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# Multiple choice question for engineering

## Set 1

1. The displacement of a particle varies according to the relation
x=4(cosπt+sinπt)
The amplitude of the particle is
a) -4
b) 4
c) 4√2
d) 8

Answer: c [Reason:] x=4(cosπt+sinπt) x=4√2 (sin⁡(π/4)cosπt+cos⁡(π/4)sinπt) x=4√2 sin⁡(πt+π/4) Clearly,amplitude=4√2

2. The displacement y of a particle in a medium can be expressed as
y=10-6 sin⁡(100t+20x+π/4)
Where t is in seconds and x in meter. The speed of the wave is
a) 2000m/s
b) 5m/s
c) 20m/s
d) 5πm/s

3. The displacement y of a wave travelling in the x direction is given by
y=10-4 sin⁡(600t-2x+π/3)
Where x is expressed in meters and t is seconds. The speed of the wave motion (in m/s) is
a) 300
b) 600
c) 1200
d) 200

4. A wave y=asin(ωt-kx), on a string meets with another wave producing a node at x = 0. Then, the equation of the unknown wave is
a) y=asin⁡(ωt+kx)
b) y=-asin⁡(ωt+kx)
c) y=asin⁡(ωt-kx)
d) y=-asin⁡(ωt-kx)

Answer: b [Reason:] For producing node, the superposing wave must travel in opposite direction (x term must have opposite sign) and its displacement must be negative. Hence the correct option is b Moreover, y=y1+y2=asin⁡(ωt-kx)-asin⁡(ωt+kx) y=-2acosωtsinkx At x=0, y = 0. That is a node is formed

5. The speed of sound in oxygen (O2) at a certain temperature is 460m/s. The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal)
a) 460m/s
b) 500m/s
c) 650m/s
d) 1420m/s

Answer: d [Reason:] vHe/v(O2) =√(γHe(O2) ×M(O2)/MHe)=√((5/3)/(7/5)×32/4)=√(200/21) =√9.52=3.086 vHe=3.086v(O2)=3.086×460=1420m/s

6. Length of a string tied to two rigid supports is 40cm. Maximum length (wavelength in cm) of a stationary wave produced on it is
a) 20
b) 80
c) 40
d) 120

Answer: b [Reason:] When the string vibrates in one segment, L=ʎ/2 ʎ=2L=2×40=80cm

7. A metal wire of linear mass density of 9.8/gm is stretched with a tension of 10kg wt between two rigid supports 1m apart. The wire passes at its middle point between the poles of a permanent magnet and it vibrates in resonance, when carrying an alternating current of frequency v. The frequency v of the alternating source is
a) 50 Hz
b) 100 Hz
c) 200 Hz
d) 25 Hz

Answer: a [Reason:] Here, m=9.8/gm=9.8×10-3 kg/m T=10kg wt = 9.8×10=98N L=1m The fundamental frequency of vibration of the string, v=1/2L×√(T/m)=1/2×√(9.8/(9.8×10-3))=50Hz

8. A sound absorber attenuates the sound level by 20dB. The intensity decreases by a factor of
a) 100
b) 1000
c) 10000
d) 10

Answer: a [Reason:] L1=10log⁡(I1/I0) L2=10log⁡(I2/I0) I1-I2=10log⁡(I1/I2) 20dB=10log⁡(I1/I2) I1/I2 =102 I2=1/100×I1

9. The ratio of velocity of sound in hydrogen and oxygen at STP is
a) 16:1
b) 8:1
c) 4:1
d) 2:1

10. It takes 2 seconds for a second wave to travel between two fixed points when the day temperature is 10°C. If the temperature rises to 30°C, the sound wave travels between the same fixed parts in
a) 1.9 sec
b) 2 sec
c) 2.1 sec
d) 2.2 sec

Answer: a [Reason:] v∝1/√T and t∝1/v t2/t1 =√(T1/T2)=√((273+10)/(273+30))=√(283/303) t2=√(283/303)×2s=1.9s

## Set 2

1. Which of the following effects can be used to produce ultrasonic waves?
a) Magnetostriction effect
b) Doppler Effect
c) Magnetic effect
d) Sound effect

Answer: a [Reason:] When an alternating magnetic field is applied to a ferromagnetic material, then the rod is thrown into vibrations, thereby producing ultrasonic waves at resonance. Therefore ultrasonic waves can be produced using magnetostriction effect.

2. It is not possible to get a constant single frequency using magnetostriction effect. True or false?
a) True
b) False

Answer: a [Reason:] It is not possible to get a constant single frequency using magnetostriction method because it depends on the temperature.

3. When is ultrasonic waves produced using piezo electric oscillator?
a) At constant temperature
b) At resonance
c) At constant pressure
d) At constant voltage

Answer: b [Reason:] Piezo electric oscillators produce ultrasonic waves at resonance. That is, When the frequency of the oscillatory circuit is equal to the frequency of the vibrating crystal.

