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MECHANICAL ENGINEERING GATE : 2003

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Read t h e fol l ow i ng i n st r uct i on s car efu l l y.

1. Th i s quest i on paper con t ai ns 90 object i ve quest i ons. Q. 1— 30 car r y one mar k each and Q. 31— 90 car ry two marks each.

2. Answer al l the quest ions.

3. Quest ions must be answered on special machine gradable Object ive Response Sheet (ORS) by darkeningthe appropr iate bubble (marked A, B, C, D) using HB pencil against the quest ion number. Each quest ionhas only one cor rect answer. In case you wish to change an answer, erase the old answer completely usinga good soft eraser.

4. There wil l be Negat i ve marking. For each wrong answer 0.25 mark for Q. 1— 30 and 0.5 mark for Q. 31—90 wil l be deducted. More than one answer marked against a quest ion wil l be deemed as an incor rectresponse and wil l be negat ively marked.

5. Write your registrat ion number, your name and name of the centre at the specified locat ions on the r ighthalf of the ORS.

6. Using HB pencil , darken the appropr iate bubble under each digit of your registrat ion number.

7. Using HB pencil , darken the appropr iate bubble under the let ters cor responding to your paper code.

8. No char ts, graph sheets or tables are provided in the examinat ion hall .

9. Use the blank pages given at the end of the quest ion paper for rough work.

10. Choose the Closest numer ical answer among the choices given.

GATE 2003MECHANICAL ENGINEERING

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

GATE : 2003 MECHANICAL ENGINEERING

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Q. 1 – Q. 30 car r y one mar k each

1. Ltx

xx0

2sin is equal to

(a) 0 (b)

(c) 1 (d) – 1

2. The accuracy of Simpson’s rule quadrature for astep size h is

(a) O(h2) (b) O(h3)

(c) O(h4) (d) O(h5)

3. For the matr ix 4 11 4LNM

OQP the eigen values are

(a) 3 and – 3

(b) – 3 and – 5

(c) 3 and 5

(d) 5 and 0

4. The second moment of a circular area about thediameter is given by (D is the diameter ).

(a)D 4

4(b)

D 4

16

(c)D 4

32(d)

D 4

64

5. A concent r at ed l oad of P act s on a simpl y

suppor ted beam of span L at a distance L3

from

the left support. The bending moment at the pointof applicat ion of the load is given by

(a)PL3

(b)2

3PL

(c)PL9

(d)2PL

9

6. Two ident ical circular rods of same diameter andsame length are subjected to same magnitude ofaxial tensi le force. One of the rods is made out ofmild steel having the modulus of elast icit y of206 GPa. The other rod is made out of cast ironhaving the modulus of elast icit y of 100 GPa.Assume both the mater ials to be homogeneousand isotropic and the axial force causes the sameamount of uniform stress in both the rods. Thestresses developed are withn the propor t ionall imit of the respect ive mater ials. Which of thefol lowing observat ions is cor rect ?

(a) Both rods elongate by the same amount

(b) M ild steel rod elongates more than the castiron rod

(c) Cast iron rod elongates more than the mildsteel rod

(d) As the stresses are equal strains are also equalin both the rods

7. Two beams, one having square cross sect ion andanother circular cross-sect ion, are subjected tothe same amount of bending moment. I f the crosssect ional area as well as the mater ial of both thebeams are the same then

(a) maximum bending stress developed in boththe beams is the same

(b) the circular beam exper iences more bendingstress than the square one

(c) the square beam exper iences more bendingstress than the circular one

(d) as the mater ial is same both the beams wil lexper ience same deformat ion

8. The mechanism used in a shaping machine is

(a) a closed 4-bar chain having 4 revolute pairs

(b) a closed 6-bar chain having 6 revolute pairs

(c) a closed 4-bar chain having 2 revolute and 2sl iding pairs

(d) an inversion of the single sl ider -crank chain

9. The lengths of the l inks of a 4-bar l inkage withrevolute pairs only are p, q, r , and s units. Giventhat p < q < r < s. Which of these l inks should bethe fixed one, for obtaining a “double crank ”mechanism ?

