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CONTENTS

VOL 1

ENGINEERING MECHANICS AM 1

Equilibrium of Forces

AM 3

AM 2

Structure

AM 40

AM 3 AM 4

Friction Virtual Work

AM 81 AM 117

AM 5 AM 6

Kinematics of Particle Kinetics of Particles

AM 128 AM 157

AM 7

Plane Kinematics of Rigid body

AM 190

AM 8

Plane Kinetics of Rigid body

AM 206

STRENGTH OF MATERIALS SM 1

Stress and Strain

SM 3

SM 2 SM 3

Axial Loading Torsion

SM 41 SM 86

SM 4 SM 5

Shear Force and Bending Moment Transformation of Stress and Strain

SM 118 SM 179

SM 6

Design of Beams and Shafts

SM 226

SM 7 SM 8

Deflection of Beams and Shafts Column

SM 270 SM 315

SM 9

Energy Methods

SM 354

THEORY OF MACHINES TM 1

Analysis of Plane Mechanism

TM 3

TM 2

Velocity and Acceleration

TM 20

TM 3 TM 4

Dynamic Analysis of Slider - Crank and Cam Gear - Trains

TM 38 TM 59

TM 5 TM 6

Fly Wheel Vibration

TM 91 TM 109

MACHINES DESIGN MD 1 MD 2

Static and Dynamic Loading Joints

MD 3 MD 22

MD 3

Shaft and Shaft Components

MD 54

MD 4 MD 5

Spur Gears Bearings

MD 71 MD 88

MD 6

Clutch and Brakes

MD 105

CONTENTS

VOL 2

FLUID MECHANICS FM 1

Basic Concepts and Properties of Fluids

FM 3

FM 2

Pressure and Fluid Statics

FM 33

FM 3 FM 4

Fluid Kinematics & Bernouli Equation Flow Analysis Using Control Volumes

FM 80 FM 124

FM 5 FM 6

Flow Analysis Using Differential Method Internal Flow

FM 172 FM 211

FM 7

External Flow

FM 253

FM 8 FM 9

Open Channel Flow Turbo Machinery

FM 289 FM 328

HEAT TRANSFER HT 1 HT 2

Basic Concepts & Modes of Heat-Transfer Fundamentals of Conduction

HT 3 HT 34

HT 3 HT 4

Steady Heat Conduction Transient Heat Conduction

HT 63 HT 94

HT 5

Fundamentals of Convection

HT 114

HT 6 HT 7

Free and Force Convection Radiation Heat Transfer

HT 129 HT 155

HT 8

Heat Exchangers

HT 181

THERMODYNAMICS TD 1

Basic Concepts and Energy Analysis

TD 3

TD 2

Properties of Pure Substances

TD 28

TD 3 TD 4

Energy Analysis of Closed System Mass and Energy Analysis of Control Volume

TD 52 TD 76

TD 5 TD 6

Second Law of Thermodynamics Entropy

TD 106 TD 136

TD 7 TD 8

Gas Power Cycles Vapor and Combined Power Cycles

TD 166 TD 199

TD 9

Refrigeration and Air Conditioning

TD 226

***********

CONTENTS MANUFACTURING PROCESS

INDUSTRIAL ENGINEERING

OPERATION RESEARCH

VOL 3

CONTENTS

VOL 4

ENGINEERING MATHEMATICS EM 1

Linear Algebra

EM 1

EM 2

Differential Calculus

EM 24

EM 3 EM 4

Integral Calculus Directional Derivatives

EM 46 EM 67

EM 5 EM 6

Differential Equation Complex Variable

EM 79 EM 103

EM 7

Probability and Statistics

EM 123

EM 8

Numerical Methods

EM 142

VERBAL ANALYSIS VA 1

Synonyms

VA 1

VA 2 VA 3

Antonyms Agreement

VA 16 VA 26

VA 4 VA 5

Sentence Structure Spellings

VA 37 VA 58

VA 6

Sentence Completion

VA 87

VA 7 VA 8

Word Analogy Reading Comprehension

VA 111 VA 135

VA 9 VA 10

Verbal Classification Critical Reasoning

VA 148 VA 153

VA 11

Verbal Deduction

VA 168

QUANTITATIVE ANALYSIS QA 1 QA 2

Number System Surds, Indices and Logarithm

QA 1 QA 14

QA 3 QA 4

Sequences and Series Average, Mixture and Alligation

QA 28 QA 44

QA 5 QA 6

Ratio, Proportion and Variation Percentage

QA 59 QA 75

QA 7

Interest

QA 89

QA 8 QA 9

Time, Speed & Distance Time, Work & Wages

QA 99 QA 112

QA 10

Data Interpretation

QA 126

QA 11

Number Series

QA 145

SOLVED PAPER SP 1

Engineering Mathematics

SP 3

SP 2

Engineering Mechanics

SP 65

SP 3 SP 4

