Category: Machine Kinematics Objective Questions

250+ TOP MCQs on Kinetics of Motion and Answers

Machine Kinematics Multiple Choice Questions on “Kinetics of Motion”.

1. The force which acts along the radius of a circle and directed ____________ the centre of the circle is known as centripetal force.
a) away from
b) towards
c) at the
d) none of the mentioned

Answer: b
Clarification: Centripetal force acts radially inwards and is essential for circular motion.

2. The unit of mass moment of inertia in S.I. units is
a) m4
b) kgf-m-s2
c) kg-m2
d) N-m

Answer: c
Clarification: Moment of inertia is the distance, from a give reference, where the whole mass of body is assumed to be concentrated to give the same value of I. The unit of mass moment of inertia in S.I. units is kg-m2.

3. Joule is a unit of
a) force
b) work
c) power
d) none of the mentioned

Answer: b
Clarification: In S.I. system of units, the practical unit of work is N-m. It is the work done by a force of 1 newton, when it displaces a body through 1 metre. The work of 1 N-m is known as joule (briefly written as J ) such that 1 N-m = 1 J.

4. The energy possessed by a body, for doing work by virtue of its position, is called
a) potential energy
b) kinetic energy
c) electrical energy
d) chemical energy

Answer: a
Clarification: Potential energy is the energy possessed by a body for doing work, by virtue of its position.
Kinetic energy is the energy possessed by a body, for doing work, by virtue of its mass and velocity of motion.

5. When a body of mass moment of inertia I (about a given axis) is rotated about that axis with an angular velocity, then the kinetic energy of rotation is
a) 0.5 I.ω
b) I.ω
c) 0.5 I.ω2
d) I.ω2

Answer: c
Clarification: When a body of mass moment of inertia I (about a given axis) is rotated about that axis, with an angular velocity ω, then it possesses some kinetic energy. In this case,
Kinetic energy of rotation = 1/ 2I.ω2

When a body has both linear and angular motions e.g. in the locomotive driving wheels and wheels of a moving car, then the total kinetic energy of the body is equal to the sum of kinetic energies of translation and rotation.
∴ Total kinetic energy = 1/ 2mv2 +1/ 2I.ω2

6. The wheels of a moving car possess
a) potential energy only
b) kinetic energy of translation only
c) kinetic energy of rotation only
d) kinetic energy of translation and rotation both.

Answer: d
Clarification: in the locomotive driving wheels and wheels of a moving car, then the total kinetic energy of the body is equal to the sum of kinetic energies of translation and rotation.

7. The bodies which rebound after impact are called
a) inelastic bodies
b) elastic bodies
c) solid bodies
d) none of the mentioned

Answer: b
Clarification: The bodies, which rebound after impact are called elastic bodies and the bodies which does not rebound at all after its impact are called inelastic bodies.

8. The coefficient of restitution for inelastic bodies is
a) zero
b) between zero and one
c) one
d) more than one

Answer: a
Clarification: The process of regaining the original shape is called restitution. Inelastic bodies can not regain their original shapes. Therefore their coefficient of restitution is zero.

9. Which of the following statement is correct ?
a) The kinetic energy of a body during impact remains constant.
b) The kinetic energy of a body before impact is equal to the kinetic energy of a body after impact.
c) The kinetic energy of a body before impact is less than the kinetic energy of a body after impact.
d) The kinetic energy of a body before impact is more than the kinetic energy of a body after impact.

Answer: d
Clarification: Total kinetic energy of the system before impact,
E1 = 1/2 m1 (u1)2 + 1/2 m2 (u2)2

When the two bodies move with the same velocity v after impact, then
Kinetic energy of the system after impact,

E2= 1/2( m1 + m2) v2

∴ Loss of kinetic energy during impact,
EL = E1 – E2

10. A body of mass m moving with a constant velocity v strikes another body of same mass m moving with same velocity but in opposite direction. The common velocity of both the bodies after collision is
a) v
b) 2 v
c) 4 v
d) 8 v

Answer: b
Clarification: If the body will move in opposite direction a negative sign would be there.
We know that Common velocity = V1 – 2
Here both the velocities are same.
Therefore Common velocity = V – (-V)
= V + V = 2V

250+ TOP MCQs on Kinematic Pair and Answers

Machine Kinematics Multiple Choice Questions on “Kinematic Pair”.

1. When the two elements of a pair have _____________ when in motion, it is said to a lower pair.
a) line or point contact
b) surface contact
c) permit relative motion
d) none of the mentioned
Answer: b
Clarification: When the two elements of a pair have surface contact when relative motion, takes place and the surface of one element slides over the surface of the other, the pair formed is known as lower pair. It will be seen that sliding pairs, turning pairs and screw pairs form lower pairs.