4. Which of the following causes acoustical grating?
a) Magnetic waves
b) Electric waves
c) Magnetostriction effect
d) Ultrasonic waves

Answer: d [Reason:] When ultrasonic waves are passed through a liquid, the density varies layer by layer due to variation in pressure and hence the liquid will act as a diffraction grating called acoustical grating.

5. What is the principle for measurement of velocity of ultrasonic waves?
a) Magnetostriction effect
b) Acoustical grating
c) Doppler Effect
d) Acceleration effect

Answer: b [Reason:] When ultrasonic waves are passed through a liquid, due to variation in pressure, the liquid will act as diffraction grating called acoustical grating. Under this condition when a monochromatic light is passed through the acoustical grating, the light gets diffracted. By using this velocity can be determined.

6. What is cold welding?
a) Welding at very low temperature
b) Welding using ultrasonic waves
c) Welding under water
d) Welding at constant temperature

Answer: b [Reason:] Some materials cannot be welded at high temperature. In such cases the welding can be done at room temperature using ultrasonics and is called cold welding.

7. What is the other name for ultrasonic flaw detector?
a) Destructive testing
b) Magnetostrictive testing
c) Non-destructive testing
d) Echo testing

Answer: c [Reason:] Whenever there is a change in medium, then the ultrasonic waves will be reflected. Thus, from the intensity of the reflected echoes, the flaws are detected without destroying the material and hence this method is known as non-destructive testing method.

8. Sonograms work under the principle of Doppler Effect. True or false?
a) False
b) True

Answer: b [Reason:] There is an apparent change is the frequency between the incident sound waves on the foetus and the reflected sound waves from the foetus. Therefore it works on the principle of Doppler Effect.

9. A quartz crystal of thickness 0.001m is vibrating at resonance. Calculate the fundamental frequency. Density of quartz = 2.650×103 kg/m3 and Young’s modulus for quartz = 7.9×1010 N/m2.
a) 2.7299×106MHz
b) 26.50×103Hz
c) 2.093×106Hz
d) 2.7299×1010MHz

Answer: a [Reason:] Fundamental frequency = 1/(2×0.001) √((7.9×1010)/(2.650×10-3)) Fundamental frequency = 2.7299×106MHz

10. An ultrasound pulse sent by a source in sea is reflected by a submerged target at a distance 597.50m and reaches the source after 0.83seconds. Find the velocity of sound in sea water.
a) 495.925m/s
b) 719.879m/s
c) 110m/s
d) 1439.75m/s

Answer: d [Reason:] Velocity = 2d/t Velocity = 1439.75m/s

## Set 3

1. If the density of planet is doubled without any change in its radius, how does g change on the planet?
a) It remains the same
b) It is tripled
c) It reduces
d) It is doubled

Answer: d [Reason:] If the density of planet is doubled without any changed in its radius, g also gets doubled, because g is proportional to the density of the planet.

2. A body can be shielded from gravitational effects. True or false?
a) True
b) False

Answer: b [Reason:] No, it is not possible to shield a body from gravitational effects because gravitational interaction does not depend upon the nature of the intervening medium.

3. Gravity acts on all bodies in proportion to their masses; therefore heavy body falls faster than light body.
a) True
b) False

Answer: b [Reason:] If F id the gravitational force on a body of mass m, then F=G Mm/R2 =mg Or g=GM/R2 Clearly, F is proportional to mass but g does not depend on m. Therefore all bodies fall with the same rapidness if there is no air resistance.

4. The mass of the moon is nearly 10% of the mass of the earth. What will be the gravitational force of the earth on the moon, in comparison to the gravitational force of the moon on the earth?
a) Both of the force will be equal
b) Gravitational force of the earth on the moon is much lesser
c) Gravitational force of the moon on the earth is much lesser
d) There is no effect

Answer: a [Reason:] If the mass of the moon is 10% of the mass of the earth, then the gravitational force of the earth on the moon will be equal in comparison with the gravitational force of the moon on earth. This is because the gravitational force between the two bodies id a mutual force.

5. A man waves his arm, while walking. This is
a) To keep constant velocity
b) To ease the tension
c) To increase the velocity
d) To balance the effect of earth’s gravity

Answer: d [Reason:] The waving of the arm helps in keeping the centre of gravity at a suitable position. This helps the man to walk comfortably.

6. Kepler’s second law is based on
a) Newton’s first law
b) Newton’s second law
c) Special theory of relativity
d) Conservation of angular momentum

Answer: d [Reason:] Kepler’s second law states that the radius vector drawn from the sun to a planet, sweeps out equal areas in equal intervals of time. It is based on the law of conservation of angular momentum.

