Category: Machine Kinematics Objective Questions

Machine Kinematics Multiple Choice Questions on “Simple Pendulum”.

1. The acceleration of the particle moving with simple harmonic motion is inversely proportional to the displacement of the particle from the mean position.
a) True
b) False
Answer: b
Clarification: The acceleration of the particle moving with simple harmonic motion is directly proportional to the displacement of the particle from the mean position.

2. In order to double the period of a simple pendulum, the length of the string should be
a) halved
b) doubled
c) quadrupled
d) none of the mentioned
Answer: c
Clarification: Periodic time, t_p = 2п√L/g
So, if period is doubled, then length should be quadrupled

3. The equivalent length of simple pendulum depends upon the distance between the point of the suspension and the center of gravity.
a) True
b) False
Answer: a
Clarification: None

4. Which of the following statement is correct?
a) The periodic time of a particle moving with simple harmonic motion is the time taken by a particle for one complete oscillation.
b) The periodic time of a particle moving with simple harmonic motion is directly proportional to its angular velocity.
c) The velocity of a particle moving with simple harmonic motion is zero at the mean position.
d) The acceleration of the particle moving with simple harmonic motion is maximum at the mean position.
Answer: a
Clarification: The time taken for one complete revolution of the particle is called periodic time.

5. The periodic time of a compound pendulum is …….. when the distance between the point of suspension and the center of gravity is equal to the radius of gyration of the body about its center of gravity.
a) zero
b) minimum
c) maximum
d) none of the mentioned
Answer: b
Clarification: 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.

6. In a simple harmonic motion, the velocity vector with respect to displacement vector
a) is in phase
b) leads by 90⁰
c) leads by 180⁰
d) lags by 90⁰
Answer: d
Clarification: None

7. The distance between the center of suspension and center of percussion is equal to the equivalent length of a simple pendulum.
a) True
b) False
Answer: a
Clarification: The periodic time and frequency of oscillation of a simple pendulum depends only upon its length and acceleration due to gravity.

8. The center of suspension and center of percussion are not interchangeable.
a) True
b) False
Answer: b
Clarification: The distance between the center of suspension and center of percussion is equal to the equivalent length of a simple pendulum.

9. When the body is suspended at the point of suspension, its periodic time and frequency will be _____________ as compared to the body suspended at the point of percussion.
a) same
b) two times
c) four times
d) eight times
Answer: a
Clarification: The distance between the center of suspension and center of percussion is equal to the equivalent length of a simple pendulum.

10. Bifilar suspension method is used to find the
a) angular acceleration of the body
b) moment of inertia of the body
c) periodic time of the body
d) frequency of vibration of the body
Answer: b
Clarification: None

Machine Kinematics Multiple Choice Questions on ” Velocity of a Point on a Link by Relative Velocity Method”.

1. The instantaneous centre is a point which is always fixed.
a) True
b) False
Answer: b
Clarification: The instantaneous center is not always fixed.

2. The angular velocity of a rotating body is expressed in terms of
a) revolution per minute
b) radians per second
c) any one of the mentioned
d) none of the mentioned
Answer: c
Clarification: Angular velocity is expressed both as revolution per minute and radians per second.

3. The linear velocity of a rotating body is given by the relation
a) v = rω
b) v = r/ω
c) v = ω/r
d) v = ω²/r
Answer: a
Clarification: The linear velocity of a rotating body is given by the relation v = rω
The linear acceleration of a rotating body is given by the relation a = rα.

4. The linear acceleration of a rotating body is given by the relation
a) a = rα
b) a = r/α
c) a = α/r
d) a = α²/r
Answer: a
Clarification: The linear velocity of a rotating body is given by the relation v = rω
The linear acceleration of a rotating body is given by the relation a = rα.

5. The relation between linear velocity and angular velocity of a cycle
a) exists under all conditions
b) does not exist under all conditions
c) exists only when it does not slip
d) exists only when it moves on horizontal plane
Answer: a
Clarification: None.

6. The velocity of piston in a reciprocating pump mechanism depends upon
a) angular velocity of the crank
b) radius of the crank
c) length of the connecting rod
d) all of the mentioned
Answer: d
Clarification: None.

7. The linear velocity of a point B on a link rotating at an angular velocity ω relative to another point A on the same link is
a) ω²AB
b) ωAB
c) ω(AB)²
d) ω/AB
Answer: b
Clarification: None.

