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# Quiz: Mechanical Engineering 29th June

Quiz: Mechanical Engineering
Exam: AE/JE
Topic: Miscellaneous

Each question carries 1 mark
Negative marking: 1/4 mark
Time: 10 Minutes

Q1. In under-damped vibrating system, the amplitude of vibration with reference to time…………
(a) Increases linearly
(b) Increases exponentially
(c) decreases linearly
(d) decreases exponentially

Q2. A body is vibrating at 10 vibrations/ second in Simple harmonic Motion with 10 cm amplitude. The maximum velocity in cm/sec can be____________.
(a) 100 π
(b) 50 π
(c) 200 π
(d) 100

Q3. A body of weight W is placed on a rough inclined plane. The inclination of the plane with the horizontal is less than the angle of friction. The body will
(a) be in equilibrium
(b) move downwards
(c) move upwards
(d) None of the above

Q4. The maximum frictional force, which force, which comes into play when a body first begins to slide over the surface of another body is known as:
(a) Sliding friction
(b) Limiting friction
(c) Kinetic friction
(d) Rolling friction

Q5. A tapering bar (diameter of end sections being d_1 and d_2) and a bar of uniform cross-section ‘d’, have the same length and are subjected to the same axial pull. Both the bars will have the same extension if ’d’
(a) (d_1+d_2)/2
(b) √(d_1 d_2 )
(c) √((d_1+d_2)/2)
(d) √(d_1+d_2 )/2

Q6. The radius taken into consideration in calculating the stress in a hollow shaft subjected to torsion

Q7. For a power transmission shaft transmitting power P at N rpm, the diameter is proportional to
(a) (〖P/N)〗^(1/3)
(b) (〖P/N)〗^(1/2)
(c) (〖P/N)〗^(2/3)
(d) P/N

Q8. For a given stress, the ratio of moment of resistance of a square beam with its sides horizontal, compared to when the diagonal is horizontal, is
(a) 2
(b) √2
(c) 2√2
(d) 1.5

Q9. Train value of a gear train is
(a) equal to speed ratio
(b) half of speed ratio
(c) reciprocal of speed ratio
(d) double the spewed ratio

Q10. Select the wrong statement:
(a) The coefficient of fluctuation of speed remains same with any change in the mean speed of prime mover.
(b) The maximum fluctuation of energy of a flywheel is directly proportional to coefficient of fluctuation of speed.
(c) For the same fluctuation of energy, the size of the flywheel is reduced at higher mean speed of rotation.
(d) For the same mass of flywheel, the rim type and disc type flywheels are equally preferable.

Solutions

S1. Ans.(d)
Sol.
(1) for and under-damped system, ς<1 (2) for and critically damped system, ς=1 (3) for an over-damped system, ς>1

S2. Ans.(c)
Sol. given, amplitude (a) = 10 cm, frequency (f) = 10 vibrations/sec
ω=2πf
Max velocity V_max=?
We know,
V_max =aω [S.H.M.]
=10×2π×10
▭(V_max=200π cm\/sec)

S3. Ans.(a)
Sol. For a body to be in motion its inclination should be more than the angle of friction. Angle of friction is the limiting angle at which body is at verge of motion.

S4. Ans.(b)
Sol. The friction between surface of stationary bodies is known as static friction.

S5. Ans (b)
Sol.
For a tapered bar of dia. varying from d_1 to d_2 and length L ,elongation due to load P is
δ_1=4PL/(πEd_1 d_2 )
For a bar of uniform dia. d and length L ,elongation due to load P is
δ_2=4PL/(πEd^2 )
Given, δ_1=δ_2
d^2=d_1 d_2
d=√(d_1 d_2 )

S6. Ans (b)
Sol. Outer radius is considered to calculate stress in hollow shaft subjected to torsion.

S7. Ans (a)
Sol. We know that Power of a rotating shaft (P)=2πNT/60…………..(1)
Here, N=Rotation speed in RPM of shaft
T=mean resisting torque of shaft
But we know that if maximum shear stress (τ) remains constant for a particular material.
So, τ=16T/(πd^3 )……………….(2)
From equation (1) and (2)
(P)=(2π^2 Nτd^3)/60X16
d^3∝P/N
d∝(〖P/N)〗^(1/3)

S8. Ans (b)
Sol.

We know from Bending equation,
Moment of resistance (M_t)∝Section modulus (Z)
Section modulus for square section (Z_1)=d^3/6
Section modulus for lateral square section (Z_2)=d^4/12 X √2/d
Ratio of Moment of resistance for square and lateral square section M_(t_1 )/M_(t_2 ) =Z_1/Z_2 =(d^3/6)/(d^4/12 X √2/d)=√2

S9. Ans (c)
Sol. Train value=1/(Speed ratio)

S10. Ans (d)
Sol. Rim type flywheel is preferred over disc type flywheel for same masses of flywheels because high mass moment of inertia of rim type flywheel leads to high energy storage capacity of flywheel.

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