THEORY OF MACHINES I QUESTION BANK

UNIT-I

A] Theory Question Bank

Q. No Description

1 Define the following terms :

(i) Kinematic chain

(ii) Structure

(iii) Kinematic pair

(iv)Degree of freedom in Mechanism.

2 Define inversion of a mechanism. Explain with the

help of neat sketches inversions of double slider

crank chain. Give their applications.

3 Calculate the number of degree of freedom of the

mechanism As shown

4 Explain the following terms with suitable examples :

(i) Completely constrained motion

(ii) Incompletely constrained motion

(iii) Successfully constrained motion.

5 Explain with neat sketches ‘Swinging and Rocking

Mechanisms’.

6 What is the condition for correct steering? Explain

with neat sketch Ackermann steering gear

mechanism.

7 Describe the three kinds of lower pairs, giving a

sketch of each kind, and state the types of relative

motion that each

pair permits.

8 Explain with a neat sketch ‘Geneva Mechanism’.

9 Fill in the blanks with correct alternative and

rewrite the

complete sentences :

(i) Oldham’s coupling is the inversion

of.............................. .

(a) Four bar mechanism

(b) Crank and lever mechanism

(c) Single slider crank mechanism

(d) Double slider crank mechanism

(ii) ..........................number of pairs are associated

with quaternary

joint.

(a) 1

(b) 2

(c) 3

(d) 4

(iii) A combination of kinematic pairs, joined in

such a way

that the relative motion between the links is

completely

constrained, is called a........................... (a)

Structure

(b) Mechanism

(c) Kinematic Chain

(d) Inversion

10 What is meant by a ‘steering gear mechanism’? Why

is it necessary? Why are steering gear mechanisms

seen in four wheelers and not in two or three-

wheelers? Explain

11 Define the Following Term

i) Grashoff’s Law

ii) Structure

iii) Degree of Freedom

iv) Mechanism

12 Explain with neat sketch whitworth Quick Return

Mechanism

13 What is a condition of correct steering? With the

help of neat sketch explain the construction and

working of Davis Steering Gear mechanism

14 Define the following

i) Machine

ii) Kinematic Chain

iii) Kinematic Link

iv] Grashoff’s law

15 Explain the following terms with suitable examples:-

i] Completely constrained motion

ii] Incompletely constrained motion

iii] Successfully constrained motion

16 Write short note on

i) Pantograph along with its application.

ii) Scotch yoke mechanism

17 In a Oldham coupling, the distance between shaft

axes is 30 mm and speed of rotation is 600 rpm,

what is maximum speed of sliding of each tongue in

the slot?

18 Define:-

1. DOF of a body

2. DOF of a mechanism

19 Define and explain with neat sketches the various

types of constrained motions

20 Define kinematic pair and discuss various types of

kinematic pairs with examples.

21 State and explain Grubler criterion for mobility of a

planer mechanism with various applications using

lower pairs and higher pairs

22 Different mechanisms may be obtained by

inversions of the same kinematic chain. Explain the

meaning of this statement with all inversions of

single slider crank chain. Give practical application

of each inversion

23 With the help of neat sketch, explain Pecullier

straight line mechanism giving proof of the tracing

point describing exact straight line

24 Explain the working of Davis steering gear with the

help of a neat sketch. Find the inclination of track

arm in terms of wheel base and the distance

between the pivots of the axle in order to satisfy the

condition of steering.

25 Write short note on “Ackermann steering gear”

26 In a Davis steering gear the distance between the

pivots of the front axle is 120 cm and the wheel

base is 260 cm. When the vehicle is moving on a

straight path, find the inclination of track arms to

the vertical

27 A car using Ackermann steering gear has a wheel

base of 2.8m and a track of 1.5m. The track rod is

1.1m and the track arm is 0.15m. The distance

between the pivots of stub axle is 1.2m. Find the

radius of turning of inner wheels for correct

steering.

28 Write a short note on elliptical trammel. State and

explain the condition for which it will trace a circle

29 In case of an elliptical trammel, prove that any point

on the coupler rod traces perfect ellipse. Hence

locate that point on the coupler, which will trace

circle

30 Write a short note on Gnome engine

31 Compare ‘Davis’ and ‘Ackermann’ steering gear

mechanisms

32 In the Davis steering gear mechanism, the distance

between the pivots of the front axles is 1.2m. The

wheel base is 3m. When a vehicle is moving along a

straight path, find the inclination of the track arms

to the longitudinal axis, provided that the

mechanism has to satisfy the condition of correct

steering

33 In case of Davis steering gear mechanism:

1. The distance between the pivots of the front

axle = 1.5m

2. The wheel base = 5m

Find the inclination of the track arms to the

longitudinal axis, provided that the mechanism has

to satisfy the condition of correct steering

34 What is kinematic pair? Give its classification in

details.