8. The linear velocity of a point relative to another point on the same link is ……….. to the line joining the points.
a) perpendicular
b) parallel
c) at 45⁰
d) none of the mentioned
Answer: a
Clarification: The total linear acceleration of a particle can be obtained by combining the two mutually perpendicular accelerations.

9. According to Kennedy’s theorem the instantaneous centres of three bodies having relative motion lie on a
a) curved path
b) straight line
c) point
d) none of the mentioned
Answer: b
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.

10. The instantaneous centers of a slider moving in a linear guide lies at
a) pin joints
b) their point of contact
c) infinity
d) none of the mentioned
Answer: c
Clarification: The instantaneous centers of a slider moving in a linear guide lies at infinity.
The instantaneous centers of a slider moving in a curved surface lies at the center of curvature.

Machine Kinematics Multiple Choice Questions on “Laws of Fluid Friction”.

1. A multiple disc clutch has five plates having four pairs of active friction surfaces. If the intensity of pressure is not to exceed 0.127 N/mm², find the power transmitted at 500 r.p.m. The outer and inner radii of friction surfaces are 125 mm and 75 mm respectively. Assume uniform wear and take coefficient of friction = 0.3.
a) 17.8 kW
b) 18.8 kW
c) 19.8 kW
d) 20.8 kW
Answer: b
Clarification: n₁ + n₂ = 5 ; n = 4 ; p = 0.127 N/mm² ; N = 500 r.p.m. or ω = 2π × 500/60 = 52.4 rad/s ; r₁ = 125 mm ; r₂ = 75 mm ; μ = 0.3
Since the intensity of pressure is maximum at the inner radius r₂, therefore
p.r₂ = C or C = 0.127 × 75 = 9.525 N/mm
We know that axial force required to engage the clutch,
W = 2 π C (r₁ – r₂) = 2 π × 9.525 (125 – 75) = 2990 N
and mean radius of the friction surfaces,
R = r₁ + r₂/2 = 125 + 75/2 = 100 mm = 0.1 m
We know that torque transmitted,
T = n.μ.W.R = 4 × 0.3 × 2990 × 0.1 = 358.8 N-m
∴ Power transmitted,
P = T.ω = 358.8 × 52.4 = 18 800 W = 18.8 kW.

2. A single plate clutch, with both sides effective, has outer and inner diameters 300 mm and 200 mm respectively. The maximum intensity of pressure at any point in the contact surface is not to exceed 0.1 N/mm². If the coefficient of friction is 0.3, determine the power transmitted by a clutch at a speed 2500 r.p.m.
a) 61.693 kW
b) 71.693 kW
c) 81.693 kW
d) 91.693 kW
Answer: a
Clarification: Given : d₁ = 300 mm or r₁ = 150 mm ; d₂ = 200 mm or r₂ = 100 mm ; p = 0.1 N/mm² ; μ = 0.3 ; N = 2500 r.p.m. or ω = 2π × 2500/60 = 261.8 rad/s
Since the intensity of pressure ( p) is maximum at the inner radius (r₂), therefore for uniform wear,
p.r₂ = C or C = 0.1 × 100 = 10 N/mm
We know that the axial thrust,
W = 2 π C (r₁ – r₂) = 2 π × 10 (150 – 100) = 3142 N
and mean radius of the friction surfaces for uniform wear,
R = r₁ + r₂/2 = 150 + 100/2 = 125 mm = 0.125m
We know that torque transmitted,
T = n.μ.W.R = 2 × 0.3 × 3142 × 0.125 = 235.65 N-m …( n = 2,for both sides of plate effective)
∴ Power transmitted by a clutch,
P = T.ω = 235.65 × 261.8 = 61 693 W = 61.693 kW.

3. A 60 mm diameter shaft running in a bearing carries a load of 2000 N. If the coefficient of friction between the shaft and bearing is 0.03, find the power transmitted when it runs at 1440 r.p.m.
a) 171.4 W
b) 271.4 W
c) 371.4 W
d) 471.4 W
Answer: b
Clarification: Given : d = 60 mm or r = 30 mm = 0.03 m ; W = 2000 N ; μ = 0.03 ; N = 1440 r.p.m.
or ω = 2π × 1440/60 = 150.8 rad/s
We know that torque transmitted,
T = μ.W.r = 0.03 × 2000 × 0.03 = 1.8 N-m
∴ Power transmitted, P = T.ω = 1.8 × 150.8 = 271.4 W.