(a) l ink of length p (b) l ink of length q

(c) l ink of length r (d) l ink of length s

10. Consider the ar rangement shown in the figurebelow wher e J i s t he combined polar massmoment of iner t ia of the disc and the shafts. K 1,K 2, K 3 are the torsional sti ffness of the respect iveshaft s. The nat ur al fr equency of t or si onalosci l lat ion of the disc is given by


3

(a)K K K

J1 2 3

(b)K K K K K K

J(K K )1 2 2 3 3 1

1 2

(c)K K K

J(K K K K K K )1 2 3

1 2 2 3 3 1

(d)K 1K K K K K

J K K2 2 3 3 1

2 3

( )

11. Maximum shear stress developed on the sur faceof a sol id cir cular shaft under pure torsion is240 MPa. I f the shaft diameter is doubled thenthe maximum shear stress developed correspondingto the same torque wil l be

(a) 120 MPa

(b) 60 MPa

(c) 30 MPa

(d) 15 MPa

12. A wir e r ope is designated as 6×19 standar dhoist ing. The numbers 6×9 represent

(a) diameter in mil l imeter × length in meter

(b) diameter in cent imeter × length in meter

(c) number of st rands × number of wires in eachstrand

(d) number of wires in each strand × number ofstrands

13. A cylindr ical body of cross-sectional area A, heightH and density s, is immersed to a depth h in al iquid of density , and t ied to the bot tom with astr ing. The tension in the str ing is

(a) ghA

(b) (s – ) ghA

(c) ( – s) ghA

(d) (h – s H) gA

14. A 2 kW, 40 l i t re water heater is switched on for20 minutes. The heat capacity Cp for water is4.2 kJ/kg K. Assuming al l the electr ical energyhas gone into heat ing the water, increase of thewater temperature in degree centrgrade is

(a) 2.7 (b) 4.0

(c) 14.3 (d) 25.25

15. An industr ial heat pump operates between thetemperatures of 27°C and – 13°C. The rates of heataddi t i on and heat r eject ion ar e 750 W and1000 W, respectively. The COP for the heat pump is

(a) 7.5 (b) 6.5

(c) 4.0 (d) 3.0

16. A plate having 10 cm2 area each side is hangingin the middle of a room of 100 m2 total sur facearea. The plate temperature and emissivity arerespectively 800°K and 0.6. The temperature andemissivity values for the surfaces of the room are300°K and 0.3 respect ively. Boltzmann’s constant = 5.67 × 10– 8 W/m2 K 4. The total heat loss fromthe two sur faces of the plate is

(a) 13.66 W

(b) 27.32 W

(c) 27.87 W

(d) 13.66 MW

17. For air with a relat ive humidity of 80%

(a) the dry bulb temperature is less than the wetbulb temperature

(b) the dew point temperature is less than wetbulb temperature

(c) the dew point and wet bulb temperatures areequal

(d) the dry bulb and dew point temperatures areequal

18. For a spark ignition engine, the equivalence ratio() of mixture enter ing the combust ion chamberhas values

(a) < 1 for idl ing and > 1 for peak powerconditions

(b) > 1 for both idling and peak power conditions

(c) > 1 for idl ing and < 1 for peak powerconditions

(d) < 1 for both idling and peak power conditions


4

19. A diesel engine is usually more efficient than aspark ignit ion engine because

(a) diesel being a heavier hydrocarbon, releasesmore heat per kg than gasoline

(b) the air standard efficiency of diesel cycle ish igher t han t he Ot t o cycle, at a f i xedcompression rat io

(c) the compression rat io of a diesel engine ishigher than that of an SI engine

(d) self ignit ion temperature of diesel is higherthan that of gasoline

20. In a Rankine cycle, regeneration results in higherefficiency because

(a) pressure inside the boiler increases

(b) heat is added before steam enters the lowpressure turbine

(c) average temperature of heat addit ion in theboiler increases

(d) total work delivered by the turbine increases

21. Consider ing the var iat ion of stat ic pressure andabsolute velocity in an impulse stream turbine,across one row of moving blades