Strength of Materials Theory of Machines

SP 90 SP 138

SP 5 SP 6

Machine Design Fluid Mechanics

SP 189 SP 218

SP 7

Heat Transfer

SP 265

SP 8 SP 9

Thermodynamics Refrigeration and Air-Conditioning

SP 303 SP 358

SP 10 SP 11

Manufacturing Engineering Industrial Engineering

SP 375 SP 448

SP 12

General Aptitude

SP 496

SM 1 STRESS AND STRAIN

Common Data For Q. 1 and 2 A long wire of tungsten (gT = 190 kN/m3 ) hangs vertically from a high-altitude balloon, is shown in figure.

SM 1.1

SM 1.2

If the ultimate strength (or breaking strength) is 1500 MPa, the greatest length that it can have without breaking, is (A) 3950 m (B) 7900 m (C) 1975 m (D) 790 m If the same wire hangs from a ship at sea (gsea water = 10 kN/m3), the greatest length is (A) 8300 m (B) 2075 m (C) 7500 m (D) 3750 m

Common Data For Q. 3 and 4 The 650 N load is applied along the centroidal axis of the member as shown in figure. Take q = 60c.

SM 1.3

The resultant internal normal and shear forces in the member at section a - a, which passes through point A , is (A) N = 0 , V = 0 (B) N = 50 N , V = 650 N (C) N = 0, V = 650 N (D) N = 650 N , V = 0

GATE Mechanical Engineering in 4 Volume NODIA SM 4

SM 1.4

Demo Ebook Stress and Strain

(D) N = 325 N , V = 1126 N

In the figure shown, link BC of 6 mm thickness is made of a steel with a 450 MPa ultimate strength in tension. If the structure is being designed to support a 20 kN load P with a factor of safety of 3, its width w should be

(A) 13.9 mm (C) 27.8 mm SM 1.6

SM 1

The resultant internal normal and shear forces in the member at section b - b, which passes through point A , is (A) N = 325 N , V = 563 N (B) N = 650 N , V = 563 N (C) N = 563 N , V = 325 N

SM 1.5

Page 4

(B) 55.6 mm (D) 41.7 mm

In figure shown, the two-member frame is subjected to the distributed loading. Member CB has a square cross section of 35 mm on each side and take w = 8 kN/m . The average normal stress and average shear stress acting at section b-b, are

(A) s = 4.41 MPa , t = 5.88 MPa (C) s = 8.82 MPa , t = 5.88 MPa

(B) s = 11.76 MPa , t = 4.41 MPa (D) s = 5.88 MPa , t = 4.41 MPa

Common Data For Q. 8 and 9 A solid bar of circular cross section has a hole of diameter d/4 drilled laterally through the center of the bar as shown in figure below. The allowable average tensile stress on the net cross section of the bar is sallow .

SM 1.7

The formula for the allowable load Pallow that the bar can carrying in tension, is (B) 0.54d 2 # sallow (A) 0.27d 2 # sallow (D) 0.54d # sallow (C) 0.675d 2 # sallow

GATE MCQ Mechanical Engineering (4 volumes) Fully Solved by NODIA and COMPANY

GATE Mechanical Engineering in 4 Volume NODIA SM 1

SM 1.8

SM 1.11

SM 1.12

Stress and Strain

SM 5

(D) 35 kN

An axial load P is supported by a short W 250 # 0.67 column of cross-sectional area A = 8580 mm 2 and is distributed to a concrete foundation by a square plate as shown in figure. If the average normal stress in the column must not exceed 150 MPa and the bearing stress on the concrete foundation must not exceed 12.5 MPa, the side a of the plate which will provide the most economical and safe design is

(A) 103 mm (C) 8.6 mm SM 1.10

Page 5

If the bar is made of brass with diameter d = 40 mm and sallow = 80 MPa, the value of Pallow is (A) 86.5 kN (B) 70 kN (C) 172 kN

SM 1.9

Demo Ebook

(B) 321 mm (D) 160 mm

The column shown in figure, is subjected to an axial force of 8 kN at its top. What is the average normal stress acting at section a -a ?

