Multiple choice question for engineering
Set 1
1. There are two points P and Q on a planar rigid body. The relative velocity between the two points
a) should always be along PQ
b) can be oriented along any direction
c) should always be perpendicular to PQ
d) should be along QP when the body undergoes pure translation
Answer
Answer: c [Reason:] Velocity of any point on a link with respect to another point (relative velocity) on the same link is always perpendicular to the line joining these points on the configuration (or space) diagram.
vQP = Relative velocity between P & Q
= vP − vQ always perpendicular to PQ.
2. For a four-bar linkage in toggle position, the value of mechanical advantage is
a) 0.0
b) 0.5
c) 1.0
d) ∞
Answer
Answer: d [Reason:] When the mechanism is toggle,then β = 00 and 1800.
So M.A = ∞.
3. The number of inversion for a slider crank mechanism is
a) 6
b) 5
c) 4
d) 3
Answer
Answer: c [Reason:] For a 4 bar slider crank mechanism, there are the number of links or inversions are 4. These different inversions are obtained by fixing different links once at a time for one inversion. Hence, the number of inversions for a slider crank mechanism is 4.
4. Match the item in columns I and II
Column I Column II
P. Addendum 1. Cam
Q. Instantaneous centre of velocity 2. Beam
R. Section modulus 3. Linkage
S. Prime circle 4. Gear
a) P-4, Q-2, R-3, S-1
b) P-4, Q-3, R-2, S-1
c) P-3, Q-2, R-1, S-4
d) P-3, Q-4, R-1, S-2
Answer
Answer: b [Reason:] Column I Column II
P. Addendum 4. Gear
Q. Instantaneous centre of velocity 3. Linkage
R. Section modulus 2. Beam
S. Prime circle 1. Cam
So correct pairs are, P-4, Q-3, R-2, S-1.
5. Match the items in columns I and II
Column I Column II
P. Higher Kinematic Pair 1. Grubler’s Equation
Q. Lower Kinemation Pair 2. Line contact
R. Quick Return Mechanism 3. Euler’s Equation
S. Mobility of a Linkage 4. Planar
5. Shaper
6. Surface contact
a) P-2, Q-6, R-4, S-3
b) P-6, Q-2, R-4, S-1
c) P-6, Q-2, R-5, S-3
d) P-2, Q-6, R-5, S-1
Answer
Answer: d [Reason:] In this question pair or mechanism is related to contact & machine related to it.
Column I Column II
P. Higher Kinematic Pair 2. Line Contact
Q. Lower Kinematic Pair 6. Surface Contact
R. Quick Return Mechanism 5. Shaper
S. Mobility of a Linkage 1. Grubler’s Equation
So correct pairs are, P-2, Q-6, R-5, S-1.
6. In a four-bar linkage, S denotes the shortest link length, L is the longest link length, P and Q are the lengths of other two links. At least one of the three moving links will rotate by 3600 if
a) S + L < P + Q
b) S + L > P + Q
c) S + P < L + Q
d) S + P > L + Q
Answer
Answer: a [Reason:] Here P,Q,R, & S are the lengths of the links.
According to Grashof’s law : “For a four bar mechanism, the sum of the shortest and longest link lengths should not be greater than the sum of remaining two link lengths, if there is to be continuous relative motion between the two links
S + L < P + Q.
7. The number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints is
a) 1
b) 2
c) 3
d) 4
Answer
Answer: c [Reason:] Given l= 8, j= 9
We know that, Degree of freedom,
n =3(l − 1)−2j = 3(8 − 1)−2 x 9 = 3.
8. The lengths of the links of a 4-bar linkage with revolute pairs are p,q,r, and s units. given that p<q<r<s. Which of these links should be the fixed one, for obtaining a “double crank” mechanism ?
a) link of length p
b) link of length q
c) link of length r
d) link of length s
Answer
Answer: a [Reason:] Given p<q<r<s
“Double crank” mechanism occurs, when the shortest link is fixed. From the given pairs p is the shortest link. So, link of length p should be fixed.
9. When a cylinder is located in a Vee-block, the number of degrees of freedom which are arrested is
a) 2
b) 4
c) 7
d) 8
Answer
Answer: b [Reason:] Number of degrees of freedom = 2 & movability includes the six degrees of freedom of the device as a whole, as the ground link were not fixed. So, 4 degrees of freedom are constrained or arrested.