(a) both pressure and velocity decrease

(b) pressure decreases but velocity increases

(c) pressur e remains constant , while velocit yincreases

(d) pressur e remains constant , while velocit ydecreases

22. Dur ing heat t reatment of steel, the hardness ofvar ious structures in increasing order is

(a) mar tensi te, f ine pear l i t e, coar se pear l i t e,spherodite

(b) fine pear l i t e, coar se pear l i t e, spher odi te,martensite

(c) mar tensi te, coarse pear l i t e, f ine pear l i t e,spherodite

(d) spher odi te, coar se pear l i t e, f ine pear l i t e,martensite

23. Hardness of green sand mould increases with

(a) increase in moisture content beyond 6 percent

(b) increase in permeabil i ty

(c) decrease in permeabil i ty

(d) i ncr ease i n bot h moist u r e cont ent andpermeabil ity

24. I n Oxyacetylene gas welding, temperature at theinner cone of the flame is around

(a) 3500 C

(b) 3200 C

(c) 2900 C

(d) 2550 C

25. Cold working of steel is defined as working

(a) at i ts recrystal l isat ion temperature

(b) above its recrystall isat ion temperature

(c) below its recrystall isat ion temperature

(d) at two thirds of the melt ing temperature ofthe metal

26. Quality screw threads are produced by

(a) thread mil l ing

(b) thread chasing

(c) thread cut t ing with single point tool

(d) thread cast ing

27. As tool and wor k ar e not in contact in EDMprocess

(a) no relat ive mot ion occurs between them

(b) no water of tool occurs

(c) no power is consumed dur ing metal cut t ing

(d) no force between tool and work occurs

28. The dimensional l imits on a shaft of 25h7 are

(a) 25.000, 25.021 mm

(b) 25.000, 24,979 mm

(c) 25.000, 25.007 mm

(d) 25.000, 24,993 mm

29. When a cyl inder is located in a Vee-block, thennumber of degrees of freedom which are arrestedis

(a) 2

(b) 4

(c) 7

(d) 8

30. The symbol used for Transpor t in work study is

(a)

(b) T

(c)

(d)


5

Q. 31 t o Q. 90 car r y t w o mar k s each

31. Consider the system of simultaneous equat ions

x + 2y + z = 6

2x + y + 2z = 6

x + y + z = 5

This system has

(a) unique solut ion

(b) infinite number of solut ions

(c) no solut ion

(d) exact ly two solut ions

32. The area enclosed between the parabola y = x2

and the straight l ine y = x is

(a) 1/8 (b) 1/6

(c) 1/3 (d) 1/2

33. The sol u t i on of t he di f fer ent i al equat i on

dydx

y 2 0 is

(a) yx c

1

(b) yx

c

3

3

(c) cex

(d) unsolvable as equat ion is non-l inear

34. The vector field F x i y j (where i j

and are

unit vectors) is

(a) divergence free, but not ir rotat ional

(b) ir rotat ional, but not divergence free

(c) divergence free and ir rotat ional

(d) neither divergence free nor ir rotat ional

35. Laplace t ransform of the funct ion sin t is

(a)s

s2 2

(b)

s2 2

(c)s

s2 2

(d)

s2 2

36. A box contains 5 black and 5 red balls. Two ballsare randomly picked one after another from thebox, without replacement. The probabil i ty forboth balls being red is

(a) 1/90

(b) 1/5

(c) 19/90

(d)

37. A truss consists of hor izontal members (AC, CD,DB and EF) and ver t ical members (CE and DE)having length l each. The members AE, DE andBF are incl ined at 45° to the hor izontal. For theuniformly dist r ibuted load "P" per unit length onthe member EF of the t russ shown in figure givenbelow, the force in the member CD is

(a)pl2

(b) pl

(c) 0 (d)23pl

38. A bullet of mass "m" travels at a very high velocity (as shown in the figure) and gets embeddedinside the block of mass “M” init ial ly at rest on arough hor izontal floor. The block with the bulletis seen to move a distance "s" along the floor.Assuming µ to be the coefficient of k inetic fr ict ionbetween the block and the floor and "g" theaccelerat ion due to gravity what is the velocity of the bullet ?