7. Statement 1- An astronaut experiences weightlessness in a space satellite
Statement 2- When a body falls freely, it does not experience gravity
a) Statement 1 and statement 2 are correct and statement 2 is the correct explanation of statement 1
b) Statement 1 and statement 2 are correct but statement 2 is not the correct explanation of statement 1
c) Statement 1 is true but statement 2 is false
d) Both statement 1 and 2 are false

Answer: b [Reason:] Both statements are true but statement 2 is not the correct explanation of statement 1. The astronaut feels weightlessness because both the astronaut and the satellite are in a state of free fall towards the earth.

8. Two spheres of masses m and M are in air and the gravitational force between them is F. The space around the masses is now filled with liquid of specific gravity 3. The gravitational force will now be
a) 3F
b) F
c) F/3
d) F/9

Answer: b [Reason:] The gravitational force between the two bodies is independent of the nature of medium between them.

9. For a satellite escape velocity from earth is 11.2 km/s. If a body is to be projected in a direction making an angle 45° to the vertical, then the escape velocity is
a) 11.2×2km/s
b) 11.2km/s
c) 11.2×√2km/s
d) 11.2/√2km/s

Answer: b [Reason:] Escape velocity does not depend on the angle of projection of the body from the earth’s surface. Therefore v = 11.2 km/s

10. If earth loses its gravity, then for a body
a) A weight becomes zero, but not the mass
b) Mass becomes zero but not weight
c) Neither mass nor weight becomes zero
d) Both mass and weight are zero

Answer: a [Reason:] Weight = mg. As g becomes zero. Mass is the quantity of matter which is dependent of g.

11. A ball is dropped from a spacecraft revolving around the earth at a height of 120km. What will happen to the ball?
a) It will go very far in space
b) It will move with the same speed tangentially to the spacecraft
c) It will fall down to the earth gradually
d) It will continue to move with the same speed along the original orbit of spacecraft

Answer: d [Reason:] In the absence of any external torque, the ball will continue to move with the same speed along the original orbit of space craft.

## Set 4

1. Which of the following is a metallic glass?
a) Argon
b) Crypton
c) Nickel
d) Gold

Answer: c [Reason:] Metallic glasses are amorphous metallic solids which have high strength, good magnetic properties and better corrosion resistance and will posses both the properties of metals and glasses. Of the following only nickel is a metallic glass.

2. How are metallic glasses formed?
a) By increasing the rate of heating
b) By increasing the rate of cooling
c) By melting it
d) By rapidly heating and then cooling slowly

Answer: b [Reason:] Metals can be made into glassy state by increasing the rate of cooling to a very high level. At that state the atoms will not be able to arrange orderly because of its rapid cooling rate. Thus, the atoms will not be allowed to go to crystalline state, rather it goes to amorphous state and it will form a new type of material. Such materials are called metallic glasses.

3. When does metal transform into glass?
a) At Curie temperature
b) At critical temperature
c) At melting point of the metal
d) At glass transition temperature

Answer: d [Reason:] The temperature at which the metals in the molten form transforms into glasses is known as glass transition temperature. It is found that the glass transition temperature for metallic alloys varies from 20℃-300℃.

4. Which of the following is the most commonly used technique for preparation of metallic glass?
a) Melt spinning system
b) Twin roller system
c) Melt extraction system
d) Sputtering

Answer: a [Reason:] Molten alloy is made to impinge on a fast rotating roller to form metallic glasses in melt spinning system. Whereas in other systems two or more steps are involved in the process making it tedious.

5. Quenching results in formation of metallic glasses. True or false?
a) True
b) False

Answer: a [Reason:] Quenching means rapid cooling. Actually atoms of any material moves freely in a liquid state. Atoms can be arranged regularly when a liquid is cooled slowly. Instead, when a liquid is quenched, there will be irregular pattern, which results in the formation of metallic glasses.

6. Which of the following is true about metallic glasses?
a) Low electrical resistance
b) Hexagonal closely packed structure
c) Non-malleable
d) Low core loss

Answer: d [Reason:] Metallic glasses can be magnetised and demagnetised easily. They have very narrow hysteresis loop. They therefore exhibit very low hysteresis loss and hence transformer core loss is very less. They have high electrical resistance and Tetrahedral closely packed structure.

7. Metallic glasses cannot be use in cores of high power transformers. True or false?
a) True
b) False

Answer: b [Reason:] Since the metallic glasses possess low magnetic loss, high permeability, saturation magnetisation and low coercivity, these materials are used in cores of high power transformers.

8. When does a shape memory alloy return to its original shape?
a) At transition temperature
b) At Curie temperature
c) At memory transfer temperature
d) At normal temperature

Answer: c [Reason:] Shape memory alloys are those which change their shape from its original shape to a new shape and while heating or cooling it will come back to its original shape. This shape recovery process doesn’t happen at a single temperature but over a range of temperature. Thus, the range at which the SMA switches from new shape to its original shape is called transformation temperature or memory transfer temperature.