(A) 1.82 MPa

(B) 3.64 MPa

(C) 0.91 MPa

(D) 2.73 MPa

A round bar of 10 mm diameter is made of aluminum alloy, as shown in figure. When the bar is stretched by axial forces P , its diameter decreases by 0.016 mm . The magnitude of the load P is (Take E = 72 GPa , n = 0.33 , sY = 480 MPa )

(A) 27.4 kN

(B) 54.8 kN

(C) 13.7 kN

(D) 37.7 kN

A steel bar of length 2.5 m with a square cross section 100 mm on each side is subjected to an axial tensile force of 1300 kN as shown in figure. The increase in

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GATE Mechanical Engineering in 4 Volume NODIA SM 6

Demo Ebook

Page 6

Stress and Strain

SM 1

volume of the bar is (Take sY = 250 MPa, E = 200 GPa , n = 0.3 )

(A) 8112 mm3 (C) 3245 mm3

(B) 4868 mm3 (D) 6490 mm3

Common Data For Q.14 and 15 Three steel plates, each 16 mm thick, are joined by two 20 mm diameter rivets as shown in the figure.

SM 1.13

If the load P = 50 kN , the largest bearing stress acting on the rivets is (A) 39 MPa (B) 156 MPa (C) 78 MPa (D) 117 MPa

SM 1.14

If the ultimate shear stress for the rivets is 180 MPa, what force Pu is required to cause the rivets to fail in shear ? (Disregard friction between the plates.) (B) 57 kN (A) 170 kN (C) 226 kN

SM 1.15

SM 1.16

(D) 113 kN

The small block of 5 mm thickness is shown in figure. If the stress distribution at the support developed by the load varies as shown, the force F applied to the block and the distance d to where it is applied, respectively, are

(A) 220 mm

(B) 110 mm

(C) 165 mm

(D) 55 mm

The bar has a cross-sectional area of (400 # 10- 6) m 2. If it is subjected to a uniform axial distributed loading along its length and to two concentrated loads as shown in figure, the average normal stress in the bar as a function of x for

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GATE Mechanical Engineering in 4 Volume NODIA SM 1

Demo Ebook

Page 7

Stress and Strain

SM 7

0 < x # 0.5 m , is

(A) ^47.5 - 20.0x h MPa (C) ^47.5 + 20.0x h MPa

(B) 67.5x MPa (D) 27.5x MPa

Common Data For Q. 18 and 19 In the figure shown, a hollow box beam ABC of length L is supported at end A by a 20 mm diameter pin that passes through the beam and its supporting pedestals. The roller support at B is located at distance L/3 from end A.

SM 1.17

If load P is equal to 10 kN , the average shear stress in the pin is (A) 15.9 MPa (B) 31.8 MPa (C) 63.6 MPa

SM 1.18

If the wall thickness of the beam is equal to 12 mm , the average bearing stress between the pin and the box beam will be (A) 41.7 MPa (B) 125.1 MPa (C) 83.4 MPa

SM 1.19

(D) 7.95 MPa

(D) 20.85 MPa

Rods AB and BC shown in figure, have diameters of 4 mm and 6 mm, respectively. The vertical load of 8 kN is applied to the ring at B . If the average normal stress in each rod is equivalent then this stress will be

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GATE Mechanical Engineering in 4 Volume NODIA SM 8

Demo Ebook

Page 8

Stress and Strain

(A) 237 MPa (C) 474 MPa

SM 1

(B) 316 MPa (D) 158 MPa

Common Data For Q. 20 amd 21 A steel plate (g = 77 kN/m3) of dimensions 2.5 # 1.2 # 0.1 m is hoisted by a cable sling that has a clevis at each end as shown in figure. The pins through the clevises are 18 mm in diameter and are located 2.0 m apart. Each half of the cable is at an angle of 32c to the vertical.

SM 1.20

For above conditions, the average shear stress taver in the pins will be (B) 6.7 MPa (A) 8.9 MPa (C) 13.4 MPa (D) 26.8 MPa

SM 1.21

The average bearing stress sb between the steel plate and the pins is (B) 15.2 MPa (A) 22.7 MPa (C) 7.57 MPa

SM 1.22

(D) 30.3 MPa

Two solid cylindrical rods AB and BC are welded together at B and loaded as shown in figure. If the average normal stress must not exceed 150 MPa in either rod, the smallest allowable values of the diameters d1 and d 2 are

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GATE Mechanical Engineering in 4 Volume NODIA SM 1

Demo Ebook

Page 9

Stress and Strain

SM 9

(A) d1 = 45.2 mm , d 2 = 20.1 mm (C) d1 = 20.1 mm , d 2 = 45.2 mm SM 1.23

SM 1.24

Members AB and AC of the truss as shown, consist of bars of square cross section made of the same alloy. It is known that a 20 mm square bar of the same alloy was tested to failure and that an ultimate load of 120 kN was recorded. If a factor of safety of 3.2 is to be achieved for both bars, the required dimension of the cross section of the bar AB is

