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# Multiple choice question for engineering

## Set 1

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 [Reason:] 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
d) none of the mentioned

Answer: c [Reason:] Periodic time, tp = 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

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 [Reason:] 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 [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.

6. In a simple harmonic motion, the velocity vector with respect to displacement vector
a) is in phase
d) lags by 900

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 [Reason:] 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 [Reason:] 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 [Reason:] 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

## Set 2

1. The quick return mechanism which is an inversion of 4-bar linkage is
b) Whitworth quick return mechanism
c) Crank and slotted lever mechanism
d) None of the mentioned

Answer: a [Reason:] Drag link mechanism is an inversion of 4-bar linkage, which is a crank mechanism with different crank lengths. It is made up of revolute pairs only.

2. Match list I with list II
List I List II
A. Pantograph 1. Scotch yoke mechanism
B. Single slider crank 2. Double lever mechanism
C. Double slider crank chain 3. Tchebicheff’s mechanism
D. Straight line motion mechanism 4. Double crank
5. Hand pump
a) A-4,B-3,C-5,D-1
b) A-2,B-5,C-1,D-3
c) A-2,B-1,C-5,D-3
d) A-4,B-5,C-2,D-1

Answer: b [Reason:] Pantograph is double lever mechanism. handpump is an inversion of single slider crank chain. Scotch yoke mechanism is an inversion of double slider crank chain.Tchebiceff’s mechanism is an approximate straight line motion mechanism.

3. Match list I with list II
List I List II
A. Scott-Russel 1. Intemittent mechanism motion
B. Geneva 2. Quick return mechanism motion
C. Offset slider crank 3. Simple motion harmonic mechanism
D. Scotch Yoke 4. Straight line mechanism motion

a) A-2,B-3,C-1,D-4
b) A-3,B-2,C-4,D-1
c) A-4,B-1,C-2,D-3
d) A-4,B-3,C-1,D-2

Answer: c [Reason:] Scott-Russel – Straight line mechanism motion Geneva – Intemittent mechanism motion Offset slider crank – Quick return mechanism motion Scotch Yoke – Simple motion harmonic mechanism.

4. 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: b [Reason:] Before placement on Vee-block, cylinder has 6 degrees of freedom. After placement on Vee-block, the cylinder has only 2 degrees of freedom. Hence, the degrees of freedom which are arrested is 6 – 2 = 4.

5. Match list I with list II

Type of joint Motion constrained
A. Revolute 1. Three
B. Cylindrical 2. Five
C. Spherical 3. Four
4. Two
5. Zero
a) A-1,B-3,C-2
b) A-5,B-4,C-3
c) A-2,B-3,C-1
d) A-4,B-5,C-3

Answer: c [Reason:] For revolute pair, degree of freedom = 1 and constrained DOF = 6 – 1 = 5 For cylindrical pair, dof =2 and constrained dof = 6 – 2 = 4 For spherical pair, dof = 3 and constrained dof = 6 – 3 = 3.

6. The number of binary links, number of binary joints and number of ternary joints in Peaucelliar mechanism is
a) 6,6,0
b) 8,2,4
c) 8,4,2
d) 8,8,0

Answer: b [Reason:] The Peaucelliar mechanism has 8 binary links, 2 binary joints nad 4 ternary joints.

7. The number of degree of freedom of a planer linkage with 8 links and 9 simple revolute joints is
a) 1
b) 2
c) 3
d) 4

Answer: c [Reason:] L = 8 = number of links P = 9 = number of simple revolute joints

F = 3(L – 1) – 2P = 3(8 – 1) – 2 x 9 = 21 – 18 = 3.

8. The following list of statements is given:
1) Grashoff’s rule states that for a planar crank-rocker 4-bar mechanism, the sum of the shortest and longest link lengths cannot be less than the sum of the remaining two link lengths.
2) Inversions of a mechanism are created by fixing different links, one at a time.
3) Geneva mechanism is an intermittent motion device.
4) Grubler’s criterion assumes mobility of a planar mechanism to be one.

The number of correct statements in the above list is
a) 1
b) 2
c) 3
d) 4

Answer: c [Reason:] Except statement 1, all other three statements are correct.

9. A mechanism has 8 links, out of which 5 are binary, 2 are ternary and 1 is quaternary. The number of instantaneous centres of rotation will be
a) 28
b) 56
c) 62
d) 66

Answer: d [Reason:] n = 5 + 4 + 3 = 12 Number of instantaneous centres, N = n(n – 1)/2 = 12 x (12 – 1)/2 = 66.

10. In a dynamically equivalent system, a uniformly distributed mass is divided into
a) Three point masses
b) Four point masses
c) Two point masses
d) Infinite point masses

Answer: c [Reason:] Dynamically equivalent system of a rigid body is made of two point masses.