10. The minimum number of links in a single degree-of-freedom planar mechanism with both higher and lower kinematic pairs is
a) 2
b) 3
c) 4
d) 5
Answer
Answer: c [Reason:] From the Kutzbach criterion the degree of freedom,
n = 3(l − 1) − 2j − h
For single degree of Freedom (n = 1),
1 = 3(l − 1) − 2j − h
3l − 2j − 4 − h = 0 …(i)
The simplest possible mechanisms of single degree of freedom is four-bar mechanism. For this mechanism j = 4, h = 0
From equation (i), we have
3l − 2 x 4 − 4 − 0 = 0
or, l = 4.
11. The total number of instantaneous centres for a mechanism consisting of n links are
a) n/2
b) n
c) n – 1/2
d) n(n – 1)/2
Answer
Answer: d [Reason:] The number of instantaneous centres in a constrained kinematic chain is equal to the number of possible combinations of two links. 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 where n = Number of links.
12. According to Aronhold Kennedy’s theorem, if three bodies move relatively to each other, their instantaneous centres will lie on a
a) straight line
b) parabolic curve
c) ellipse
d) none of the mentioned
Answer
Answer: a [Reason:] 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.
13. In a mechanism, the fixed instantaneous centres are those centres which
a) remain in the same place for all configurations of the mechanism
b) vary with the configuration of the mechanism
c) moves as the mechanism moves, but joints are of permanent nature
d) none of the mentioned
Answer
Answer: a [Reason:] Fixed instantaneous centres remain in the same place for all configurations of the mechanism. The permanent instantaneous centres move when the mechanism moves, but the joints are of permanent nature.
14. The instantaneous centres which vary with the configuration of the mechanism, are called
a) permanent instantaneous centres
b) fixed instantaneous centres
c) neither fixed nor permanent instantaneous centres
d) none of the mentioned
Answer
Answer: c [Reason:] Fixed instantaneous centres remain in the same place for all configurations of the mechanism. The permanent instantaneous centres move when the mechanism moves, but the joints are of permanent nature. Neither fixed nor permanent instantaneous centres vary with the configuration of the mechanism.
15. When a slider moves on a fixed link having curved surface, their instantaneous centre lies
a) on their point of contact
b) at the centre of curvature
c) at the centre of circle
d) at the pin joint
Answer
Answer: b [Reason:] When the slider link moves on fixed link having constant radius of curvature, the instantaneous centre lies at the centre of curvature i.e. the centre of the circle, for all configuration of the links.
Set 2
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
Answer: d [Reason:] 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
Answer: c
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
Answer: a [Reason:] 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
Answer: d [Reason:] 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
Answer: d [Reason:] 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
Answer: b
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
Answer: d
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
Answer: c [Reason:] 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
Answer: a [Reason:] 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
Answer: d [Reason:] 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
Answer: b [Reason:] 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.
Set 3
1. Gearing contact is which one of the following?
a) Sliding contact
b) Sliding contact, only rolling at pitch point
c) Rolling contact
d) Rolling and sliding at each point of contact
Answer
Answer: b [Reason:] When pair of teeth touch at the pitch point ,they have for the instant pure rolling action. At any other position they have the sliding action.
2. An external gear with 60 teeth meshes with a pinion of 20 teeth, module being 6 mm. What is the centre distance in mm?
a) 120
b) 180
c) 240
d) 300
Answer
Answer: c [Reason:] Centre distance in mm = m/2 (T1 + T2)
= 6/2 (60 + 20)
= 240 mm
3. Which one of the following is true for involute gears?
a) Interference is inherently absent
b) Variation in centre distance of shafts increases radial force
c) A convex flank is always in contact with concave flank
d) Pressure angle is constant throughout the teeth engagement
Answer
Answer: d [Reason:] For involute gears, the pressure angle is constant throughout the teeth engagement.
4. In involute gears the pressure angle is
a) Dependent on the size of teeth
b) dependent on the size of gears
c) Always constant
d) always variable
Answer
Answer: c [Reason:] The pressure angle is always constant in involute gears.
5. Consider the following statements:
1. A stub tooth has a working depth larger than that of a full-depth tooth.
2. The path of contact for involute gears is an arc of a circle.
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
Answer
Answer: d [Reason:] 1. A stub tooth has a working depth lower than that of a full-depth tooth.
2. The path of contact for involute gears is a line.
6. Consider the following statements regarding the choice of conjugate teeth for the profile of mating gears:
1. They will transmit the desired motion
2. They are difficult to manufacture.
3. Standardisation is not possible
4. The cost of production is low.
Which of these statements are correct?
a) 1, 2 and 3
b) 1, 2 and 4
c) 2, 3 and 4
d) 1, 3 and 4
Answer
Answer: a [Reason:] Cost of production of conjugate teeth, being difficult to manufacture is high.