4. The force of friction is inversely proportional to the normal load between the surfaces.
a) True
b) False
Answer: b
Clarification: The force of friction is directly proportional to the normal load between the surfaces.

5. The force of friction is dependent of the area of the contact surface for a given normal load.
a) True
b) False
Answer: b
Clarification: The force of friction is independent of the area of the contact surface for a given normal load.

6. The force of friction depends upon the material of which the contact surfaces are made.
a) True
b) False
Answer: a
Clarification: Following are the laws of solid friction :
1. The force of friction is directly proportional to the normal load between the surfaces.
2. The force of friction is independent of the area of the contact surface for a given normal load.
3. The force of friction depends upon the material of which the contact surfaces are made.
4. The force of friction is independent of the velocity of sliding of one body relative to the other body.

7. The force of friction is dependent of the velocity of sliding of one body relative to the other body.
a) True
b) False
Answer: b
Clarification: The force of friction is independent of the velocity of sliding of one body relative to the other body.

8. The force of friction is almost dependent of the load.
a) True
b) False
Answer: b
Clarification: The force of friction is almost independent of the load.

9. The force of friction is dependent of the substances of the bearing surfaces.
a) True
b) False
Answer: b
Clarification: The force of friction is independent of the substances of the bearing surfaces.

10. The force of friction is _____________ for different lubricants.
a) same
b) different
c) zero
d) none of the mentioned
Answer: a
Clarification: The force of friction is different for different lubricants.

Machine Kinematics Multiple Choice Questions on “Toothed Gearing – 1”.

1. The two parallel and coplanar shafts are connected by gears having teeth parallel to the axis of the shaft. This arrangement is called
a) spur gearing
b) helical gearing
c) bevel gearing
d) spiral gearing
Answer: a
Clarification: The two parallel and co-planar shafts connected by the gears. These gears are called spur gears and the arrangement is known as spur gearing. These gears have teeth parallel to the axis of the wheel as shown in Fig. 12.1. Another name given to the spur gearing is helical gearing, in which the teeth are inclined to the axis.

2. The type of gears used to connect two non-parallel non-intersecting shafts are
a) spur gears
b) helical gears
c) spiral gears
d) none of the mentioned
Answer: c
Clarification: The two non-intersecting and non-parallel i.e. non-coplanar shaft connected by gears. These gears are called skew bevel gears or spiral gears and the arrangement is known as skew bevel gearing or spiral gearing. This type of gearing also have a line contact, the rotation of which about the axes generates the two pitch surfaces known as hyperboloids.

3. An imaginary circle which by pure rolling action, gives the same motion as the actual gear, is called
a) addendum circle
b) dedendum circle
c) pitch circle
d) clearance circle
Answer: c
Clarification: Pitch circle is an imaginary circle which by pure rolling action, would give the same motion as the actual gear.
Addendum circle is the circle drawn through the top of the teeth and is concentric with the pitch circle.
Dedendum circle is the circle drawn through the bottom of the teeth. It is also called root circle.

4. The size of a gear is usually specified by
a) pressure angle
b) circular pitch
c) diametral pitch
d) pitch circle diameter
Answer: d
Clarification: Pitch circle diameter is the diameter of the pitch circle. The size of the gear is usually specified by the pitch circle diameter. It is also known as pitch diameter.

5. The radial distance of a tooth from the pitch circle to the bottom of the tooth, is called
a) dedendum
b) addendum
c) clearance
d) working depth
Answer: a
Clarification: Addendum is the radial distance of a tooth from the pitch circle to the top of the tooth.
Dedendum is the radial distance of a tooth from the pitch circle to the bottom of the tooth.

6. The product of the diametral pitch and circular pitch is equal to
a) 1
b) 1/π
c) π
d) 2π
Answer: c
Clarification: Diametral pitch, p_d = T/D = π/p_c
where, p_c = circular pitch.

7. The module is the reciprocal of
a) diametral pitch
b) circular pitch
c) pitch diameter
d) none of the mentioned
Answer: a
Clarification: It is the ratio of the pitch circle diameter in millimeters to the number of teeth.
It is usually denoted by m. Mathematically,
Module, m = D /T.

8. Which is the incorrect relationship of gears?
a) Circular pitch × Diametral pitch = π
b) Module = P.C.D/No.of teeth
c) Dedendum = 1.157 module
d) Addendum = 2.157 module
Answer: d
Clarification: None.