2. The two elements of a pair are said to form a higher pair, when they
a) have a surface contact when in motion
b) have a line or point contact when in motion
c) are kept in contact by the action of external forces, when in motion
d) permit relative motion
Answer: b
Clarification: When the two elements of a pair have a line or point contact when relative motion takes place and the motion between the two elements is partly turning and partly sliding, then the pair is known as higher pair.

3. In a force-closed pair, the two elements of a pair are not held together mechanically.
a) True
b) False
Answer: b
Clarification: When the two elements of pair are not connected mechanically but are kept in contact by the action of external forces, the pair is said to be a forced-closed pair.

4. The two elements of a pair are said to form a ___________ when they permit relative motion between them.
a) open pair
b) kinematic pair
c) higher pair
d) lower pair
Answer: b
Clarification: The two links or elements of a machine, when in contact with each other, are said to form a pair. If the relative motion between them is completely or successfully constrained, the pair is known as kinematic pair.

5. In an open pair, the two elements of a pair
a) have a surface contact when in motion
b) have a line or point contact when in motion
c) are kept in contact by the action of external forces, when in motion
d) are not held mechanically
Answer: d
Clarification: When the two elements of a pair are not held mechanically, they are called open pair.

6. The sliding pairs, turning pairs and screw pairs form lower pairs.
a) True
b) False
Answer: a
Clarification: When the two elements of a pair have surface contact when relative motion, takes place and the surface of one element slides over the surface of the other, the pair formed is known as lower pair. It will be seen that sliding pairs, turning pairs and screw pairs form lower pairs.

7. 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
Answer: c
Clarification: A kinematic chain is defined as a combination of kinematic pairs, joined in such a way that each link forms a part of two pairs and the relative motion between the links or elements is completely or successfully constrained.

8. The relation between number of pairs(p) forming a kinematic chain and the number of links(l) is
a) l = 2p – 2
b) l = 2p – 3
c) l = 2p – 4
d) l = 2p – 5
Answer: c
Clarification: If each link is assumed to form two pairs with adjacent links, then the relation between the number of pairs(p) forming a kinematic chain and the number of links(l) may be expressed in the form of an equation : l = 2p – 4

9. The relation between number of links(l) and number of joints(j) in a kinematic chain is
a) l = 1/2 (j+2)
b) l = 2/3 (j+2)
c) l = 3/4 (j+2)
d) l = j+4
Answer: b
Clarification: Another relation between the number of links (l) and the number of joints(j) which constitute a kinematic chain is given by the expression : l = 2/3 (j+2)

10. The relation l = 2/3(j+2) apply to kinematic chains in which lower pairs are used. This may be used to kinematic chains in which higher pairs are used, but each higher pair may be taken as equivalent to
a) one lower pair and two additional links
b) two lower pairs and one additional link
c) two lower pairs and two additional links
d) all of the mentioned
Answer: b
Clarification: None

250+ TOP MCQs on Properties of Instantaneous Centre and Answers

Machine Kinematics Multiple Choice Questions on “Properties of Instantaneous Centre”.

1. Which is the false statement about the properties of instantaneous centre?
a) at the instantaneous centre of rotation, one rigid link rotates instantaneously relative to another for the configuration of mechanism considered
b) the two rigid links have no linear velocities relative to each other at the instantaneous centre
c) the two rigid links which have no linear velocity relative to each other at this centre have the same linear velocity to the third rigid link
d) the double centre can be denoted either by O21 or O12, but proper selection should be made
Answer: d
Clarification: The following properties of the instantaneous centre are important from the subject point of view :
1. A rigid link rotates instantaneously relative to another link at the instantaneous centre for the configuration of the mechanism considered.
2. The two rigid links have no linear velocity relative to each other at the instantaneous centre. At this point (i.e. instantaneous centre), the two rigid links have the same linear velocity relative to the third rigid link. In other words, the velocity of the instantaneous centre relative to any third rigid link will be same whether the instantaneous centre is regarded as a point on the first rigid link or on the second rigid link.

2. Instantaneous center of rotation of a link in a four bar mechanism lies on
a) right side pivot of this link
b) left side pivot of this link
c) a point obtained by intersection on extending adjoining links
d) none of the mentioned
Answer: c
Clarification: None.

3. The total number of instantaneous centers for a mechanism of n links is
a) n(n – 1)/2
b) n
c) n – 1
d) n(n – 1)
Answer: a
Clarification: The number of pairs of links or the number of instantaneous centres is the number of combinations of n links taken two at a time. Mathematically, number of instantaneous centres,
N = n(n – 1)/2.