35 Explain types of kinematic links with neat sketches

36 Explain types of kinematic joints with neat sketches

37 Explain Kutzbach criterion.

38 Differentiate between Machine and Mechanism

39 What is four bar chain mechanism? Explain any

one Inversion with neat sketch

40 Explain Beam engine with neat sketch

41 Explain Fourth Inversion of Single slider crank

mechanism with neat sketch

42 Explain Skotch yoke mechanism with neat sketch

43 Write a short note on Equivalent linkage of

mechanism


mechanism As shown in Fig


mechanism As shown in Fig


mechanism As shown


mechanism As shown


mechanism As shown


mechanism As shown

50 What are rigid and resistant bodies? Elaborate.

MCQ QUESTION BANK

Q. No Description

1 In a Kinematic chain, a quaternary joint is equivalent to:

(a) One binary joint (b) Two binary joints(c) Three binary joints (d)

Four binary joints

Ans. (c) when ‘l ’ number of links are joined at the same connection,

the joint is equivalent to

(L - 1) binary joints

2 A round bar A passes through the cylindrical hole in B as shown in the

given figure. Which one of the following statements is correct in this

regard?

a) The two links shown form a kinematic pair.

b) The pair is completely constrained.

c) The pair has incomplete constraint.

d) The pair is successfully constrained.

Ans. (c)

3 Consider the following statements

1. A round bar in a round hole form a turning pair.

2. A square bar in a square hole forms a sliding pair.

3. A vertical shaft in a footstep bearing forms a successful

constraint.

Of these statements

(a) 1 and 2 are correct

(b) 2 and 3 are correct

(c) 1 and 3 are correct

(d) 1, 2 and 3 are correct

Ans. (b)

4 Consider the following statements:

1. Lower pairs are more resistant than the higher pairs in a

plane mechanism.

2. In a 4-bar mechanism (with 4 turning pairs), when the link opposite to

the shortest link is fixed, a double rocker mechanism results.

Which of the statements given above is/are correct?

(a) Only 1 (b) Only 2 (c) Both 1 and 2 (d) Neither 1 nor 2

Ans. (c)

5 Consider the following pairs of parts:

1. Pair of gear in mesh

2. Belt and pulley

3. Cylinder and piston

4. Cam and follower

Among these, the higher pairs are

(a) 1 and 4 (b) 2 and 4 (c) 1, 2 and 3 (d) 1, 2 and 4

Ans. (a)

6 Which of the following is a higher pair?

(a) Belt and pulley (b) Turning pair (c) Screw pair (d) Sliding pair

Ans. (a) A higher pair have point or line contact.

7 Which of the following disciplines provides study of relative

motion between the parts of a machine

(a) theory of machines (b) applied mechanics (c)mechanisms (d)

kinetics

(e) kinematics

Ans: e

8 Which of the following is a lower pair

(a) ball and socket (b) piston and cylinder (c) cam and follower

(d) (a) and (b) above

(e) belt drive.

Ans: d

9 If two moving elements have surface contact in motion, such

pair is known as

(a) sliding pair (b) rolling pair

(c) surface pair (d) lower pair (e) higher pair.

Ans: e

10 The example of lower pair is

(a)shaft revolving in a bearing

(b)straight line motion mechanisms

(c)automobile steering gear

(d)all of the above

(e)none of the above.

Ans: d

11 Pulley in a belt drive acts as

(a)cylindrical pair (b)turning pair (c) rolling pair (d)sliding pair

(e)surface pair.

Ans: c

12 The example of rolling pair is

(a)bolt and nut (b)lead screw of a lathe (c)ball and socket joint (d)ball

bearing and roller bearing (e) all of the above.

Ans: d

13 A universal joint is an example of

(a)higher pair (b)lower pair (c)rolling pair (d)sliding pair (e)turning

pair.

Ans: b

14 The example of spherical pair is

(a)bolt and nut (b)lead screw of a lathe (c)ball and socket joint (d)ball

bearing and roller bearing (e)none of the above.

Ans: c

15 Cross head and guides form a

(a)lower pair (b)higher pair (c)turning pair (d)rolling pair (e)sliding

pair.