11. A crank and slotted lever mechanism used in a shaper has a centre distance of 300 mm between the centre of oscillation of the slotted lever and the centre of rotation of the crank. The radius of the crank is 120 mm. Find the ratio of the time of cutting to the time of return stroke.
a) 1.62
b) 1.72
c) 1.82
d) 1.92

Answer: b [Reason:] Given : AC = 300 mm ; CB = 120 mm sin∠CAB = sin (90°−α/ 2) CB/AC = 120/300 = 0.4

∠CAB = 90°−α/ 2 or α / 2 = 90° – 23.6° = 66.4° α = 2 × 66.4 = 132.8°

We know that Time of cutting stroke/ Time of return stroke = 1.72.

12. The magnitude of velocities of the points on a rigid link is directly proportional to the distances from the points to the instantaneous centre.
a) True
b) False

Answer: b [Reason:] The magnitude of velocities of the points on a rigid link is inversely proportional to the distances from the points to the instantaneous centre and is perpendicular to the line joining the point to the instantaneous centre.

13. The velocity of the instantaneous centre relative to any third rigid link will be different.
a) True
b) False

Answer: b [Reason:] 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.

14. When the pin connects one sliding member and the other turning member, the angular velocity of the sliding member is __________
a) 0
b) 1
c) 2
d) 3

Answer: a [Reason:] When the pin connects one sliding member and the other turning member, the angular velocity of the sliding member is zero. In such cases, Rubbing velocity at the pin joint = ω.r where ω = Angular velocity of the turning member, and r = Radius of the pin.

15. In a slider crank mechanism, the velocity of piston becomes maximum when
a) Crank and connecting rod are in line with each other
b) Crank is perpendicular to the line of stroke of the piston
c) Crank and connecting rod are mutually perpendicular
d) Crank is 1200 with the line of stroke

## Set 3

1. The gears are termed as medium velocity gears, if their peripheral velocity is
a) 1–3 m / s
b) 3–15 m / s
c) 15–30 m / s
d) 30–50 m / s

Answer: b [Reason:] The gears having velocity less than 3 m/s are termed as low velocity gears and gears having velocity between 3 and 15 m / s are known as medium velocity gears. If the velocity of gears is more than 15 m / s, then these are called high speed gears.

2. The size of gear is usually specified by
a) pressure angle
b) pitch circle diameter
c) circular pitch
d) diametral pitch

Answer: b [Reason:] It is the diameter of the pitch circle. The size of the gear is usually specified by the pitch circle diameter. It is also called as pitch diameter.

3. A spur gear with pitch circle diameter D has number of teeth T. The module m is defined as
a) m = d / T
b) m = T / D
c) m = π D / T
d) m = D.T

Answer: a [Reason:] Module is the ratio of the pitch circle diameter in millimetres to the number of teeth. It is usually denoted by m. Mathematically, Module, m = D / T.

4. In a rack and pinion arrangement, the rack has teeth of _______________ shape.
a) square
b) trepazoidal
c) oval
d) circular

5. The radial distance from the _______________ to the clearance circle is called working depth.
b) dedendum circle
c) pitch circle
d) none of the mentioned

Answer: a [Reason:] Working depth is radial distance from the addendum circle to the clearance circle. It is equal to the sum of the addendum of the two meshing gears.

6. The product of the diametral pitch and circular pitch is equal to
a) 1
b) 1/π
c) π
d) π × No. of teeth

Answer: c [Reason:] Diametral pitch, pd =T/D = π/pc Circular pitch, pc = πD/T Therefore, pd x pc = π.

7. The backlash for spur gears depends upon
a) module
b) pitch line velocity
c) tooth profile
d) both (a) and (b)

Answer: d [Reason:] Backlash is the difference between the tooth space and the tooth thickness, as measured on the pitch circle.

8. The contact ratio for gears is
a) zero
b) less than one
c) greater than one
d) none of the mentioned

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.

9. If the centre distance of the mating gears having involute teeth is increased, then the pressure angle
a) increases
b) decreases
c) remains unchanged
d) none of the mentioned

Answer: a [Reason:] The pressure angle increases with the increase in centre distance.

10. The form factor of a spur gear tooth depends upon
a) circular pitch only
b) pressure angle only
c) number of teeth and circular pitch
d) number of teeth and the system of teeth

Answer: d [Reason:] Form factor is independent of the size of the tooth and depends only on the number of teeth on a gear and the system of teeth.

11. Lewis equation in spur gears is used to find the
a) tensile stress in bending
b) shear stress
c) compressive stress in bending
d) fatigue stress

12. The minimum number of teeth on the pinion in order to avoid interference for 20° stub system is
a) 12
b) 14
c) 18
d) 32

13. The allowable static stress for steel gears is approximately ____________ of the ultimate tensile stress.
a) one-fourth
b) one-third
c) one-half
d) double

Answer: b [Reason:] The allowable static stress (σo) for steel gears is approximately one-third of the ultimate tensile strength (σu) i.e. σo = σu / 3.