(a)M

m

mgs2

(b)M

m

mgs2

(c) (M m

mgs

)2

(d)Mm

gs2


6

39. A simply suppor ted lateral ly loaded beam wasfound to deflect more than a specified value. Whichof t he fol l owing measur es wi l l r educe t hedeflect ion ?

(a) Increase the area moment of iner t ia

(b) Increase the span of the beam

(c) Select a di ffer ent mater ial having l essermodulus of elast icity

(d) Magnitude of the load to be increased

40. A shaft subjected to torsion exper iences a pureshear st ress on the sur face. The maximumpr incipal st ress on the sur face which is at 45° tothe axis wil l have a value

(a) cos 45°

(b) 2 cos 45°

(c) cos2 45°

(d) 2 sin 45° cos 45°

41. For a cer tain engine having an average speed of1200 rpm, a flywheel approximated as a solid disc,is required for keeping the fluctuat ion of speedw i t h i n 2% abou t t he aver age speed. Thefluctuat ion of k inet ic energy per cycle is found tobe 2kJ. What is the least possible mass of theflywheel i f i ts diameter is not to exceed 1m ?

(a) 40 kg

(b) 51 kg

(c) 62 kg

(d) 73 kg

42. A flexible rotor-shaft system compr ises of a 10 kgrotor disc placed in the middle of a mass-less shaftof diameter 30mm and length 500 mm betweenbear ings (shaft is being taken mass-less as theequivalent mass of the shaft is included in therotor mass) mounted at the ends. The bear ingsar e assumed t o simulat e simply suppor t edboundary condit ions. The shaft is made of steelfor which the value of E is 2.1 × 1011 Pa. What isthe cr i t ical speed of rotat ion of the shaft ?

(a) 60 Hz

(b) 90 Hz

(c) 135 Hz

(d) 180 Hz

43. Square key of side “d/4” each and length l is usedto t ransmit torque “T” from the shaft of diameter“d” to the hub of a pul ley. Assuming the length ofthe key to be equal to the thickness of the pulley,the average shear st ress developed in the key isgiven by

(a)4Tld

(b)16

2T

ld

(c)8

2T

ld

(d)16

3T

d

44. In a band brake the rat io of t ight side band tensionto the tension on the slack side is 3. I f the angleof over lap of band on the dr um is 180° t hecoefficient of fr ict ion required between drum andthe band is

(a) 0.20 (b) 0.25

(c) 0.30 (d) 0.35

45. A water container is kept on a weighing balance.Water from a tap is fal l ing ver t ical ly into thecontainer with a volume flow rate of Q; the velocityof the water when it hits the water sur face is U.At a par t icular instant of t ime the total mass ofthe container and water is m. The force registeredby the weighing balance at this instant of t ime is

(a) mg + QU

(b) mg + 2 QU

(c) mg + QU2/2

(d) QU2/2

46. I n a counter flow heat exchanger, for the hot fluidt he heat capaci t y = 2 k J/k g°K , mass f l owrate = 5 kg/s, inlet temperature = 150°C, out lettemperature = 100°C. For the cold fluid, heatcapacity = 4 kJ/kg K, mass flow rate = 10 kg/s,i n let temper at ur e = 20°C. Neglect i ng heatt r ansfer t o t he su r r oundi ngs, t he ou t l ettemperature of the cold fluid in °C is

(a) 7.5 (b) 32.5

(c) 45.5 (d) 70.0


7

47. Air flows through a ventur i and into atmosphere.Air density is ; atmospheric pressure is Pa; throatdiameter is Dt; exit diameter is D and exit velocityis U . The thr oat i s connected t o a cyl i ndercontaining a fr ict ionless piston at tached to aspr ing. The spr ing constant is k. The bot tomsur face of the piston is exposed to atmosphere.Due to the flow, the piston moves by distance x.Assuming incompressible fr ict ionless flow, x is

(a) (U2/2k) Ds2

(b) ( / ) UD

DD2

2

228 1k

ts

FHG

IKJ

(c) ( / ) UD

DD2

2

222 1k

ts

FHG

IKJ

(d) ( / ) UD

DD2

4

428 1k

ts

FHG

IKJ

48. Consider a laminar boundary layer over a heatedflat plate. The free stream velocity is U. At somedistance x from the leading edge the veloci tyboundary layer thickness is v and the thermalboundary layer thickness is T. I f the Prandt lnumber is greater than 1, then

(a) v > T

(b) T > v

(c) v T ~ (U x)– 1/2

(d) v T ~ x– 1/2

49. Consider ing the relat ionship TdS = dU + pdVbetween the entropy (S), internal energy (U),pressure (p), temperature (T) and volume (V),which of the fol lowing statements is cor rect ?