Ans: e

16 If there are L number of links in a mechanism then number of

possible inversions is equal to

(a)L+1

(b)L-1

(c)L

(d)L+2

(e)L-2.

Ans: c

17 The lower pair is a

(a)open pair (b)closed pair (c)sliding pair (d)point contact pair (e)does

not exist.

Ans: b

18 Which of the following would constitute a link

(a)piston, piston rings and gudgeon pin

(b)piston, and piston rod

(c)piston rod and cross head

(d)piston, crank pin and crank shaft

(e)piston, piston-rod and cross head.

Ans:e

19 Ackermann steering gear consists of

(a)sliding pairs

(b)turning pairs

(c)rolling pairs

(d)higher pairs

(e)lower pairs.

Ans: b

20 Oldham's coupling is the

(a)second inversion of double slider crank chain

(b)third inversion of double slider crank chain

(c)second inversion of single slider crank chain

(d)third inversion of slider crank chain

(e)fourth inversion of double slider crank chain.

Ans: b

21 The number of links in pantograph mechanism is equal to

(a) 2

(b) 3

(c) 4

(d) 5

(e) 6.

Ans:c

22 Rectangular bar in a rectangular hole is the following type of

pair

(a)completely constrained motion

(b) partially constrained motion

(c) incompletely constrained motion

(d) freely constrained motion

(e) none of the above.

Ans: a

23 Governor is used in automobile to

(a)decrease the variation of speed

(b)to control

(c)to control SN

(d)all of the above


Ans: c

24 Idler pulley is used

(a)for changing the direction of motion of the belt

(b)for applying tension

(c)for increasing -velocity ratio

(d)all of the above


Ans: b

25 The locus of a point on a thread unwound from a cylinder will

be

(a) a straight line

(b) a circle

(c) involute

(d) cycloid

(e) helix.

Ans: c

26 Throw of a cam is the maximum distance of the follower from

(a)base circle

(b)pitch circle

(c)root circle

(d)prime circle

(e)inner circle.

Ans: a

27 Kinematic pairs are those which have

(a)point or line contact between the two elements when in motion

(b)surface contact between the two elements when in motion

(c)elements of pairs not held together mechanically

(d)two elements that permit relative motion


Ans: d

28 A pantograph is a mechanism with

(a)lower pairs

(b)higher pairs

(c)rolling pairs

(d)turning pairs

(e)spherical pairs.

Ans: a

29 The approximate straight line mechanism is a

(a)four bar linkage

(b)6 bar linkage

(c)8 bar linkage

(d)3 bar linkage

(e)5 bar linkage.

Ans: a

30 Peaucellier mechanism has

(a)eight links

(b)six links

(c)four links

(d)twelve links

(e)five links.

Ans: a

31 Hart mechanism has

(a)eight links

(b)six links

(c)four links

(d)twelve links

(e)five links.

Ans: b

32 The main disadvantage of the sliding pair is that it is

(a)bulky

(b)wears rapidly

(c)difficult to manufacture

(d)(a) and (b) above

(e)(a) and (c) above.

Ans: d

33 A kinematic chain requires at least

(a)2 links and 3 turning pairs

(b)3 links and 4 turning pairs

(c)4 links and 4 turning pairs

(d)5 links and 4 turning pairs


Ans: c

34 Kinematic pairs are those which have

(a)two elements held together mechanically

(b)two elements having relative motion

(c)two elements having Coroili's component

(d)minimum of two instantaneous centers

(e)all of the above.

Ans: b

35 A ball and socket joint form a

a.turning pair

b.rolling pair

c.sliding pair

d.spherical pair

answer :- d.spherical pair

36 If a kinematic chain has 'l' links, then the number of

mechanism obtained are

a. l - 1

b. l - 2

c. l+1

d. l

answer :- d.l

37 A rigid body possesses_____degrees of freedom.

a. One b. Two c. Four d. Six

(Ans:d)

38 Which of the following is an open pair?

a. Journal bearing b. Ball and Socket joint

c. Leave screw and nut d. None of the above

(Ans:c)

39 . ________ is an inversion of Double slider crank chain.

a. Coupling rod of a locomotive b. Scotch yoke mechanism

c. Hand pump d. Reciprocating engine

(Ans:b)

40 The Kutzbach criterion for determining the number of degrees

of freedom (n) is (where l = number of links, j = number of joints

and h = number of higher pairs)

a. n = 3(l-1)-2j-h b. n = 2(l-1)-2j-h

c. n = 3(l-1)-3j-h d. n = 2(l-1)-3j-h

(Ans:a)

41 What is the number of instantaneous centres for an eight link

mechanism?

a. 15 b. 28 c. 30 d. 8

(Ans:b)

42 Consider the following mechanisms:

1. Oscillating cylinder engine mechanism

2. Toggle mechanism

3. Radial cylinder engine mechanism

4. Quick return mechanism

Which of the above are inversions of slider crank mechanism?