9. If the module of a gear be m, the number of teeth T and pitch circle diameter D, then
a) m = D/T
b) D = T/m
c) m = D/2T
d) none of the mentioned
Answer: a
Clarification: Module, m = D /T.

10. Mitre gears are used for
a) great speed reduction
b) equal speed
c) minimum axial thrust
d) minimum backlash
Answer: b
Clarification: When equal bevel gears (having equal teeth) connect two shafts whose axes are mutually perpendicular, then the bevel gears are known as mitres.

Machine Kinematics Multiple Choice Questions on “Gearing”.

1. Radial distance between the pitch circle and the top of the tooth is known as
a) pitch
b) addendum
c) base circle
d) none of the mentioned
Answer: b
Clarification: The circle from which an involute curve is generated is known as base circle.
Radial distance between the pitch circle and the top of the tooth is known as addendum.

2. The circle from which an involute curve is generated is known as
a) pitch
b) addendum
c) base circle
d) none of the mentioned
Answer: c
Clarification: The circle from which an involute curve is generated is known as base circle.
Radial distance between the pitch circle and the top of the tooth is known as addendum.

3. Length of the arc of the pitch circle between the centres or other corresponding points of adjacent teeth is known as
a) pitch
b) circular pitch
c) base circle
d) none of the mentioned
Answer: b
Clarification: Length of the arc of the pitch circle between the centres or other corresponding points of adjacent teeth is known as circular pitch.
The circle from which an involute curve is generated is known as base circle.
Radial distance between the pitch circle and the top of the tooth is known as addendum.

4. The curve formed by the point on a circle as it rolls along a straight line is known as
a) cycloid
b) addendum
c) base circle
d) none of the mentioned
Answer: a
Clarification: Length of the arc of the pitch circle between the centres or other corresponding points of adjacent teeth is known as circular pitch.
The circle from which an involute curve is generated is known as base circle.
The curve formed by the point on a circle as it rolls along a straight line is known as cycloid.

5. That surface of the tooth which is between the pitch circle and the top of the tooth is known as
a) cycloid
b) addendum
c) face of tooth
d) none of the mentioned
Answer: c
Clarification: The circle from which an involute curve is generated is known as base circle.
The curve formed by the point on a circle as it rolls along a straight line is known as cycloid.
That surface of the tooth which is between the pitch circle and the top of the tooth is known as face of tooth.

6. The distance between similar, equally spaced tooth surfaces, in a given direction and along a given curve or line is known as
a) pitch
b) addendum
c) base circle
d) none of the mentioned
Answer: a
Clarification: The curve formed by the point on a circle as it rolls along a straight line is known as cycloid.
That surface of the tooth which is between the pitch circle and the top of the tooth is known as face of tooth.
The distance between similar, equally spaced tooth surfaces, in a given direction and along a given curve or line is known as pitch.

7. The angle between a tooth profile and a radial line at its pitch point is known as
a) pressure angle
b) dedendum angle
c) spiral angle
d) none of the mentioned
Answer: a
Clarification: The angle subtended at the centre of a base circle from the origin of an involute to the point of tangency of the generatrix from any point on the same involute is known as roll angle.
The angle between a tooth profile and a radial line at its pitch point is known as pressure angle.

8. The angle subtended at the centre of a base circle from the origin of an involute to the point of tangency of the generatrix from any point on the same involute is known as
a) pressure angle
b) dedendum angle
c) roll angle
d) none of the mentioned
Answer: c
Clarification: The angle subtended at the centre of a base circle from the origin of an involute to the point of tangency of the generatrix from any point on the same involute is known as roll angle.
The angle between a tooth profile and a radial line at its pitch point is known as pressure angle.

9. Surface of the gear between the fillets of adjacent teeth is known as
a) cycloid
b) addendum
c) bottom land
d) none of the mentioned
Answer: c
Clarification: Surface of the gear between the fillets of adjacent teeth is known as bottom land.

10. The angle, at the base cylinder of an involute gear, that the tooth makes with the gear axis is known as
a) pressure angle
b) base helix angle
c) roll angle
d) none of the mentioned
Answer: b
Clarification: The angle subtended at the centre of a base circle from the origin of an involute to the point of tangency of the generatrix from any point on the same involute is known as roll angle.
The angle between a tooth profile and a radial line at its pitch point is known as pressure angle.
The angle, at the base cylinder of an involute gear, that the tooth makes with the gear axis is known as base helix angle.