7. Common contact ratio of a pair of spur pinion and gear is
a) Less than 1·0
b) Equal to 1
c) Between 2 and 3
d) Greater than 3
Answer
Answer: c [Reason:] The ratio of the length of arc of contact to the circular pitch is known as contact ratio i.e. number of pairs of teeth in contact. The contact ratio for gears is greater than one. Contact ratio should be at least 1.25. For maximum smoothness and quietness, the contact ratio should be between 1.50 and 2.00. High-speed applications should be designed with a face-contact ratio of 2.00 or higher for best results.
8. In gears, interference takes place when
a) The tip of a tooth of a mating gear digs into the portion between base and root circles
b) Gears do not move smoothly in the absence of lubrication
c) Pitch of the gear is not same
d) gear teeth are undercut
Answer
Answer: a [Reason:] In gears, interference takes place when the tip of a tooth of a mating gear digs into the portion between base .and root circle.
9. Consider the following characteristics:
1. Small interference
2. Strong tooth.
3. Low production cost
4. Gear with small number of teeth.
Those characteristics which are applicable to stub 20° involute system would include
a) 1 alone
b) 2, 3 and 4
c) 1, 2 and 3
d) 1, 2, 3 and 4
Answer
Answer: b [Reason:] Involute system is very interference prone.
10. A spur gear transmits 10 kW at a pitch line velocity of 10 m/s; driving gear has a diameter of 1.0 m. Find the tangential force between the driver and the follower, and the transmitted torque respectively.
a) 1 kN and 0.5 kN-m
b) 10 kN and 5 kN-m
c) 0.5 kN and 0.25 kN-m
d) 1 kN and 1 kN-m
Answer
Answer: a [Reason:] Power transmitted = Force × Velocity
Force = 10 x 103/10
= 1000 N/m
Torque Transmitted = Force x diameter/2
= 1000 x 1/2
= 500 N-m
= 0.5 kN-m
Set 4
1. The periodic time (tp) is given by
a) ω / 2 π
b) 2 π / ω
c) 2 π × ω
d) π/ω
Answer
Answer: b [Reason:] Periodic time is the time taken for one complete revolution of the particle.
∴ Periodic time, tp = 2 π/ω seconds.
2. The velocity of a particle moving with simple harmonic motion is . . . . at the mean position.
a) zero
b) minimum
c) maximum
d) none of the mentioned
Answer
Answer: c [Reason:] At mean the value of x = 0. Therefore, it is maximum at mean position.
Vmax = ω.r.
3. The velocity of a particle (v) moving with simple harmonic motion, at any instant is given by
a) ω √r2 − x2
b) ω √x2 − r2
c) ω2 √r2 − x2
d) ω2√x2 − r2
Answer
Answer: a [Reason:] Velocity of any particle vN = vsinθ = ω.rsinθ = ω √r2 − x2.
4. The maximum acceleration of a particle moving with simple harmonic motion is
a) ω
b) ω.r
c) ω2.r
d) ω2/r
Answer
Answer: c [Reason:] Acceleration, aN = ω2.rcosθ = ω2.r.
5. The frequency of oscillation for the simple pendulum is
a) 1/2π √L/g
b) 1/2π √g/L
c) 2π √L/g
d) 2π√g/L
Answer
Answer: b [Reason:] The motion of the bob from one extremity to the other is known as beat or swing. Thus one beat = 1/2 oscillation.
∴ Periodic time for one beat = π √g/L
∴ Frequency = 1/2π √g/L.
6. When a rigid body is suspended vertically and it oscillates with a small amplitude under the action of the force of gravity, the body is known as
a) simple pendulum
b) torsional pendulum
c) compound pendulum
d) second’s pendulum
Answer
Answer: c [Reason:] When a rigid body is suspended vertically, and it oscillates with a small amplitude under the action of the force of gravity, the body is known as compound pendulum. Thus the periodic time of a compound pendulum is minimum when the distance between the point of suspension and the centre of gravity is equal to the radius of gyration of the body about its centre of gravity.
7. The frequency of oscillation of a compound pendulum is
a) 1/2π √g.h/k2G +h2
b) 1/2π √k2G +h2/g.h
c) 2π√g.h/k2G +h2
d) 2π√k2G +h2/g.h
Answer
Answer: a [Reason:] We know that the periodic time,
tp = 2π√Displacement/Accleration = 2π√θ/α
and frequency of oscillation,n = 1/tp = 1/2π √g.h/k2G +h2
where kG = Radius of gyration about the centroidal axis, and
h = Distance between the point of suspension and centre of gravity of the body.