1. 1, 2 and 4

2. 2, 3 and 4

3. 1, 2 and 3

4. 1, 3 and 4

(Ans: d)

43 The kinematic chain shown in the above figure is a

(a) structure

(b) mechanism with one degree of freedom

(c) mechanism with two degree of freedom

(d)mechanism with more than two degrees of

freedom

Ans. (d)

44 In the given figure, ABCD is a four-bar mechanism. At the

instant shown, AB and CD are vertical and BC is horizontal AB

is shorter than CD by 30 cm. AB is rotating at 5 radius and CD

is rotating at 2 rad/s. The length of AB is

(a) 10cm (b) 20 cm (c) 30 cm (d) 50 cm

Ans. (b) 5L=2(L+30), 3L=60, L=20

45 In a single slider four-bar linkage, when the slider is fixed, it

forms a mechanism of

(a) hand pump (b) reciprocating engine

(c) quick return (d) oscil1ating cylinder

Ans. (a)

46 The type of quick return mechanism employed mostly in

shaping machines is:

(a) DC reversible motor (b) Fast and loose pulleys(c) Whitworth

motion (d) Slotted link mechanism

Ans. (d)

47 The Whitworth quick return mechanism is formed in a slider-

crank chain when the

(a) coupler link is fixed (b) longest link is a fixed link(c) slider is

a fixed link (d) smallest link is a fixed link

Ans. (d)

48 ABCD is a mechanism with link lengths AB = 200, BC = 300, CD

= 400 and DA =350. Which one of the following links should be

fixed for the resulting mechanism to be a double crank

mechanism? (All lengths are in mm)

a)A B (b) BC (c) CD (d) DA

Ans. (c)

49 Scotch yoke mechanism is used to generate

(a) sine functions (b) square roots (c) logarithms (d) inversions

Ans. (a)

50 Which one of the following is an exact straight line mechanism

using lower pairs?

(a) Watt's mechanism (b) Grasshopper mechanism

(c) Robert's mechanism (d) Paucellier’s mechanism

Ans. (d)

UNIT-II

A] Theory Question Bank

Q.

No

Description

01 Explain the difference between static and dynamic force analysis

02 Explain the following

i) Inertia

ii) D’Alembert’s Principle

iii) SHM

iv) Radius of Gyration

03 What is the difference between simple pendulum and compound

pendulum

04 Derive relation for periodic time of oscillation of a connecting rod

(Compound Pendulum)

05 Derive relation for periodic time of oscillation of a bar when it is

suspended by two long strings attached at its ends (Bifilar

Suspension)

06 Derive relation for periodic time of oscillation of a circular disc when

it is suspended by three long strings attached at its periphery

(Trifilar Suspension)

07 Explain the concept of Dynamically (or Kinetically) Equivalent

System

08 Sometimes why it is required to have ‘Correction Couple’ for two

mass dynamically equivalent system

09 How to calculate ‘Correction Couple’ for two mass dynamically

equivalent system

10 Neglecting Inertia force derive a relation for Piston Side Thrust

11 Neglecting Inertia force derive a relation for Tangential force acting

on crank pin

12 Considering the Inertia Forces derive a relation for Torque exerted

on the crank shaft due to inertia forces


on the crank shaft due to correction couple


on the crank shaft due to weight of mass m2 at big end centre

15 Explain T-θ diagram for a single cylinder four stroke IC Engine

16 Describe Types of Friction

17 Describe Laws of Dry Friction

18 Derive a relation for Limiting angle of Friction

19 Describe Friction in Turning Pairs

20 Describe Friction Circle

21 Describe Friction Axis of a Link

22 Explain friction circle. Deduce an expression for the radius of friction

circle in terms of the journal and the angle of friction.

23 Compare compound pendulum and bifilar pendulum suspension

method of finding the mass moment of inertia of rod like body.

