# Multiple choice question for engineering

## Set 1

1. Rest and motion are relative terms. True or false?

a) True

b) False

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2. A train is under a journey of several hundred kilometres. How can it be regarded?

a) An object in motion

b) An object under rest

c) An object under absolute motion

d) A point object

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3. A car is moving along a zigzag path on a level road. This is an example for which of the following?

a) Point object

b) Two dimensional motion

c) Three dimensional motion

d) One dimensional motion

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4. Which of the following can be regarded as an example for three dimensional motions?

a) Motion of planets around the sun

b) Motion of a train along a straight track

c) Motion of a free falling body

d) A kite flying on a windy day

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5. Displacement is a scalar quantity. True or false?

a) True

b) False

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6. A body travels from A to B at 40m/s and from B to A at 60m/s. Calculate the average speed.

a) 0

b) 48m/s

c) 240m/s

d) 3.5m/s

### View Answer

_{1}+t

_{2}= AB/40 + AB/60 = AB/24 s Total distance covered = AB + BA = 2AB Average speed = 2AB/(t

_{1}+t

_{2}) = 48m/s

7. On a 60km track travels the first 30km with a uniform speed of 30km/h. How fast must the train travel the next 30km so as to average 40km.h for the entire trip?

a) 60km.h

b) 90km/h

c) 120km/h

d) 30km/h

### View Answer

_{av}= (2v

_{1}v

_{2})/(v

_{1}+v

_{2}) 40 = (2×30×v

_{2})/(30+v

_{2}) v

_{2}= 60km/h

8. What is the acceleration of a bus approaching a bus stop?

a) Uniform acceleration

b) Instantaneous acceleration

c) Average acceleration

d) Negative acceleration

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9. A jet plane starts from rest with an acceleration of 3m/s^2 and makes a run for 35s before taking off. What is the minimum length of the runway?

a) 105 m

b) 1837.5 m

c) 2451 m

d) 1204 m

### View Answer

^{2}= 0 + 1/2 × 3 × 35 × 35 = 1837.5 m

10. A driver takes 0.20 s to apply the brakes after he sees a need for it. This is called the reaction time of the driver. If he is driving at a speed of 54km/h and the brakes cause a deceleration of 6.0m/s^{2}, find the distance travelled by the car after he sees the need to put the brakes.

a) 18.75m

b) 225 m

c) 21.5 m

d) 12 m

### View Answer

^{2}As v

^{2}– u

^{2}= 2as s = 18.75 m Total distance travelled = 3.0 + 18.75 = 21.75 m

## Set 2

1. For motion in two or three dimensions, what is the angle between velocity and acceleration vectors?

a) 0°

b) 180°

c) Between 0° and 180°

d) 90°

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2. A cyclist moves along a circular path of radius 70m. If he completes one round in 11s, calculate total length of path.

a) 40m

b) 440m

c) 0m

d) 11m

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3. An object thrown from an aeroplane is an example for

a) Projectile motion

b) Resolution of forces

c) Composition of vectors

d) Addition of vectors

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4. A ball is dropped downward from the roof of a building and simultaneously another ball is thrown in a horizontal direction, when will the balls reach the ground?

a) Same time and same place

b) The first ball will reach later than the second ball

c) The second ball will reach later than the second ball

d) Same time but different places

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5. A body is projected horizontally from the top of a cliff with a velocity of 9.8m/s. What time elapses before horizontal and vertical velocities become equal? Take g = 9.8m/s^{2}

a) 9.8s

b) 0s

c) 10s

d) 1s

### View Answer

_{x}= u = 9.8m/s Vertical velocity at any instant, v

_{y}= 0 + gt = 9.8t 9.8 = 9.8t t = 1s

6. Motion of the tip of second hand of the clock is an example for

a) Uniform circular motion

b) Projectile motion

c) Motion in a plane with uniform velocity

d) Motion in a plane with constant acceleration

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7. M^{0} L^{0} T^{(-1)} is an example for

a) Angular displacement

b) Angular velocity

c) Frequency

d) Time period

### View Answer

^{0}L

^{0}T

^{(-1)}

8. A circular motion is an accelerated motion. True or false?

a) True

b) False

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9. In projectile motion, magnitude remains constant but the direction continuously changes. True or false?

a) True

b) False

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10. Calculate the angular speed of flywheel making 420 revolutions per minute.

a) 42300 rad/sec

b) 1200 rad/sec

c) 10/4200 rad/sec

d) 44 rad/sec

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11. Find the magnitude of the centripetal acceleration of a particle on the tip of a fan blade, 0.30 metre in diameter, rotation at 1200 rev/minute

a) 40 m/s^{2}

b) 4737.6 m/s^{2}

c) 245 m/s^{2}

d) 20 m/s^{2}

### View Answer

^{2}= 0.30×(40π)

^{2}= 4737.6 m/s

^{2}

12. Pressure is a vector. True or false?

a) True

b) False

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13. What is the minimum number of coplanar vectors of different magnitudes which can give zero resultant?

