Quiz: Mechanical Engineering 30th April

Quiz: Mechanical Engineering
Exam: DFCCIL
Topic: Theory of machines

Each question carries 2 mark
Negative marking: 1/3 mark
Time: 10 Minutes

Q1. Instantaneous center of a body rolling without sliding on a stationary curved surface lie.
(a) at the point of contact
(b) on the common normal at the point of contact
(c) on the common tangent at the point of contact
(d) at the centre of curvature of the stationary surface

Q2. For a certain engine having an average speed of 1200 rpm, a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within 2% about the average speed. The fluctuation of kinetic energy per cycle is found to be 2kJ. What is the least possible mass of the flywheel if its diameter is not to exceed 1m?
(a) 40 kg
(b) 51 kg
(c) 62 kg
(d) 73 kg

Q3. A universal joint is an example of
(a) Lower pair
(b) Higher pair
(c) Rolling pair
(d) Sliding pair

Q4. Gear tooth vernier is used to measure
(a) To measure the addendum
(b) To measure the addendum and dedendum
(c) To measure the circular pitch
(d) To measure pitch line thickness of tooth

Q5. Consider the following statements in respect of four bar mechanism:
1. It is possible to have the length of one link greater than the sum of lengths of other three links.
2. If the sum of the lengths of the shortest and the longest links is less than the sum of lengths of the other two, It is known as Grasshoff’s linkage.
3. It is possible to have the sum of lengths of the shortest and the longest links greater than that of remaining two links.
Which of these statements is/are correct ?
(a) 1,2 and 3
(b) 2 and 3
(c) 2 only
(d) 3 only

Q6. A rack is a gear of
(a) Infinite diameter
(b) Infinite module
(c) Zero pressure angle
(d) Large pitch

Q7. The safe rim velocity of a flywheel is influenced by the
(a) Centrifugal stresses
(b) Fluctuation of energy
(c) Fluctuation of speed
(d) Mass of flywheel

Q8. For an epicyclic gear train, the input torque is 100 Nm. RPM of the input gear is 1000(clockwise). While that of the output gear is 50 RPM (Anticlockwise). What is the magnitude of the holding torque for the gear train?
(a) Zero
(b) 500 Nm
(c) 2100 Nm
(d) None of these

Q9. Which one of the following is the correct statement? Transmissibility is defined as the ratio of the
(a) Force applied to the machine to the force transmitted to the foundation
(b) Force transmitted to the foundation to the force applied to the machine
(c) Force applied to the machine to the vector sum of spring forces
(d) Damping forces to the spring forces

Q10. Consider the following statements:
1. Critical or whirling speed of the shaft is the speed at which it tends to vibrate violently in the transverse direction.
2. To find the natural frequency of a shaft carrying several loads, the energy method gives approximate results.
3. Dunkerley’s method gives accurate results of the natural frequency of a shaft carrying several loads.
Which of these statements is/are correct?
(a) 1 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1,2 and 3

Solutions

S1. Ans.(a)
Sol. because without sliding only contact point has zero velocity.

S2. Ans.(b)
Sol. Average speed, ω=(2π×1200)/60=123.66 rad\/sec
We know that, ∆E = Iω² Cs
And,
∆E=(MR^2)/2×ω^2×Cs
=(2×2000)/((1/2)^2×(123.66)^2×0.02)=50.66≈51 kg

S3. Ans(a)
Sol. Universal joint is also known as Hooke’s joint. And we already know that Hooke’s joint is used to connect two Non parallel intersecting shaft or Non parallel Co-planer shafts.
And Hooke’s joint makes a surface contact which comes in the category of lower pair.
S4. Ans(d)
Sol. Gear tooth Vernier is used to measure the thickness of the tooth at the pitch line by using the distance from the top of a tooth to the chord.
S5. Ans(b)
Sol. It is not possible that length of one link is greater than the sum of other three links.
In grasshoff’s linkage s+l≤p+q i.e the sum of the shortest and longest link is less than or equal to the sum of other two links.
It is possible to have the sum of the lengths of shortest and longest links greater than that of other two links but that is not grasshoff’s linkage.
S6. Ans(a)
Sol. A rack is a gear which is like a straight line. As we know that straight line is circle of infinite radius therefore rack is gear of infinite radius.
S7. Ans(a)
Sol. The safe rim velocity of flywheel is determined by the centrifugal stresses.
v=√(σ/ρ)
Where v is velocity, 𝜎 is centrifugal stress and 𝞀 is density of rim material.
S8. Ans(c)
Sol. T_i ω_i+T_o ω_o=0
100×1000+T_o (-50)=0
T_o=2000 Nm
Again,
T_i+T_o+T_holding=0
100+2000+T_holding=0
T_holding= -2100 Nm

S9. Ans(b)
Sol. Transmissibility is defined as the ratio of the force transmitted (to the foundation) to the force applied. It is the measure of the effectiveness of vibrating isolating material.
S10. Ans(a)
Sol. There are two methods to find the natural frequency of the system/shaft carrying several loads.
(i) Dunkerley’s method which is semi-empirical gives approximate results but is simple.
(ii) The energy method (also known as rayleigh’s method) gives accurate results but involves heavy calculations in case there are many loads.

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