24 Draw and explain turning moment diagram of a 4 stroke cylinder

Engine. State significance of it

25 A connecting rod of mass of 3.5 kg is suspended by two wires each of

2 m length. The wires are attached to the rod at points 150 mm on

either side of the centre of gravity. if the connecting rod makes 35

oscillations in 60 seconds. Find the radius of gyration and the mass

moment of inertia of the connecting rod about its centre of gravity.

26 A machine component of mass 5 kg is placed on a rectangular

horizontal platform which is suspended by two equal strings of

length 1.25 mm from rigid support and equidistance of 125 from C.G.

of the platform .when the mass of centre of the component coincides

with the axis of the platform ,it takes 45 seconds for 15 oscillations.

The platform alone has a mass of 1.5 kg and takes 60 seconds for 15

oscillations. Find the radius of gyration and the mass moment of

inertia of the machine component about an axis through its mass

centre.

27 The mass of a connecting rod of an engine 5 kg and is 600 mm long

between the centers .its C.G. IS 400mm from the centre of small end

about which the connecting rod oscillates in a vertical plane .the

rod is found by experimentally to complete 50 oscillations in 72

seconds . find the radius of gyration and the mass moment of inertia

of the connecting rod about an axis through its centre of gravity.

What is the length of the equivalent simple pendulum?

28 A connecting rod of mass of 1.7 kg is suspended by two wires each of

1.5 m length. The wires are attached to the rod at points 120 mm on

either side of the centre of gravity. if the connecting rod makes 25

oscillations in 40 seconds .find the radius of gyration and the mass

moment of inertia of the connecting rod about a vertical axis

through the centre of gravity.

29 The wheel of vehicle complete with tyre is suspended at three

vertical strings each equal 1.5 m long, equally spaced the periphery

of the tyre at a radius of 350 mm. the oscillations of small torsional

vibration of the wheel is 20 cycles per minute. Find the radius of

gyration of wheel about its axis.

30 The connecting rod of an engine has a length equal to 220 mm

between centers and has a mass equal to 2 kg. Its centre of gravity is

at 150 mm from the small end centre and the moment of inertia of

0.02 kg-m2about its centre of gravity.

Find :

(i)the two mass dynamically equivalent system when one mass is

located at the small end centre,

(ii)the correction couple, if two masses are placed at the two ends

and the angular acceleration of the connecting rod is 20,000

rad/s2anticlockwise

31 A high speed vertical engine has a connecting rod length five times

the crank which is 60 mm. Its mass is 3 kg and has a C.G. 200mm

from the small end bearing. When suspended in a small end bearing,

it makes 50 oscillations in 52 seconds. The reciprocating parts have

a mass of 1.5 kg. Determine the torque exerted on the crankshaft

due to inertia of the moving parts when the crank makes an angle of

135º with TDC, and speed of rotation is 1200 rpm

32 A single cylinder horizontal steam engine has a stroke of 0.75 m and

a connecting rod 1.8 m long. The mass of reciprocating parts is 520

kg and that of the connecting rod is 230 kg. Centre of gravity of the

connecting rod is 0.8 m from crank pin and the moment of inertia

about an axis through the centre of gravity perpendicular to the

plane of motion is 100 kg.m2 . For an engine speed of 90 rpm and a

crank position of 45° from the IDC, determine the torque on the

crankshaft due to the inertia of these parts by analytical method

33 A connecting rod is suspended from a point 25 mm above the small

end centre and 650 mm above its C.G. It makes 20 oscillations in 35

seconds.

Find dynamically equivalent two masses when one mass is placed at

small end centre. Take mass of connecting rod as 40 kg

34 A rigid link 500 mm long, mass 2 kg and radius of gyration 200 mm

.replace this link by dynamically equivalent system of two masses

located at the ends of the link.

35 Explain dynamic equivalence of two mass systems, for a connecting

rod of an IC engine having mass ‘m’ and radius of gyration ‘k’. Obtain

a two mass dynamically equivalent system, having one of the two

masses at the small end. How dynamical equivalence is achieved if it

is required that the other mass located at the big end

36 An IC engine has a stroke of 100 mm and bore of 80 mm. The

connecting rod is 160 mm between centers and has total mass of 1.3

kg. Its center of mass is 130 mm away from small end center and

radius of gyration about the mass center is 75 mm. The reciprocating

mass is 1.8 kg. Determine magnitude of resultant forces on the crank

pin, neglecting friction and gravity, when the crank is 300 after the

TDC position and rotating at 1600 rpm clockwise. The gas pressure

on the piston is 2 N/mm2

37 The connecting rod of an engine has length equal to 200 mm

between centers and has mass equal to 3.5 kg. Its CG is at 80 mm

from the big end centre and the radius of gyration about an axis

through CG is 100 mm. Determine :

(i) The two mass dynamically equivalent system when one mass is

placed at the small end.