4. The number of links and instantaneous centers in a reciprocating engine mechanism are
a) 4,4
b) 4,5
c) 5,4
d) 4,6
Answer: d
Clarification: First of all, determine the number of instantaneous centres (N) by using the relation
N = n(n – 1)/2
In present case, N = 4(4 – 1)/2 (n = 4)
= 6.

5. According to Kennedy’s theorem, if three bodies have plane motions, their instantaneous centres lie on
a) a triangle
b) a point
c) two lines
d) a straight line
Answer: d
Clarification: The Aronhold Kennedy’s theorem states that if three bodies move relatively to each other, they have three instantaneous centres and lie on a straight line.

6. In a rigid link OA, velocity of A w.r.t. O will be
a) parallel to OA
b) perpendicular to OA
c) at 450 to OA
d) along AO
Answer: b
Clarification: None.

7. Two systems shall be dynamically equivalent when
a) the mass of two are same
b) c.g. of two coincides
c) M.I. of two about an axis through c.g. is equal
d) all of the mentioned
Answer: d
Clarification: None.

8. A link is rotating about O. Velocity of point P on link w.r.t. point Q on link will be perpendicular to
a) OP
b) OQ
c) PQ
d) line in between OP and OQ
Answer: c
Clarification: A link is rotating about O. Velocity of point P on link w.r.t. point Q on link will be perpendicular to PQ.
The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line joining the corresponding points.

9. The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line
a) joining the corresponding points
b) perpendicular to line
c) at 450 to line
d) none of the mentioned
Answer: a
Clarification: A link is rotating about O. Velocity of point P on link w.r.t. point Q on link will be perpendicular to PQ.
The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line joining the corresponding points.

10. The absolute acceleration of any point P in a link about center of rotation O is
a) along PO
b) perpendicular to PO
c) at 450 to PO
d) none of the mentioned
Answer: d
Clarification: The coriolis component of acceleration is always perpendicular to the link.

11. Angular acceleration of a link can be determined by dividing the
a) centripetal component of acceleration with length of link
b) tangential component of acceleration with length of link
c) resultant acceleration with length of link
d) all of the mentioned
Answer: b
Clarification: The angular acceleration of the link AB is obtained by dividing the tangential components of the acceleration of B with respect to A to the length of the link.

250+ TOP MCQs on Double Hooke’s Joint and Answers

Machine Kinematics Multiple Choice Questions on “Double Hooke’s Joint”.

1. What is the purpose of double hooke’s joint?
a) Have constant linear velocity ratio of driver and driven shafts
b) Have constant acceleration ratio of driver and driven shafts
c) Have constant angular velocity ratio of driver and driven shafts
d) Have constant angular acceleration ratio of driver and driven shafts
Answer: c
Clarification: The velocity of the driven shaft is not constant, but varies from maximum to minimum values. In order to have a constant velocity ratio of the driving and driven shafts, an intermediate shaft with a Hooke’s joint at each end is used.

2. Double hooke’s joint can be used to keep the angular velocity of the shaft constant.
a) True
b) False
Answer: b
Clarification: Double hooke’s joint is used to keep the velocity ratio of driver shaft and driven shaft, It does not necessarily keeps the velocity constant.

3. Two shafts having an included angle of 150° are connected by a Hooke’s joint. The driving shaft runs at a uniform speed of 1500 r.p.m. The driven shaft carries a flywheel of mass 12 kg and 100 mm radius of gyration. Using the above data, calculate the maximum angular acceleration of the driven shaft in rad/s2.
a) 6853
b) 6090
c) 6100
d) 6500
Answer: a
Clarification: α = 180 -150 = 30⁰
cos2θ = 2sin2 α/1-sin2 α = 0.66
angular acc = dω/dt
= 6853.0 rad/s2.

4. Two shafts having an included angle of 150° are connected by a Hooke’s joint. The driving shaft runs at a uniform speed of 1500 r.p.m. The driven shaft carries a flywheel of mass 12 kg and 100 mm radius of gyration. Using the above data, calculate the maximum torque required in N-m.
a) 822
b) 888
c) 890
d) 867
Answer: a
Clarification: α = 180 -160 = 30⁰
cos2θ = 2sin2 α/1-sin2 α = 0.66
angular acc = dω/dt
= 6853 rad/s2
I = 0.12 Kg-m2
Therefore max torque = I.ang acc.
= 822 N-m.

