(b) 6.48 mm, 4.2 mm(c) 6.28 mm, 4.3 mm(d) 6.28 mm, 4.1 mm

63. While cooling, a cubical cast ing of side 40 mmundergoes 3%, 4% and 5% volume shr inkagedur ing the l iquid state, phase t ransit ion and solidst at e, r espect i vel y. The vol ume of met alcompensated from the r iser is(a) 2% (b) 7%(c) 8% (d) 9%

64. I n a single point turning tool, the side rake angleand or thogonal r ake angle ar e equal. is thepr incipal cut t ing edge angle and it s r ange is090. The chip flows in the orthogonal plane.The value of is closest to(a) 0 (b) 45(c) 60 (d) 90

65. A researcher conducts electrochemical machining(ECM) on a binary alloy (density 6000 kg/m3) of iron(at omic weight 56, valency 2) and met alP (atomic weight 24, valency 4). Faraday’s constant= 96500 coulomb/mole. Volumetr ic mater ial removalrate of the alloy is 50 mm3/s at a current of 2000 A.Percentage of metal P in the alloy is closest to(a) 4 0 (b) 25(c) 15 (d) 79

66. I n a single pass rol l ing operat ion, a 20 mm thickplate with plate width of 100 mm, is reduced to18 mm. The rol ler radius is 250 mm and rotationalspeed is 10 rpm. The average flow stress for theplate mater ial is 300 MPa. The power requiredfor the rol l ing operat ion in kW is closest to(a) 15.2 (b) 82(c) 30.4 (d) 45.6

67. I n arc welding of a but t joint , the welding speed isto be selected such that highest cooling rate isachieved. Melt ing efficiency and heat t ransferefficiency are 0.5 and 0.7, respectively. The area ofthe weld cross section is 5 mm2 and the unit energyrequired to melt the metal is 10 J/mm3. I f weldingpower is 2 kW, welding speed in mm/s is closest to(a) 4 (b) 14(c) 24 (d) 34

68. I n the deep dr awing of cups, blanks show atendency to wr inkle up around the per iphery(flange). The most l ikely cause and remedy of thephenomenon are, respect ively,(a) Buckl ing due to circumferent ial compression;

Increase blank holder pressure(b) High blank holder pressure and high fr ict ion;

Reduce blank holder pressure and apply lubricant(c) H i gh t emper at u r e causi ng i ncr ease i n

circumferential length; Apply coolant to blank(d) Buckl ing due to circumferent ial compression;

decrease blank holder pressure


10

69. The figure shows an incomplete schemat ic of aconvent ional lathe to be used for cut t ing threadswith, different pitches. The speed gear box U r isshown and the feed gear box U s is to be placed. P,Q, R and S denote locat ions and have no othersignificance. Changes in U r should NOT affect thepitch of the thread being cut and changes in U s

should NOT affect the cut t ing speed.

The correct connections and the cor rect placementof U s are given by

(a) Q and E are connected. U s is placed between Pand Q.

(b) S and E are connected. U s is placed between Rand S.

(c) Q and E are connected. U s is placed betweenQ and E.

(d) S and E are connected. U s is placed between Sand E.

70. A displacement sensor (a dial indicator ) measuresthe lateral displacement of a mandrel mounted onthe taper hole inside a dr il l spindle. The mandrelaxis is an extension of the dr il l spindle taper holeaxis and the protruding por tion of the mandrelsurface is per fect ly cyl indr ical. measurements aretaken with the sensor placed at two posit ionsP and Q as shown in the figure. The readings arer ecor ded as Rx = maximum deflect ion minusminimum deflect ion, cor r esponding to sensorposit ion at X, over one rotation.