a) One

b) Two

c) Three

d) Four

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14. Two persons are pulling the ends of a string in such a way that the string is stretched horizontally. When a weight of 10kg is suspended in the middle of the string the string does not remain horizontal. Can the persons make it horizontal again by pulling it with a greater force?

a) Yes

b) No

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## Set 3

1. In which of the following the atoms do not move from each other?

a) Shape memory alloys

b) Nano materials

c) Dielectrics

d) Static materials

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2. Which of the following uses radio frequency to produce nano-particles?

a) Plasma arching

b) Chemical vapour deposition

c) Sol-gel technique

d) Electro deposition

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3. Which of the following methods can be used to produce nano-powders of oxides?

a) Plasma arching

b) Sol-gel technique

c) Chemical vapour deposition

d) Mechanical crushing

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4. Which of the following is used to make both nano-particles and nano-powders?

a) Chemical vapour deposition

b) Sol-gel technique

c) Plasma arching

d) Electro deposition

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5. Which method can be used to prepare iron nitriles nano-crystals using ammonia gas?

a) Pulsed laser deposition

b) Sol-gel technique

c) Electro-deposition

d) Mechanical crushing

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6. Nano-particles exhibit super plastic behaviour. True or false?

a) True

b) False

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7. Which of the following is used to modify the optical properties of a material system?

a) Electricity

b) Magnetic field

c) Pressure

d) Light

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8. Find the odd one out.

a) Frequency mixing

b) Second-harmonic generation

c) Optical mixing

d) Raman and Rayleigh scattering

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9. Which of the following is used in electro optic modulators?

a) Lithium tantalite

b) Barium sodium niobate

c) Lithium niobate

d) Lithium sodium niobate

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## Set 4

1. Two plane harmonic sound waves are expressed by the equations:

y_{1} (x,t)=Acos(0.5πx-100πt)

y_{2} (x,t)=Acos(0.46πx-92πt)

All the parameters are in mks system. How many times does an observer hear maximum intensity in one second?

a) 4

b) 6

c) 8

d) 10

### View Answer

_{1}=2πv_1=100π v

_{1}=50Hz Beat frequency=v

_{1}-v

_{2}=4Hz Hence the intensity of sound becomes maximum 4 times in one second.

2. A vibrating string of length l under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased the number of sound in sir to 340m/s, the frequency n of the tuning fork in Hz is

a) 344

b) 336

c) 117.3

d) 109.3

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3. A whistle giving out 450Hz approaches a stationary observer at a speed of 33m/s. The frequency heard by the observer in Hz is (speed of sound = 330m/s)

a) 409

b) 429

c) 517

d) 500

### View Answer

^{‘}=v/(v-v

_{s})×v v

^{‘}=330/(330-33)×450=500Hz

4. A train moves towards a stationary observer with speed 34m/s. The train sounds a whistle and its frequency registered by the observer is f_{1}. If the train’s speed is reduced to 17m/s, the frequency registered is f_{2}. If the speed of sound is 340m/s, then the ratio f_{1}/f_{2} is

a) 18/19

b) ½

c) 2

d) 19/18

### View Answer

^{‘}=v/(v-v

_{s})×f f

_{1}=340/(340-34)×f f

_{2}=340/(340-17)×f f

_{1}/f

_{2}=(340-17)/(340-34)=19/18

5. A siren placed at a railway platform is emitting sound of frequency 5kHz. A passenger sitting in a moving train ‘A’ records a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6kHz while approaching the same siren. The ratio of the velocity of train B to that train A is

a) 242/252

b) 2

c) 5/6

d) 11/6

### View Answer

^{‘}=(v+v

_{0})/v×γ For train A,5.5=(v+v

_{A})/v×5 or v

_{A}=0.1v For train B,6=(v+v

_{B})/v×5 or v

_{B}=0.2v v

_{B}/v

_{A}=2

6. A transverse wave is described by the equation

y=y_{0} sin2π(ft-x/ʎ)

The maximum particles velocity is equal to four times the wave velocity if

a) ʎ=πy_{0}/4

b) ʎ=πy_{0}/2

c) ʎ=πy_{0}

d) ʎ=2πy_{0}

### View Answer

_{0}sin2π(ft-x/ʎ) u=dy/dt=2πfy

_{0}cos2(ft-x/ʎ) u

_{max}=2πfy

_{0}Wave velocity, v=fʎ 2πfy

_{0}=4×ʎf ʎ=(πy

_{0})/2

7. The displacement of particles in a string stretched in the x-direction is represented by y. Among the following expressions for y, those describing wave motion are

a) coskxsinωt

b) k^{2} ω^{2}-ω^{2} t^{2}

c) cos^{2} (kx+ωt)

d) cos^{2} (k^{2} x^{2}-ω^{2} t^{2})