(ii) The correction couple if two masses are placed at the two ends

and angular acceleration of connecting rod is 100 rad/s2 clockwise.

38 The connecting rod of a vertical reciprocating engine is 2000 mm

long between centres and its weights 250 kg. The mass centre is 800

mm from the big end centre. When it suspended as a pendulum from

the small end axis, it makes 8 complete oscillations in 22 seconds.

The crank is 400 mm long and rotates at 200 rpm. Determine by

analytical method :

(i) The mass moment of inertia of connecting rod about an axis

through as mass centre.

(ii) The inertia torque exerted on the crank shaft, when the crank has

turned through 40° from the top dead centre and piston is moving

downwards.

39 A connecting rod is suspended from a point 25 mm above the centre

of small end, and 650 mm above its centre of gravity, its mass being

37.5 kg. When permitted to oscillate, the time period is found to be

1.87 seconds. Find the dynamical equivalent system constituted of

two masses, one of which is located at the small end centre.

40 A vertical engine running at 1200 r.p.m. with a stroke of 110 mm has

a connecting rod 250 mm between centers and mass 1.25 kg. The

mass centre of the connecting rod is 75 mm from the big end centre

and when suspended as pendulum from the gudgeon pin axis makes

21 complete oscillations in 20 seconds :

(i) Calculate the radius of gyration of the connecting rod about an

axis through its mass centre.

(ii) When the crank is at 40º from the top dead centre and the piston

is moving downwards, find analytically, the acceleration of the

piston and the angular acceleration of the connecting rod. Hence

find the inertia torque exerted on the crankshaft. To make the two-

mass system to be dynamically equivalent to the connecting rod,

necessary correction torque has to be applied and since the engine is

vertical gravity effects are to be considered.

41 The connecting rod of an engine has a length equal to 220 mm

between centers and has a mass equal to 2 kg. Its centre of gravity is

at 150 mm from the small end centre and the moment of inertia of

0.02 kg-m2about its centre of gravity.

Find :

(I) the two mass dynamically equivalent system when one mass is

located at the small end centre,

(II) The correction couple, if two masses are placed at the two ends

and the angular acceleration of the connecting rod is 20,000

rad/s2anticlockwise.

42 Explain dynamic equivalence of two mass systems, for a connecting

rod of an IC engine having mass ‘m’ and radius of gyration ‘k’. Obtain

a two mass dynamically equivalent system, having one of the two

masses at the small end. How dynamical equivalence is achieved if it

is required that the other mass located at the big.

43 The following data refers to horizontal reciprocating engine:

Mass of reciprocating parts = 100 Kg,

Stroke Length = 200 mm,

Speed of engine = 900 rpm clockwise, Connecting rod mass = 80 Kg.

Length between centers = 400 mm,

Distance of C.G. from end center = 160 mm,

Radius of gyration of connecting rod about an axis through C.G = 120

mm.

Determine analytically the inertia torque on crankshaft when the

crank has turned 400

from I.D.C

44 The following data refers connecting rod of a reciprocating engine:

Mass = 55 Kg,

Diameter of the small end bearing= 75 mm

Diameter of the big end bearing= 100 mm

Distance between bearing centers = 850 mm,

Time of oscillation when the connecting rod is suspended from small

end 1.83 seconds. Time of oscillation when the connecting rod is

suspended from big end 1.68 second.

Determine

1) The radius of gyration of connecting rod about an axis through

C.G and perpendicular to the plane of oscillation

2) The moment of inertia of the rod about the same axis.

45 The piston diameter of an internal combustion engine is 125Mm and

the stroke is 220 mm. The connecting rod is 4.5 times the crank

length and has a mass of 50 kg. The mass of the reciprocating parts

is 30 kg. The centre of mass of connecting rod is 170 mm from the

crank pin centre and the radius of gyration about an axis through the

centre of mass is 148 mm. The engine runs at 320 rpm.

Find the magnitude and the direction of the inertia force and the

corresponding torque on the crankshaft when the angle turned by

the crank is 140º from the inner dead centre.