9. Why is NI-Ti alloy used in making eye frames?
a) Because they are hard
b) Because they are not flexible
c) Because they are hard to break
d) Because they are SMA

Answer: d [Reason:] NI-Ti alloys are shape memory alloys. Recently manufactured eye glass frames can be bent back and forth and can retain its original shape within fraction of time. All these materials are made up of NI-Ti alloys, which can withstand maximum deformation.

10. Can SMA be used to control and prevent fire?
a) No
b) Yes

Answer: b [Reason:] SMA is mainly used to control and prevent fire to a large extent. For example, an SMA is placed in a fire safety valve, when fire occurs, due to change in temperature the SMA changes its shape and shuts off fire.

11. Which of the following can be used to prepare nano-powder and nano-particles?
a) Sol-gel technique
b) Plasma arching
c) Chemical vapour deposition
d) Electro deposition

Answer: a [Reason:] Sol-gel process is based on hydrolysis of liquid precursors and formation of colloidal solutions. In every other technique either only nano-powder or nano-particles can be formed. Only in sol-gel technique both nano-powder and nano-particles can be formed.

## Set 5

1. A gun fires a bullet of mass 50g with a velocity of 30m/s. Because of this, the gun is pushed back with a velocity of 1m/s. The mass of the gun is
a) 5.5kg
b) 3.5kg
c) 1.5kg
d) 0.5kg

Answer: c [Reason:] By conservation of momentum, MV = mv M = mv/V = 1.5kg

2. A body of mass 5kg is raised vertically to a eight of 10m by a force of 170N. The velocity of the body at this height will be
a) 37m/s
b) 22m/s
c) 15m/s
d) 9.8m/s

Answer: b [Reason:] W = Gain in potential energy+Gain in kinetic energy Fh = mgh + 1/2 mv2 170×10=5×10×10+1/2×5×v2 v = √480 = 22m/s

3. A position dependent force, F = 7-2x+3x2-N acts on a small body of mass 2kg and displaces it from x = 0 to x = 5m. The work done in joules is
a) 135
b) 270
c) 35
d) 70

Answer: a [Reason:] W = ∫Fdx = ∫(7-2x+3x2 )dx = [7x-x2+x3] W = 35-25+125=135J

4. A particle of mass M is moving in a horizontal circle of radius R with uniform speed v. When it moves from one point to a diametrically opposite point, its
a) Kinetic energy changes by (Mv)2/4
b) Momentum does not change
c) Momentum changes by 2Mv
d) Kinetic energy changes by (Mv)2

Answer: c [Reason:] At any two diametrically opposite points, velocities of the particle have the same magnitude but opposite directions. Therefore change in momentum = Mv-(-MV)=2Mv

5. Two identical balls A and B collide head on elastically. If velocities of A and B, before the collision are +0.5m/s and -0.3m/s respectively, then the velocities after the collision, are
a) -0.5m/s and +0.3m/s
b) +0.5m/s and +0.3m/s
c) +0.3m/s and -0.5m/s
d) -0.3m/s and +0.5m/s

Answer: d [Reason:] In an elastic collision between two bodies of equal masses, velocities get exchanges after collision. vA=-0.3m/s and vB=+0.5m/s

6. The kinetic energy acquires by a mass m in travelling distance d, starting from rest, under the action of a constant force is directly proportional to
a) m
b) m0
c) √m
d) 1/√m

Answer: b [Reason:] v2-u2=2as v2-0=2×F/m×d = 2Fd/m Kinetic energy = 1/2 mv2=1/2 m×2Fd/m = Fd Hence, kinetic energy does not depend on m or it is directly proportional to m0.

7. A simple pendulum hanging freely and at rest is vertical because in that position
a) Kinetic energy is zero
b) Potential energy is zero
c) Kinetic energy is minimum
d) Potential energy is minimum

Answer: d [Reason:] In the position of equilibrium, the potential energy of the simple pendulum is minimum. Therefore a simple pendulum hanging freely and at rest is vertical because in that position potential energy is minimum.

8. A bullet is fired and gets embedded in a block kept on table. If table is frictionless, then
a) Kinetic energy gets conserved
b) Potential energy gets conserved
c) Momentum gets conserved
d) Kinetic energy and potential energy gets conserved

Answer: c [Reason:] Only momentum gets conserved when a bullet is fired and gets embedded in a block kept on frictionless table. Some kinetic energy is lost when the pullet penetrates the block.

9. A ball moves in a frictionless inclined table without slipping. The work done by the table surface on the ball is
a) Positive
b) Negative
c) Zero
d) Infinity