(a) I t is applicable only for a reversible process

(b) For an ir reversible process, TdS > dU + pdV

(c) I t is val id only for an ideal gas

(d) I t is equivalent to 1 law, for a r ever sibleprocess

50. I n a gas turbine, hot combust ion products witht he speci f i c heat s Cp= 0.98 k J /k gK , andCv = 0.7538 kJ/kg K enter the turbine at 20 bar,1500°K and exit at 1 bar. The isoentropic efficiencyof the turbine is 0.94. The work developed by theturbine per kg of gas flow is

(a) 689.64 kJ/kg

(b) 794.66 kJ/kg

(c) 1009.72 kJ/kg

(d) 1312.00 kJ/kg

51. An automobile engine operates at a fuel air rat ioof 0.05, volumetr ic efficiency of 90% and indicatedthermal efficiency of 30%. Given that the calor ificvalue of the fuel is 45 MJ/kg and the density ofair at intake is 1 kg/m3, t he indicated meaneffect ive pressure for the engine is

(a) 6.075 bar

(b) 6.75 bar

(c) 67.5 bar

(d) 243 bar

52. For an engine operating on air standard Otto cycle,the clearance volume is 10% of the swept volume.The specific heat ratio of air is 1.4 The air standardcycle efficiency is

(a) 38.3% (b) 39.8%

(c) 60.2% (d) 61.7%

53. A centr ifugal pump running at 500 rpm and at itsmaximum efficiency is del iver ing a head of 30 mat a flow rate of 60 l i t res per minute. I f the rpmis changed to 1000, then the head H in metresand flow rate Q in li t res per minute at maximumefficiency are est imated to be

(a) H = 60, Q = 120

(b) H = 120, Q = 120

(c) H = 60, Q = 480

(d) H = 120, Q = 30

54. Hardness of steel great ly improves with

(a) annealing (b) cyaniding

(c) normalising (d) temper ing

55. With a sol idificat ion factor of 0.97 ×976 s/m2, thesolidificat ion t ime (in seconds) for a spher icalcast ing of 200 mm diameter is

(a) 539 (b) 1078

(c) 4311 (d) 3233


8

56. A shell of 100 mm diameter and 100 mm heightwith the corner radius of 0.4 mm is to be producedby cup drawing. The required blank diameter is

(a) 118 mm

(b) 161 mm

(c) 224 mm

(d) 312 mm

57. A brass bi l let is to be extruded from its init ialdi amet er of 100mm t o a f i nal di amet er of50mm. The working temperature of 700°C andthe extr usion constant is 250M Pa. The forcerequired for extrusion is

(a) 5.44 MN

(b) 2.72 MN

(c) 1.36 MN

(d) 0.36 MN

58. A metal disc of 20 mm diameter is to be punchedfrom a sheet of 2 mm thickness. The punch andthe die clearance is 3%. The requir ed punchdiameter is

(a) 19.88 mm

(b) 19.94 mm

(c) 20.06 mm

(d) 20.12 mm

59. A batch of 10 cut t ing tools could produce 500components while working at 50 rpm with a toolfeed of 0.25 mm/rev and depth of cut of 1 mm. Asimilar batch of 10 tools of the same specificat ioncould produce 122 components while working at80 rpm with a feed of 0.25 mm/rev and 1 mmdepth of cut . How many components can beproduced with one cut t ing tool at 60 rpm ?