46 A gear of mass 4.5 kg is placed on a horizontal circular platform

whose mass is 2.5 kg. it is suspended by three equal wires, each 1.5

m long ,from a rigid support .the wires are equally spaced round the

circumference of a circle of 110 mm radius .when the C.G. of the

gear coincides with the axis of the circular platform ,the platform

makes 12 angular oscillations in 30 seconds .determine the mass

moment of inertia of combined system about an axis through its C.G.

47 A rectangular cross section bar is suspended horizontally with the

help of two equal strings equidistance from C.G. the length o0f each

string is 300 mm and the distance between is each string and C.G. of

the bar is 175 mm. the bar cross section is 30 mm x 20 mm and the

length of the bar is 700 mm. the bar mass density is 7.8 gm / cc .

Two identical cylindrical components each with mass 300 gm are

kept on the bar on either sides of the C.G. of the bar. The distance

between C. G. of the bar and the C. G. of the component is 225 mm.

The bar together with the components is made to oscillate in the

horizontal plane about the C. G. of the bar. The number of

oscillations is 90 in 150 seconds. Assuming amplitude of oscillations

as small calculate radius of gyration of the cylindrical components

about the C. G.

48 In a slider crank mechanism, the crank is 200 mm long and

connecting rod is 750 mm long. The piston is 80 mm in diameter and

a pressure difference of 2 MPa exists between two sides of piston

when the crank is moved through 45 degrees from top dead centre

position find

i) Thrust in connecting rod

ii) Reaction from guide

iii) Torque active on crank shaft

iv) Load on main bearings

49 The mass of reciprocating parts of a steam engine is 225 kg.

Diameter of the cylinder is 400 mm. Length of the Stroke is 500 mm

and the ration of the connecting rod to crank is 4.2 When the crank

is at inner dead centre, the difference in the pressure of the two

sides of the piston is 5 bar. At what speed must the engine should

run so that the thrust in the connecting rod in this position is equal

to 5200 N

50 The obliquity ratio of a vertical reciprocating engine is 4.5 The

engine bore and stroke is 75 mm and 90 mm respectively. The mass

of the reciprocating parts is 1.2 kg. The gas pressure intensity is 5.5

bar when it has moved through 50 degrees from the i. d. c. on its

power stroke. Determine:

i) Piston Effort

ii) Net load on gudgeon pin and crank pin

iii) Thrust in cylinder walls

iv) Thrust on the crank bearing

Assuming speed of the engine as 2200 rpm.

Calculate at what speed the load on gudgeon pin and the crank pin

be zero.

MCQ

Q.

No

Description

1 4. The angle which the normal

reaction makes with the

resultant reaction is called …...

A. normal angle

B. angle of friction

C. coff. of friction

D. None of the above

Answer- B

2 15. A body of weight W is required

to move up the rough inclined

plane whose angle of inclination

with the horizontal is α. The

effort applied parallel to the

plane is given by (where μ = tan

φ = Coefficient of friction

between the plane and the body)

A. P = W tan α

B. P = W tan (α + φ)

C. P = W (sin α + μ cos α)

D. P = W (cos α + μ sin α)

Answer: C

3 The essential condition of placing

the two masses, so that the system

becomes dynamically equivalent, is

(where l1 and l2 = Distance of two

masses from the centre of gravity of

the body, and kG = Radius of

gyration of the body)

A.l1 = kG

B.l2 = kG

C.l1l2 = kG

D.l1l2 = kG2

Answer: D

4 Which of the following statements

regarding laws governing the

friction between dry surfaces are

correct?

A. The friction force is dependent

on the materials of the contact

surfaces.

B. The friction force is directly

proportional to the normal force.

C. The friction force is independent

of me area of contact.

D.all of the above

Answer: D

5 The length of a simple pendulum

which gives the same frequency as

the compound pendulum, is

A.kG + l1

B.kG2 + l1

C.

D.

Answer: C

6 The friction experienced by a body,

when at rest, is known as…..

A. static friction

B. Dynamic friction

C. Both A &B


Answer: A

7

The inertia force is equal to the …….in magnitude, but opposite in

direction.

A.Accelerating force

B.Velocity

C. Mass moment of inertia

D.All of the above

Answer: A

8 Which of the following statements

regarding laws governing the

friction between dry surfaces are

correct?

A. The friction force is dependent on

the materials of the contact

surfaces.

B. The friction force is directly

proportional to the normal force.

C. The friction force is independent

of me area of contact.

D.all of the above

Answer: D

9 The acceleration of the particle

moving with simple harmonic

motion from the mean position is.