I f RP = RQ > 0, which one of the following would beconsistent with the observat ion?(a) The dr i l l spindle rotat ional axis is coincident

with the dr i l l spindle taper hole axis(b) The dr i ll spindle rotat ional axis intersects the

dr i l l spindle taper hole axis at point P(c) The dr i l l spindle rotat ional axis is paral lel to

the dr i l l spindle taper hole axis(d) The dr i ll spindle rotat ional axis intersects the

dr i l l spindle taper hole axis at point Q

Common Dat a Quest i onsCommon Dat a for Quest i ons 71, 72 and 73:

I n the figure shown, the system is a pure substancekept in a piston-cyl inder arrangement. The system isinit ially a two-phase mixture containing 1 kg of liquidand 0.03 kg of vapour at a pressure of 100 kPa. Init ially,the piston rests on a set of stops, as shown in thefigure. A pressure of 200 kPa is required to exact lybalance the weight of the piston and the outsideatmospher ic pressure. Heat t ransfer takes place intothe system unt i l i ts volume increases by 50%. Heatt ransfer to the system occurs in such a manner thatthe piston, when al lowed to move, does so in a veryslow (quasi-stat ic / quasi-equil ibr ium) process. Thethermal reservoir from which heat is t ransfer red tothe system has a temperature of 400C. Averagetemperature of the system boundary can be taken as175C. The heat transfer to the system is 1 kJ, dur ingwhich i ts entropy increases by 10 J/K .

Specific volume of l iquid (vf) and vapour (vg) phases,as well as values of saturat ion temperatures, aregiven in the table below.

Pressure Saturation temperature, vf(m3/kg) vg(m3/kg)

(kPa) Tsat (C)

100 100 0.001 0.1

200 200 0.0015 0.002

71. At the end of the pr ocess, which one of thefol lowing situat ions wil l be t rue?(a) superheated vapour wil l be left in the system(b) no vapour wil l be left in the system(c) a l iquid + vapour mixture wil l be left in the

system(d) the mixture will exist at a dry saturate vapour

state

72. The work done by the system dur ing the process is(a) 0.1 kJ (b) 0.2 kJ(c) 0.3 kJ (d) 0.4 kJ

73. The net entr opy gener at ion (consider ing thesystem and the thermal reservoir together) dur ingthe process is closest to

(a) 7.5 J/K (b) 7.7 J/K

(c) 8.5 J/K (d) 10 J/K


11

Common Dat a for Quest i ons 74 and 75:

Consider the L inear Programme (LP)Max 4x + 6ysubject to3x + 2y 62x + 3y 6x, y 0

74. After introducing slack var iables s and t, the init ialbasic feasible solut ion is represented by the tablebelow (basic var iables are s = 6 and t = 6, and theobject ive funct ion value is 0).

4 6 0 0 0

s 3 2 1 0 6

t 2 3 0 1 6x y s t RHS

After some simplex iterations, the fol lowing tableis obtained

0 0 0 2 12

s 5 / 3 0 1 1 / 3 2

y 2 / 3 1 0 1 / 3 2x y s t RHS

From this, one can conclude that

(a) the LP has a unique opt imal solut ion

(b) the LP has an opt imal solut ion that is notunique

(c) the LP is infeasible

(d) the LP is unbounded

75. The dual for the LP in Q 74 is

(a) M in 6u + 6v (b) Max 6u + 6vsubject to subject to3u + 2v 4 3u + 2v 42u + 3v 6 2u + 3v 6u, v 0 u, v 0

(c) M ix 4u + 6v (d) M in 4u + 6vsubject to subject to3u + 2v 6 3u + 2v 62u + 3v 6 2u + 3v 6u, v 0 u, v 0

L ink ed Answ er Quest i ons: Q.76 t o Q.85 car r yt w o mar k s each .St at em en t for L i n k ed An sw er Qu est i on s 76and 77:

A cylindr ical container of radius R = 1 m, wall thickness1 mm is fi lled with water up to a depth of 2 m andsuspended along its upper r im. The density of water is1000 kg/m3 and acceleration due to gravity is 10 m/s2.

The self-weight of the cylinder is negligible. The formulafor hoop stress in a thin-walled cylinder can be used atall points along the height of the cylindr ical container.