5. Two shafts connected by a Hooke’s joint have an angle of 18 degrees between the axes.
Find the angle through which it should be turned to get the velocity ratio maximum.
a) 180
b) 30
c) 45
d) 90
Answer: a
Clarification: Velocity ratio is ω1/ω = cosα/(1 – cos2θsin2α)
now this to be maximum cos2θ = 1
therefore θ = 0 or 180 degrees.

6. Two shafts connected by a Hooke’s joint have an angle of 18 degrees between the axes.
Find the angle through which it should be turned to get the velocity ratio equal to 1.
a) 30.6
b) 30.3
c) 44.3
d) 91.2
Answer: c
Clarification: Velocity ratio is ω1/ω = cosα/(1 – cos2θsin2α)
now this to be 1
we get, cosα = 1 – cos2θsin2α
solving this equation we get
θ = 44.3 or 135.7 degrees.

7. Two shafts with an included angle of 160° are connected by a Hooke’s joint. The driving shaft runs at a uniform speed of 1500 r.p.m. The driven shaft carries a flywheel of mass 12 kg and 100 mm radius of gyration. Find the maximum angular acceleration of the driven shaft.
a) 3090 rad/s2
b) 4090 rad/s2
c) 5090 rad/s2
d) 6090 rad/s2
Answer: a
Clarification: Given : α = 180° – 160° = 20°; N = 1500 r.p.m.; m = 12 kg ; k = 100 mm = 0.1 m
We know that angular speed of the driving shaft,
ω = 2 π × 1500 / 60 = 157 rad/s
and mass moment of inertia of the driven shaft,
I = m.k2 = 12(0.1)2 = 0.12 kg – m2

Let dω1 / dt = Maximum angular acceleration of the driven shaft, and
θ = Angle through which the driving shaft turns.
We know that, for maximum angular acceleration of the driven shaft,

cos 2θ = 2sin2α/2 – sin2α = 2sin220°/2 – sin220° = 0.124
2θ = 82.9° or θ = 41.45°
and dω1 / dt = ω2cosα sin2θsin2α/(1 – cos2θsin2α)2
= 3090 rad/s2.

8. The angle between the axes of two shafts connected by Hooke’s joint is 18°. Determine the angle turned through by the driving shaft when the velocity ratio is maximum.
a) 90°
b) 180°
c) 270°
d) 360°
Answer: b
Clarification: Given : α = 98°
Let θ = Angle turned through by the driving shaft.
We know that velocity ratio,
ω1/ω = cosα/1 – cos2θsin2α

The velocity ratio will be maximum when cos2 θ is minimum, i.e. when
cos2 θ = 1 or when θ = 0° or 180°.

contest

250+ TOP MCQs on Types of Belts – 1 and Answers

Machine Kinematics Multiple Choice Questions on “Types of Belts – 1”.

1. In a cone pulley, if the sum of radii of the pulleys on the driving and driven shafts is constant, then
a) open belt drive is recommended
b) crossed belt drive is recommended
c) both open belt drive and crossed belt drive is recommended
d) the drive is recommended depending upon the torque transmitted
Answer: b
Clarification: Cone pulley drive, is used for changing the speed of the driven shaft while the main or driving shaft runs at constant speed. This is accomplished by shifting the belt from one part of the steps to the other.

2. Due to slip of belt, the velocity ratio of the belt drive increases.
a) True
b) False
Answer: b
Clarification: The result of the belt slipping is to reduce the velocity ratio of the system.

3. When two pulleys of different diameters are connected by means of an open belt, the angle of contact at the _________pulley must be taken into consideration.
a) smaller
b) larger
c) medium
d) none of the mentioned
Answer: a
Clarification: None.

4. The power transmitted by a belt is maximum when the maximum tension in the belt is __________of centrifugal tension.
a) one-third
b) two-third
c) double
d) three times
Answer: d
Clarification: When the power transmitted is maximum, 1/3rd of the maximum tension is absorbed as centrifugal tension.

5. The velocity of the belt for maximum power is
a) T/3
b) T.g/3
c) √T/3m
d) √3m/T
Answer: c
Clarification: None.

6. The centrifugal tension on the belt has no effect on the power transmitted.
a) True
b) False
Answer: a
Clarification: None.

7. V-belts are usually used for
a) long drives
b) short drives
c) long and short drives
d) none of the mentioned
Answer: b
Clarification: V-belt is mostly used in factories and workshops where a great amount of power is to be transmitted from one pulley to another when the two pulleys are very near to each other.