A. Inversely proportional to the

displacement of the particle

B.Directly proportional to the

displacement of the particle.

C.Directly proportional to

frictional force

D. All of the above

Answer: B

10 When a body moves with simple

harmonic motion, the product of its

periodic time and frequency is equal

to

A. zero

B. one

C. π/2

D. π

Answer: B

11. The minimum force required to slide a body of weight W on a rough

horizontal plane is

A. W sin θ

B. W cos θ

C. W tan θ

D. W cosec θ

Answer: A

12

Correction couple is applied when ---

A. If the Distance of m2 mass is selected arbitrarily

B. If the Distance of m1 mass is selected arbitrarily

C. Both masses m1 & m2 have to be selected arbitrarily

D. All of the above

Answer- C

13 While analyzing the inertia effect of connecting rod of slider crank

mechanisms ,mass m1 is placed at small end which is –

A.PISTON SIDE

B.Crank side

C. Both A & B

D.None of the above

Answer - A

14 The connecting rod of an engine has a length equal to 25cm

between centers and has a mass equal to 3 kg. Its centre of gravity

is at 175 mm from the small end centre and the moment of inertia

of 0.025 kg-m2about its centre of gravity. when any one mass is

located at small end, position of the second mass for dynamically

equivalent system is …mm

A. 55.2

B. 33.8

C. C.65.9

D. 47.6

Answer – D

15 In static force analysis Fp.tanφ is the equation of force

A.gas force on piston

B. piston side thrust

C. piston effort

D. inertia force due to piston

Answer- B

16 In a slider crank mechanism, The crank is 0.3 m long and

connecting rod is 0.85 m long .the piston is of 9 cm in diameter

and gas pressure acting on the piston is 5Mpa .the piston effort is

…..KN.

A.45.78

B. 31.81

C.83.19

D. 19.10

Answer- B

17

In case of ……engine the effort of weight of reciprocating parts is

also considered.

A. Vertical

B. Horizontal

C. Both A &B

D. None of the above.

Answer- A

18 Normal reaction acting on the cylinder wall is also called as

A. Piston side thrust

B. Piston effort

C.Net axial force on piston


Answer- A

19 Radial force acting on crank shaft is also called as …

A. Torque on the crank

B. Radial force acting on the crank

C. Tangential force on the crank

D. All of the above

Answer- C

20 Turning moment diagram is also called as…

A.T-θ diagram

B. Crank effort diagram

C. Stress-strain diagram

D. Both A&B

Answer- D

21

When T-θ diagram is positive, the crankshaft ……

A. Accelerates

B. Retards

C. Constant

D. Linear

Answer- B

22 In case of three cylinder engine the crank placed at …..to each

other.

A.00

B.900

C.1200

D.2700

Answer- C

23 In case of horizontal engine ,if the crank makes an angle of 1400

and rotates clockwise with IDC then torque due to mass at big end

is

A. Anticlockwise

B. Clockwise

C. Both A&B


Answer- B

24

A shaft of radius 50 mm rotates in a bearing. If the coefficient of

friction µ=0.25,then the radius of friction circle is -----

A. 0.025 m

B. 0.075 m

C. 0.0955m

D. 0.0125 m

Answer- D

25 A shaft of radius 75 mm rotates in a bearing at 400 rpm. IF µ=0.35,

then the diameter of friction circle is -----cm

A. 10.00

B. 10.50

C. 2.12

D. 5.25

Answer- D

26

Friction torque is T= -----

A. P x (r/µ)

B. P x (r.µ)

C. P x (r-µ)

D. All of the above

Answer- B

27 Journal is also called as ---

A. Hub

B. Coupling

C. Bearing

D. Shaft

Answer- D

28 A 300 N force is required to pull the body resting on a horizontal

plane .the force is inclined at an angle of 300 with horizontal. If

µ=0.1332, then the mass of the body is -----kg.

A.214.5

B. 500

C.144.29

D.125.3

Answer- A

29 Sliding friction is the type of ----friction

A. Film Friction

B. Greasy Friction

C. Dry Friction

D. Kinematic Or Dynamic Friction

Answer-C

30 MMI of a pulley is found by using ----method

A. Simple pendulum

B. Bifilar suspension

C. Trifilar suspension

D. Compound pendulum

Answer-C

31 Time period of oscillations of torsional pendulum does not depend

on ---

A. Length of each wire

Engineering

THEORY OF MACHINES I QUESTION BANK