(a) 29 (b) 31

(c) 37 (d) 42

60. A threaded nut of M16, ISO metr ic type, having2mm pitch with a pitch diameter of 14.701 mm isto be checked for i ts pitch diameter using two orthree numbers of bal ls or rol lers of the fol lowingsizes

(a) Rollers of 2 mm

(b) Rollers of 1.155 mm

(c) Balls of 2 mm

(d) Balls of 1.155 mm

61. Two sl ip gauges of 10 mm width measur ing1.000 mm and 1.002 mm are kept side by side incontact with each other lengthwise. An opt icalflat is kept rest ing on the sl ip gauges as shown inthe figure. Monochromat ic l ight of wavelength0.0058928 mm is used in the inspect ion. The totalnumber of st raight fr inges that can be observedon both sl ip gauges is

(a) 2 (b) 6

(c) 8 (d) 13

62. A par t shown in the figure is machined to thesizes given below

P = 35.00 ± 0.08 mm

Q = 12.00 ± 0.02 mm

R = 13 00 0 020 04. .

. mm

With 100% confidence, the resultant dimensionW wil l have the specificat ion

(a) 9.99 ± 0.03 mm

(b) 9.99 ± 0.13 mm

(c) 10.00 ± 0.03 mm

(d) 10.00 ± 0.13 mm

63. Two machines of the same product ion rate areavailable for use. On machine 1, the fixed cost isRs. 100 and the var iable cost is Rs. 2 per pieceproduced. The cor responding numbers for themachine 2 are Rs. 200 and Re. 1 respect ively. Forcer tain strategic reasons both the machines areto be used concurrently. The sale pr ice of the first800 units is Rs. 3.50 per unit and subsequent ly i tis only Rs. 3.00. The breakeven product ion ratefor each machine is

(a) 75 (b) 100

(c) 150 (d) 600


9

64. A resident ial school st ipulates the study hours as8.00 pm to 10.30 pm. War den makes randomchecks on a cer tain student 11 occasions a daydur ing the study hours over a per iod of 10 daysand observes that he is studying on 71 occasions.Using 95% confidence interval, the est imatedminimum hours of his study dur ing that 10 dayper iod is

(a) 8.5 hours

(b) 13.9 hours

(c) 16.1 hours

(d) 18.4 hours

65. The sale of cycles in a shop in four consecut ivemonths are given as 70, 68, 82, 95. Exponent iallysmoothing aver age method wi th a smoothingfactor of 0.4 is used in forecast ing. The expectednumber of sales in the next month is

(a) 59

(b) 72

(c)

(d) 136

66. Market demand for spr ings is 8,00,000 per annum.A company purchases these spr ings in lots andsells them. The cost of making a purchase orderis Rs. 1,200. The cost of storage of spr ings is Rs.120 per stored piece per annum. The economicorder quant ity is

(a) 400

(b) 2,828

(c) 4,000

(d) 8,000

67. A manufacturer produces two types of products,1 and 2, at pr oduct i on l evel s of x1 and x2respect ively. The profi t is given is 2x1 + 5x2. Theproduct ion constraints are

x1 + 3x2 40

3x1 + x2 24

x1 + x2 10

x1 > 0, x2 > 0

The maxi mum pr of i t whi ch can meet t heconstraints is

(a) 29 (b) 38

(c) 44 (d) 75

68. A Project consists of act ivit ies A to M shown inthe net in the fol lowing figure with the durat ionof the act ivit ies marked in days

The project can be completed

(a) between 18, 19 days

(b) between 20, 22 days

(c) between 24, 26 days

(d) between 60, 70 days

69. Match the fol lowing

P Cur tis 1 React ion steam turbine

Q Rateau 2 Gas turbine

R Kaplan 3 Velocity compounding

S Francis 4 Pressure compounding

5 Impulse water turbine

6 Axial turbine

7 Mixed flow turbine

8 Centr ifugal pump

(a) (b) (c) (d)

P – 2 P – 3 P – 1 P – 3

Q – 1 Q – 1 Q – 3 Q – 4

R – 7 R – 5 R – 1 R – 7

S – 6 S – 7 S – 5 S – 6

70. Match the fol lowing

Wor k mater i al Type of joi n i ng

P Aluminium 1 Submerged Arc Welding

Q Die Steel 2 Soldering

R Copper Wire 3 Thermit Welding

S Titanium sheet 4 Atomic Hydrogen Welding

5 Gas Tungsten Arc Welding

6 Laser Beam Welding

(a) (b) (c) (d)

P – 2 P – 6 P – 4 P – 5

Q – 5 Q – 3 Q – 1 Q – 4

R – 1 R – 4 R – 6 R – 2

S – 3 S – 4 S – 2 S – 6


10

Dat a for Q. 71 – 72 ar e gi ven below.Sol ve t he pr oblems and choose cor r ect answer s.

