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ISRO Mechanical Engineering Theory of Machines and Mechanical Vibrations Questions, Answers and Explanation

ISRO Mechanical Engineering Theory of Machines and Mechanical Vibrations

Gear and Gear Trains

2014. 80. Which type of gear meshing should be employed to transmit torque to a linear force?
a) Epicyclic gear
b) Helical gear
c) Bevel gear
d) Rack and pinion
Answer
d) Rack and pinion
Explanation
Epicyclic gear trains have one or more axes of gears in motion. In all other gear types the gear rotates about an axis but the axis does not move.
Helical gears are smoother in operations and create a thrust load and hence required support to compensate this load. They can also be used to transmit torques at 90o 
Bevel gears are the ones in which the axes of gears intersect normally at 90o. But they can work at other angles also.
Rack and pinion gears are used to convert rotation into linear motion.

2017.2.8. Which of the following is FALSE?
a) A reverted gear train is one in which the first and last gears are on the same axis.
b) Train value for a gear is the ratio of product of driven tooth numbers to product of driving tooth numbers.
c) A planetary gear train is one in which the axes of some of the gears may have a motion.
d) A compound gear train is one which has two or more gears on each axis.

Answer
b) Train value for a gear is the ratio of product of driven tooth numbers to product of driving tooth numbers.

Explanation 
By definition the axes of first driver and last driven of a reverted gear is co-axial.
Train value of a gear train is the ratio of the speed of the driven gear to the speed of the driving gear. As the speed of a gear is inversely proportional to the number of teeth in it the correct definition of the train ratio is the "ratio of product of driving tooth numbers to the product of the driven tooth numbers".
In a planetary gear train at-least one of the gears revolve around another gear in the gear train.
A compound gear train is one which at-least one pair of gears are rigidly mounted on the same shaft and thus having same revolution speed.

Spring System

2006. 11. A mass m attached to a light spring oscillates with a period of 2 sec. If the mass is increased by 2 kg, the period increases by 1 sec. The value of m is
a) 1 kg
b) 1.6 kg
c) 2 kg
d) 2.4 kg

Answer
b) 1.6 kg

Explanation
T = 2π √(m/k)
Case 1 - T = 2 sec, m = m kg, 2 = 2π √(m/k)
Case 2 - T = 3 sec, m = m + 2 kg, 3 = 2π √((m+2)/k)
Dividing one by another
2/3 = √ (m/(m+2))
squaring on both sides
4/9 = m/(m+2)
4m + 8 = 9m
5m = 8
m = 8/5 = 1.6 kg

Simple Harmonic Motion

2010.50. In simple harmonic motion the acceleration is proportional to
a) Displacement
b) Linear Velocity
c) Angular Velocity
d) Rate of change of angular velocity

Answer
a) Displacement

Explanation
In simple harmonic motion (SHM), some physical quantity varies sinusoidally. 
Example, simple harmonic motion is a spring object system on a friction-less surface. The object is attached to one end of a spring. The other end of the spring is attached to a wall at the left. the spring force depends on the distance x , the acceleration is not constant.It is a second order linear differential equation, in which the second derivative of the dependent variable is proportional to the negative of the dependent variable.

Natural Frequency and Resonance

2017.2.75. A cantilever beam of cross section area 'A', moment of Inertia 'I' and length 'L' is having natural frequency ω1. If the beam is accidentally broken into two halves, the natural frequency of the remaining cantilever beam ω2 will be such that
a) ω2
b) ω2> ω1
c) ω2=ω1
d) Cannot be obtained from the given data

Answer
b) ω2> ω1

 Explanation
The natural frequency ωn ∝ 1/L2 √ (EI/ρA)
So when the length is halved the natural frequency quadruples.
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