14. Lewis equation in spur gears is applied
a) only to the pinion
b) only to the gear
c) to stronger of the pinion or gear
d) to weaker of the pinion or gear

Answer: d [Reason:] The Lewis equation is applied only to the weaker of the two wheels (i.e. pinion or gear).

a) less than
b) greater than
c) equal to
d) none of the mentioned

Answer: b [Reason:] For safety, against tooth breakage, the static tooth load should be greater than the dynamic load.

## Set 4

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 [Reason:] 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 [Reason:] 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 [Reason:] 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 [Reason:] 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 [Reason:] 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
b) 2 dedendum
c) 3.1416 module
d) 2.157 module

Answer: a [Reason:] 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 [Reason:] 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 [Reason:] 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 [Reason:] 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 [Reason:] The correct relationship is chordal thickness = a + t2/4D

## Set 5

1. Lewis equation for design of involute gear tooth predicts the dynamic load capacity of a cantilever beam of uniform strength.
a) True
b) False

Answer: b [Reason:] Lewis equation for design of involute gear tooth predicts the static load capacity of a cantilever beam of uniform strength.

2. For a pair of gears in mesh, pressure angle and module must be different to satisfy the condition of interchangeability and correct gearing.
a) True
b) False

Answer: b [Reason:] For a pair of gears in mesh, pressure angle and module must be same to satisfy the condition of interchangeability and correct gearing.

3. In skew bevel gears, the axes are
a) non-parallel and non-intersecting, and teeth are curved
b) non-parallel and non-intersecting, and teeth are straight
c) intersecting, and teeth are curved and oblique
d) intersecting, and teeth are curved and can be ground

Answer: a [Reason:] Skew bevel gears imply non-parallel, non-intersecting and curved them.

4. In case the number of teeth on two bevel gears in mesh is 30 and 60 respectively, then the pitch cone angle of the gear will be
a) tan-12
b) п/2 + tan-12
c) п/2 – tan-10.5
d) tan-10.5

Answer: d [Reason:] tanɸ = NP/NG NP = No. of teeth of pinion NG = No. of teeth of gear ɸ = Pitch cone angle ɸ = tan-1(30/60) ɸ = tan-10.5.

5. Consider the following statements:
The axes of spiral bevel gear are non-parallel and intersecting.
1. The most common pressure angle for spiral bevel gear is 20o.
2. The most common spiral angle for spiral bevel gear is 35o.
3. Spiral bevel gears are generally interchangeable.
4. Spirals are noisy and recommended for low speeds of 10 m/s.

Which of the above statements are correct?
a) 1 and 4
b) 1 and 2
c) 2 and 3
d) 3 and 4

Answer: a [Reason:] Commonly used pressure angle is 20o, spiral gear operation is noisy hence recommended for low speed operation.

6. Consider the following statements:
In case of helical gears, teeth are cut at an angle to the axis of rotation of the gears.
1. Helix angle introduces another ratio called axial contact ratio.
2. Transverse contact ratio is equal to axial contact ratio in helical gears.
3. Large transverse contact ratio does not allow multiple teeth to share the load.
4. Large axial contact ratio will cause larger axial force component.

Which of the above statements are correct?
a) 1 and 2
b) 2 and 3
c) 1 and 4
d) 3 and 4

Answer: c [Reason:] Transverse contact ratio may not be equal to axial contact ratio. Larger contact ratio means sharing of multiple teeth.

7. A worm gear set is designed to have pressure angle of 300 which is equal to the helix angle. The efficiency of the worm gear set at an interface friction of 0.05 is
a) 87.9%
b) 77.9%
c) 67.9%
d) 57.9%

Answer: a [Reason:] ȵ = tanλ(cosɸ – μtanλ)/cosɸtanλ + μ tanλ = -μ + √1 + μ2 tanλ = -(0.05) + √1 + (0.05)2 tanλ = 0.9512

ȵ = 89.1%

So most suitable option is ‘a’.

8. The use of straight or curved external gear teeth in mesh with internal teeth in gear and spline couplings is specifically employed accommodate
a) torsional misalignment
b) parallel misalignment
c) angular misalignment
d) substantial axial movements between shafts

Answer: c [Reason:] Straight or curved external gear teeth are used to correct the angular misalignment.

9. A planetary gear train is gear train having
a) a relative motion of axes and the axis of at least one of the gears also moves relative to the frame
b) no relative motion of axes and no relative motion of axes with respect to the frame
c) no relative motion of axes and the axis of at least one of the gears also moves relative to the frame
d) a relative motion of axes and none of the axes of gears has relative motion with the frame