(A) a = 27 mm

(B) a = 12 mm

(C) a = 13.5 mm

(D) a = 6 mm

The two steel members are joined together using a 60c scarf weld as shown in figure. The average normal and average shear stress resisted in the plane of the weld are

(A) savg = 8 MPa , tavg = 4.62 MPa (C) savg = 4.62 MPa , tavg = 16 MPa SM 1.25

(B) d1 = 22.6 mm , d 2 = 40.2 mm (D) d1 = 40.2 mm , d 2 = 22.6 mm

(B) savg = 4.62 MPa , tavg = 8 MPa (D) savg = 16 MPa , tavg = 4.62 MPa

A steel pipe of 300 mm outer diameter is fabricated from 6 mm thick plate by welding along a helix which forms an angle of 25c with a plane perpendicular to the axis of the pipe. If a 250 kN axial force P is applied to the pipe, the normal and shearing stresses in directions respectively normal and tangential to the weld are

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GATE Mechanical Engineering in 4 Volume NODIA SM 10

Demo Ebook Stress and Strain

(A) - 18.5 MPa , 17.28 MPa (C) - 18.5 MPa , 34.56 MPa SM 1.26

SM 1

(B) - 37.1 MPa , 34.56 MPa (D) - 37.1 MPa , 17.28 MPa

A 6 kN load is supported by two wooden members of 75 mm # 125 mm uniform rectangular cross section which are joined by the simple glued scarf splice as shown in figure. The normal and shearing stresses in the glued splice respectively, are

(A) 565 kPa , 206 kPa (C) 565 kPa , 103 kPa SM 1.27

Page 10

(B) 282 kPa, 206 kPa (D) 282 kPa, 103 kPa

In the figure shown, the wooden members A and B are to be joined by plywood splice plates which will be fully glued on the surface in contact. If the clearance between the ends of the members is to be 8 mm and the average shearing stress in the glue is not to exceed 800 kPa , the smallest allowable length L will be

(A) 308 mm

(B) 150 mm

(C) 300 mm

(D) 292 mm

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GATE Mechanical Engineering in 4 Volume NODIA SM 1

SM 1.28

SM 1.29

Page 11

Stress and Strain

SM 11

In the figure shown, the frame is subjected to the distributed loading of 2 kN/m. What is the required diameter of the pins at A and B if the allowable shear stress for the material is tallow = 100 MPa ? Both pins are subjected to double shear.

(A) d = 2.6 mm

(B) d = 7.8 mm

(C) d = 5.2 mm

(D) d = 10.4 mm

A specially designed wrench is used to twist a circular shaft by means of a square key that fits into slots (or keyways) in the shaft and wrench as shown in the figure. The shaft has diameter d, the key has a square cross section of dimensions b # b and the length of the key is c . The key fits half into the wrench and half into the shaft (i.e., the keyways have a depth equal to b/2). When a load P is applied at distance L from the center of the shaft, the formula for the average shear stress taver in the key is ( Hints : Disregard the effects of friction, assume that the bearing pressure between the key and the wrench is uniformly distributed)

PL 2 bc ^ d + b h 3 PL (C) bc ^2 d + bh

(A)

SM 1.30

Demo Ebook

2PL bc ^2d + b h 4 PL (D) bc ^2 d + b h (B)

The two wooden members shown in figure supports a 20 kN load, are joined by plywood splices fully glued on the surface in contact. The ultimate shearing stress in the glue is 2.8 MPa and the clearance between the members is 8 mm. If

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GATE Mechanical Engineering in 4 Volume NODIA SM 12

Demo Ebook

Page 12

Stress and Strain

SM 1

a factor of safety of 3.5 is to be achieved, the required length L of each splice is

(A) 216 mm (C) 200 mm SM 1.31

(C) 12.72 kN -m

(B) 8.48 kN- m (D) 4.24 kN -m

The cross section of an aluminium tube serving as a compression brace in the fuselage of a small airplane is shown in the figure. The outer diameter of the tube is d = 25 mm and the wall thickness is t = 2.5 mm . If the factors of safety with respect to the yield stress and the ultimate stress are 4 and 5 respectively, the allowable compressive force Pallow is (Take sY = 270 MPa , su = 310 MPa )

(A) 9.5 kN (C) 11.0 kN SM 1.33

(D) 104 mm

A torque T0 is transmitted between two flanged shafts by means of four 20 mm bolts as shown in figure. The diameter of the bolt circle is d = 150 mm . If the allowable shear stress in the bolts is 90 MPa , the maximum permissible torque will be

(A) 16.96 kN -m

SM 1.32

(B) 208 mm

(B) 12.0 kN (D) 13.7 kN

In the fi...