A reel of mass “m” and radius of gyrat ion “k” is roll ingdown smoothly from rest with one end of the threadwound on it held in the ceiling as depicted in the figure.Consider the thickness of the thread and its massnegligible in compar ison with the radius “ r ” of thehub and the reel mass “m” . Symbol “g” representsthe accelerat ion due to gravity.

71. The l inear accelerat ion of the reel is

(a)gr

r k

2

2 2( )(b)

gk

r k

2

2 2( )

(c)grk

r k( )2 2 (d)mgr

r k

2

2 2( )

72. The tension in the thread is

(a)mgr

r k

2

2 2( )(b)

mgrk

r k( )2 2

(c)mgk

r k

2

2 2( )(d)

mg

r k( )2 2

Dat a for Q. 73 – 74 ar e gi ven below. Sol ve t hepr oblems and choose cor r ect answ er s.

The state of st ress at a point “P” in a two dimensionalloading is such that the Mohr ’s circle is a point locatedat 175 MPa on the posit ive normal st ress axis.

73. Determine the maximum and minimum principalstresses respect ively from the Mohr ’s circle

(a) + 175 MPa, – 175MPa

(b) +175 MPa, + 175 MPa

(c) 0, – 175 MPa

(d) 0, 0

74. Det er mine t he di r ect ions of maximum andminimum principal stresses at the point “P” fromhe Mohr ’s circle

(a) 0, 90° (b) 90°, 0

(c) 45°, 135° (d) al l directions

Dat a for Q. 75 – 76 ar e gi ven below.Sol ve t he pr oblems and choose cor r ect answer s.

The circular disc shown in i ts plan view in the figurerotates in a plane paral lel to the hor izontal planeabout the point O at a uniform angular velocity .Two other points A and B are located on the l ineOZ at distances r A and r B from O respect ively.

75. The velocity of point B with respect to point A is avector of magnitude

(a) 0

(b) (r B – r A) and di r ect ion opposi te to thedirect ion of mot ion of point B

(c) (r B – r A) and direct ion same as the direct ionof mot ion of point B

(d) (r B – r A) and direct ion being from O to Z.

76. The accelerat ion of point B with respect to pointA is a vector of magnitude

(a) 0

(b) (r B – r A) and direct ion same as the direct ionof mot ion of point B

(c) 2 (r B – r A) and di r ect ion opposi te to bedirect ion of mot ion of point B

(d) 2(r B – r A) and direct ion being from Z to O.


A uniform r igid slenderbar of mass 10 kg, hinged atthe left end is suspended with the help of spr ing anddamper ar rangement as shown in the figure whereK = 2 kN/m, C = 500 Ns/m and the st i ffness of thetorsional spr ing K is 1kN/m/rad. Ignore the hingedimensions.

77. The un-damped natural frequency of oscil lat ionsof the bar about the hinge point is

(a) 42.43 rad/s (b) 30 rad/s

(c) 17.32 rad/s (d) 14.14 rad/s


11


78. The damping coefficient in the vibrat ion equationis given by

(a) 500 Nms/rad (b) 500 N/(m/s)

(c) 80 Nms/rad (d) 80 N/(m/s)

The overall gear ratio in a 2 stage speed reductiongear box (w i t h al l spu r gear s) i s 12.The input and output shafts of the gear box arecoll inear. The countershaft which is paral lel tothe input and output shafts has a gear (Z2 teeth)and pinion (Z3 = 15 teeth) to mesh with pinion(Z1 = 16 t eeth) on the input shaft and gear(Z4 teeth) on the output shaft respect ively. I t wasdecided to use a gear rat io of 4 with 3 module inthe first stage and 4 module in the second stage.