8. In a multiple V-belt drive, if one of the belt is broken, then we should replace
a) the broken belt only
b) all the belts
c) the broken belt and the belts on either side of it
d) none of the mentioned
Answer: b
Clarification: In multiple V-belt drive, all the belts should stretch at the same rate so that the load is equally divided between them. When one of the set of belts break, the entire set should be replaced at the same time. If only one belt is replaced, the new unworn and unstressed belt will be more tightly stretched and will move with different velocity.

9. The included angle for the v-belt is usually
a) 100 to 200
b) 200 to 300
c) 300 to 400
d) 600 to 800
Answer: c
Clarification: None.

250+ TOP MCQs on Standard Proportions of Gear Systems and Answers

Machine Kinematics Multiple Choice Questions on “Standard Proportions of Gear Systems”.

1. If T is the actual number of teeth on a helical gear and φ is the helix angle for the teeth, the formative number of teeth is written as
a) T sec3 φ
b) T sec2 φ
c) T/sec3φ
d) T cosec φ

Answer: a
Clarification: The formative or equivalent number of teeth for a helical gear may be defined as the number of teeth that can be generated on the surface of a cylinder having a radius equal to the radius of curvature at a point at the tip of the minor axis of an ellipse obtained by taking a section of the gear in the normal plane. Mathematically, formative or equivalent number of teeth on a helical gear,T sec3 φ

2. In helical gears, the distance between similar faces of adjacent teeth along a helix on the pitch cylinders normal to the teeth, is called
a) normal pitch
b) axial pitch
c) diametral pitch
d) module

Answer: a
Clarification: Normal pitch is the distance between similar faces of adjacent teeth along a helix on the pitch cylinders normal to the teeth.
Axial pitch is the distance, parallel to the axis, between similar faces of adjacent teeth.

3. In helical gears, the right hand helices on one gear will mesh ____________ helices on the other gear.
a) right hand
b) left hand
c) opposite
d) none of the mentioned

Answer: b
Clarification: A helical gear has teeth in form of helix around the gear. Two such gears may be used to connect two parallel shafts in place of spur gears. The helixes may be right handed on one gear and left handed on the other.

4. The helix angle for single helical gears ranges from
a) 10° to 15°
b) 15° to 20°
c) 20° to 35°
d) 35° to 50°

Answer: c
Clarification: In single helical gears, the helix angle ranges from 20° to 35°, while for double helical gears, it may be made upto 45°.

5. The helix angle for double helical gears may be made up to
a) 45°
b) 60°
c) 75°
d) 90°

Answer: a
Clarification: In single helical gears, the helix angle ranges from 20° to 35°, while for double helical gears, it may be made upto 45°.

6. The outside diameter of an involute gear is equal to pitch circle diameter plus
a) 2 addendum
b) 2 dedendum
c) 3.1416 module
d) 2.157 module

Answer: a
Clarification: Addendum is the portion of gear tooth above the pitch circle diameter (PCD). Therefore outside diameter of involute gear = PCD + 2 addendum.

7. Pick out the false statement about relationships of spur gears.
a) Pitch diameter = module x No. of teeth
b) Module = 25.4/diametral pitch
c) dedendum = 1.25 x module
d) Base pitch = module x п x sinɸ

Answer: d
Clarification: The false statement is
Base pitch = module x п x sinɸ
Correct relationship of base pitch = module x п x cosɸ

8. Which of the following is not the correct property of involute curve?
a) The form or shape pf an involute curve depends upon the diameter of base circle from which it is derived
b) The angular motion of two involute gear teeth rotating at a uniform rate will be uniform, irrespective of the centre distance
c) The relative rate of motion between driving and driven gears having involute tooth curves, is established by the diameters of their pitch circles
d) the pitch diameters of mating involute gears are directly proportional to the diameters of their respective base circles

Answer: c
Clarification: All statements except at (c) are correct. The correct statement for (c) is – The relative rate motion between driving and driven gears having involute tooth curves, is established by the diameters of their base circles.

9. Which of the following gear ratio does not result in hunting tool
a) 77/20
b) 76/21
c) 75/22
d) 71/25

Answer: d
Clarification: When several pairs of gears operating at the same centre distance are required to have hunting ratios, this can be accomplished by having the sum of the teeth in each pair equal to a prime number.

10. In measuring the chordal thickness, the vertical scale of a gear tooth caliper is set to the chordal or corrected addendum to locate the caliper jaws at the pitch line.If a = addendum, t = circular thickness of tooth at pitch diameter D, then chordal thickness is equal to
a) a + t/D
b) a + t2/D
c) a + t3/2D
d) a + t2/4D

Answer: d
Clarification: The correct relationship is chordal thickness = a + t2/4D