1mm

1m

2R

2m

76. The axial and ci r cumfer ent ial st r ess (d, c)exper ienced by the cyl inder wall at mid-depth(1 m as shown) are

(a) (10, 10) MPa (b) (5, 10) MPa

(c) (10, 5) MPa (d) (5, 5) MPa

77. I f the Young’s modulus and Poisson’s rat io of thecon t ai ner mat er i al ar e 100 GPa and 0.3,respect ively, the axial st rain in the cyl inder wallat mid-depth is

(a) 2 × 10– 5 (b) 6 × 10– 5

(c) 7 × 10– 5 (d) 1.2 × 10– 4

St at emen t for L i n k ed An sw er Quest i ons 78and 79:

A steel bar of 10 × 50 mm is cant i levered with two M12 bolts (P and Q) to suppor t a stat ic load of 4 kN asshown in the figure.

78. The pr imary and secondary shear loads on bolt P,respect ively, are

(a) 2 kN, 20 kN

(b) 20 kN, 2 kN

(c) 20 kN, 0 kN

(d) 0 kN, 20 kN

79. The resultant shear st ress on bolt P is closest to

(a) 132 MPa

(b) 159 MPa

(c) 178 MPa

(d) 195 MPa


12

St at em en t f o r L i n k ed A n sw er Qu est i on s80 and 81 :

The gap between a moving ci rcular plate and astat ionary sur face is being cont inuously reduced, asthe circular plate comes down at a uniform speed Vtowards the stat ionary bot tom sur face, as shown inthe figure. In the process, the fluid contained betweenthe two plates flows out radially. The fluid is assumedto be incompressible and inviscid.

80. The radial velocity vr at any radius r, when thegap width is h, is

(a) vr = Vr2h

(b) vr = Vrh

(c) vr = 2Vh

r(d) vr =

Vhr

81. The radial component of the fluid accelerat ion atr = R is

(a)3V R

4h

2

2 (b)V R

4h

2

2

(c)V R

2h

2

2 (d)V R

4h

2

2

St a t em en t f o r L i n k ed A n sw er Qu est i on s82 and 83 :

Or thogonal turning is per for med on a cyl indr icalwor kpiece wi th shear st r ength of 250 M Pa. Thefol lowing condi t ions are used: cut t ing veloci t y is180 m/min, feed is 0.20 mm/rev, depth of cut is 3 mm,chip thickness rat io = 0.5. The or thogonal rake angleis 7. Apply Merchant’s theory for analysis.

82. The shear plane angle (in degrees) and the shearforce respect ively are

(a) 52 ; 320 N (b) 52 ; 400 N

(c) 28 ; 400 N (d) 28 ; 320 N

83. The cut ting and fr ict ional forces, respect ively, are

(a) 568 N ; 387 N (b) 565 N ; 381 N

(c) 440 N ; 342 N (d) 480 N ; 356 N

St a t em en t f o r L i n k ed A n sw er Qu est i on s84 an d 85 :

I n the feed dr ive of a Point – to– Point open loop CNCdrive, a stepper motor rotat ing at 200 steps/rev dr ivesa table thr ough a gear box and l ead scr ew-nutmechanism (pitch = 4 mm, number of star ts = 1). The

gear rat io = Output rotat ional speedInput rotat ional speed

FHG

IKJ is given by U

= 14

. The stepper motor (dr iven by voltage pulses from

a pulse generator ) executes 1 step/pulse of the pulsegenerator. The frequency of the pulse t rain from thepulse generator is f = 10,000 pulses per minute.

84. The basic Length Uni t (BLU), i .e., the tablemovement cor responding to 1 pulse of the pulsegenerator, is

(a) 0.5 microns

(b) 5 microns

(c) 50 microns

(d) 500 microns

85. A customer insists on a modificat ion to changethe BLU of the CNC dr ive to 10 microns withoutchanging the table speed. The modificat ion canbe accomplished by

(a) changing U to 12

and reducing f to f2

(b) changing U to 18

and increasing f to 2f

(c) changing U to 12

and keeping f unchanged

(d) keeping U unchanged and increasing f to 2f

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