79. Z2 and Z4 are

(a) 64 and 45 (b) 45 and 64

(c) 48 and 60 (d) 60 and 48

80. The centre distance in the second stage is

(a) 90 mm (b) 120 mm

(c) 160 mm (d) 240 mm


A syr inge with a fr ict ionless plunger contains waterand has at i ts end a 100 mm long needle of 1 mmdiameter. The internal diameter of the syr inge is10 mm. Water density is 1000 kg/m3. The plunger ispushed in at 10 mm/s and the water comes out as a jet

81. Assuming ideal f low, the for ce F in newtonsrequired on the plunger to push out the water is

(a) 0 (b) 0.04

(c) 0.13 (d) 1.15

82. Neglect losses in the cyl inder and assume ful lydeveloped laminar viscous flow throughout theneedle; the Darcy fr ict ion factor is 64/Re. WhereRe is t he Reynolds number. Gi ven t hat theviscosity of water is 1.0 × 10– 3 kg/s m, the force Fin newtons required on the plunger is

(a) 0.13 (b) 0.16

(c) 0.3 (d) 4.4


Heat is being t ransfer red by convect ion from waterat 48°C to a glass plate whose sur face that is exposedto the water is at 40°C. The thermal conduct ivity ofwater is 0.6 W/mK and the thermal conduct ivity ofgl ass i s 1.2 W/mK . The spat i al gr adi en t oftemperature in the water at the water -glass inerfaceis dT/dy =1 × 104 K /m.

83. The value of the temperature gradient in the glassat the water -glass inter face in K /m is

(a) – 2 × 104 (b) 0.0

(c) 0.5 × 104 (d) 2 × 104

84. The heat t ransfer coefficient h in W/m2 K is

(a) 0.0 (b) 4.8

(c) 6 (d) 750


Nitrogen gas (molecular weight 28) is enclosed in acyl inder by a piston, at the init ial condit ion of 2 bar,298°K and 1 m3. I n a particular process, the gas slowlyexpands under isothermal condition, unt il the volumebecomes 2m3. H eat exchange occur s wi t h t heatmosphere at 298°K dur ing this process.

85. The work interact ion for the Nit rogen gas is

(a) 200 kJ (b) 138.6 kJ

(c) 2 kJ (d) – 200 kJ

86. The entropy change for the Universe dur ing theprocess in kJ/K is

(a) 0.4652 (b) 0.0067

(c) 0 (d) – 0.6711


A refr igerator based on ideal vapour compression cycleoperates between the temperature limits of – 20°C and40°C. The r efr i ger ant ent er s t he condenser assaturated vapour and leaves as saturated liquid. Theenthalpy and entropyvalues for saturated l iquid andvapour at these temperatures are given in the tablebelow.


12

T(°C) hf (kJ/kg) hg(kJ/kg) sf(kJ/kg K) sg(kJ/kg K)

– 20 20 180 0.07 0.7366

40 80 200 0.3 0.67

87. I f refr ierant circulat ion rate is 0.025 kg/s, therefr igerat ion effect is equal to

(a) 2.1 kW (b) 2.5 kW

(c) 3.0 kW (d) 4.0 kW

88. The COP of the refr igerator is

(a) 2.0 (b) 2.33

(c) 5.0 (d) 6.0

Dat a for Q. 89 – 90 ar e gi ven below. Sol ve t hepr oblems and choose cor r ect answ er s.A cyl inder is turned on a lathe wi th or thogonalmachining pr inciple. Spindle rotates at 200 rpm. Theaxial feed rate is 0.25 mm per revolut ion. Depth ofcut is 0.4 mm. The rake angle is 10°° In the analysisit is found that the shear angle is 27.75°.

89. The thickness of the produced chip is

(a) 0.511 mm (b) 0.528 mm

(c) 0.818 mm (d) 0.846 mm

90. I n the above problem, the coefficient of fr ict ionat the chip tool inter face obained using Earnestand Merchant theory is

(a) 0.18 (b) 0.36

(c) 0.71 (d) 0.908

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