8. The equivalent length of a simple pendulum which gives the same frequency as the compound pendulum is
a) h/ k2G +h2
b) k2G +h2/h
c) h2/k2G +h2
d) k2G +h2/h2
Answer
Answer: b [Reason:] By comparing the frequencies of simple pendulum to compound pendulum we get the equivalent length of simple pendulum as k2G +h2/h.
9. The centre of percussion is below the centre of gravity of the body and is at a distance equal to
a) h / kG
b) h.kG
c) h2/kG
d) k2G/h
Answer
Answer: d [Reason:] The centre of oscillation is sometimes termed as centre of percussion. It is defined as that point at which a blow may be struck on a suspended body so that the reaction at the support is zero. The centre of percussion is below the centre of gravity and at a distance k2G/h. The distance between the centre of suspension and the centre of percussion is equal to the equivalent length of a simple pendulum.
10. The frequency of oscillation of a torsional pendulum is
a) 2πkG/r √g/I
b) r/2πkG√g/I
c) 2πkG/r√I/g
d) r/2πkG√I/g
Answer
Answer: b
Set 5
1. In a reciprocating steam engine, which of the following forms a kinematic link ?
a) cylinder and piston
b) piston rod and connecting rod
c) crank shaft and flywheel
d) flywheel and engine frame
Answer
Answer: c [Reason:] in a reciprocating steam engine, piston, piston rod and crosshead constitute one link ; connecting rod with big and small end bearings constitute a second link ; crank, crank shaft and flywheel a third link and the cylinder, engine frame and main bearings a fourth link.
2. The motion of a piston in the cylinder of a steam engine is an example of
a) completely constrained motion
b) incompletely constrained motion
c) successfully constrained motion
d) none of the mentioned
Answer
Answer: a [Reason:] The piston and cylinder in a steam engine form a pair and the motion of the piston is limited to a definite direction (i.e. it will only reciprocate) relative to the cylinder irrespective of the direction of motion of the crank.
3. The motion transmitted between the teeth of gears in mesh is
a) sliding
b) rolling
c) may be rolling or sliding depending upon the shape of teeth
d) partly sliding and partly rolling
Answer
Answer: d [Reason:] 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, and in mesh the gears have a point contact.
4. The cam and follower without a spring forms a
a) lower pair
b) higher pair
c) self closed pair
d) force closed pair
Answer
Answer: c [Reason:] When the two elements of a pair are connected together mechanically in such a way that only required kind of relative motion occurs, it is then known as self closed pair. The lower pairs are self closed pair and the motion of cam and follower is relative to each other.
5. A ball and a socket joint forms a
a) turning pair
b) rolling pair
c) sliding pair
d) spherical pair
Answer
Answer: d [Reason:] When the two elements of a pair are connected in such a way that one element (with spherical shape) turns or swivels about the other fixed element, the pair formed is called a spherical pair, and ball and socket joint are such pairs.
6. The lead screw of a lathe with nut forms a
a) sliding pair
b) rolling pair
c) screw pair
d) turning pair
Answer
Answer: c [Reason:] When the two elements of a pair are connected in such a way that one element can turn about the other by screw threads, the pair is known as screw pair. The lead screw of a lathe with nut, and bolt with a nut are examples of a screw pair.
7. When the elements of the pair are kept in contact by the action of external forces, the pair is said to be a
a) lower pair
b) higher pair
c) self closed pair
d) force closed pair
Answer
Answer: d [Reason:] When the two elements of a pair are not connected mechanically but are kept in contact by the action of external forces, the pair is said to be a force-closed pair. The cam and follower is an example of force closed pair, as it is kept in contact by the forces exerted by spring and gravity.
8. Which of the following is a turning pair ?
a) Piston and cylinder of a reciprocating steam engine
b) Shaft with collars at both ends fitted in a circular hole
c) Lead screw of a lathe with nut
d) Ball and socket joint
Answer
Answer: b [Reason:] When the two elements of a pair are connected in such a way that one can only turn or revolve about a fixed axis of another link, the pair is known as turning pair. A shaft with collars at both ends fitted into a circular hole, the crankshaft in a journal bearing in an engine, lathe spindle supported in head stock, cycle wheels turning over their axles etc. are the examples of a turning pair.
9. 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
Answer: c [Reason:] When the kinematic pairs are coupled in such a way that the last link is joined to the first link to transmit definite motion (i.e. completely or successfully constrained motion), it is called a kinematic chain. In other words, a kinematic chain may be 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.
10. The relation between the 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
Answer: c [Reason:] If each link is assumed to form two pairs with two 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 = 2 p – 4