### View Answer

^{2}y)/∂x

^{2}=constant×(∂

^{2}y)/∂t

^{2}Only first expression satisfies this condition

8. A tube closed at one end and containing air produces, when excited, the fundamental note of frequency 512Hz. If the tube is open at both ends, the fundamental frequency that can be excited is (in Hz)

a) 1024

b) 512

c) 256

d) 128

### View Answer

^{‘}=v/4L=2γ=2×512=1024Hz

9. An organ pipe P_{1} closed at one end of vibrating in its first harmonic and another pipe P_{2} open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of P_{1} to that of P_{2} is

a) 8/3

b) 3/8

c) 1/6

d) 1/3

### View Answer

_{1})=3×v/(2L

_{2}) L

_{1}/L

_{2}=1/6

10. A string of length 0.4m and mass 10^{(-2)} kg is tightly clamped at its ends. The tension in the string is 1.6N. Identical wave pulses are produced at one end at equal intervals of time, ∆t. The minimum value of ∆t which allows constructive interference between successive pulses is

a) 0.05s

b) 0.10s

c) 0.20s

d) 0.40s

### View Answer

^{-2}/0.4=2.5×(10

^{-2}S)kg/m Velocity of the wave in the string, v=√(T/m)=√(1.6/(2.5×10

_{min}=2L/v=(2×0.4)/8=0.10s

## Set 5

1. A particle in simple harmonic motion is described by the displacement function x(t)=Acos(ωt+θ). If the initial (t=0) position of the particle is 1cm and its initial velocity isπcm/s, what is its amplitude? The angular frequency is the particle is πrad/s

a) 1 cm

b) √2 cm

c) 2 cm

d) 2.5 cm

### View Answer

^{2}-x

^{2}) π=π√(A

^{2}-1) A

^{2}-1=1 or A

^{2}=2 A=√2cm

2. A particle executes simple harmonic motion, its time period is 16s. If it passes through the centre of oscillation, then its velocity is 2 m/s at time 2s. The amplitude will be

a) 7.2m

b) 4cm

c) 6cm

d) 0.72m

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3. A body is executing the simple harmonic motion with an angular frequency of 2rad/sec. Velocity of the body at 20m displacement, when amplitude of motion is 60m, is

a) 90 m/s

b) 118 m/s

c) 113 m/s

d) 131 m/s

### View Answer

^{2}-y

^{2})=2√(60

^{2}-20

^{2}) v=80√2 v=113m/s

4. A particle is executing simple harmonic motion of amplitude 10cm. Its time period of oscillation is π seconds. The velocity of the particle when it is 2 cm from extreme position is

a) 10 cm/s

b) 12 cm/s

c) 16√16 cm/s

d) 16 cm/s

### View Answer

^{2}-y

^{2}) v=2π/π √(10

^{2}-8

^{2}) =2×6=12cm/s

5. The magnitude of acceleration of particle executing simple harmonic motion at the position of maximum displacement is

a) Zero

b) Minimum

c) Maximum

d) Infinity

### View Answer

^{2}y At y

_{max}=A,a

_{max}=ω

^{2}A Acceleration is maximum at the position of maximum displacement.

6. The maximum velocity and maximum acceleration of a body moving in a simple harmonic motion are 2m/s and 4m/s^{2} respectively. Then the angular velocity will be

a) 4 rad/sec

b) 3 rad/sec

c) 2 rad/sec

d) 8 rad/sec

### View Answer

_{max}=ωA,a

_{max}=ω

^{2}A ω=a

_{max}/v

_{max}=4/2 ω=2rad/sec

7. A particle executing simple harmonic motion has amplitude 0.01 and frequency 60Hz. The maximum acceleration of the particle is

a) 144 π^{2} m/s^{2}

b) 80 π^{2} m/s^{2}

c) 120 π^{2} m/s^{2}

d) 60 π^{2} m/s^{2}

### View Answer

_{max}=ω

^{2}A=4π

^{2}v

^{2}A =4π

^{2}×60×60×0.01=144 π

^{2}m/s

^{2}

8. A particle having potential energy 1/3 of the maximum value at a distance of 4 cm from mean position. Amplitude of motion is

a) 4√3

b) 6/√2

c) 2/√6

d) 2√6

### View Answer

_{p}=1/3 E 1/2 ky

^{2}=1/3×1/2×kA

^{2}A=√3 y=√3×4=4√3 cm

9. A particle executes simple harmonic motion of amplitude A. At what distance from the mean position is its kinetic energy equal to its potential energy?

a) 0.51A

b) 0.71A

c) 0.61A

d) 0.81A

### View Answer

_{k}=E

_{p}1/2 k(A

^{2}-y

^{2})=1/2×ky

^{2}y=±A/√2 y=±0.71A

10. To show that a simple pendulum executes simple harmonic motion, it is necessary to assure that

a) Length of the pendulum is small

b) Amplitude of oscillation is small

c) Mass of the pendulum is small

d) Acceleration due to gravity is small

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11. Time period of a simple pendulum will be double, if we

a) Decrease the length 2 times

b) Decrease the length 4 times

c) Increase the length 2 times

d) Increase the length 4 times

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12. The time period of a simple pendulum is 2 sec. If its length is increased by 4 times, then its period becomes

a) 16 sec

b) 8 sec

c) 12 sec

d) 4 sec

### View Answer

^{‘}∝√4l T

^{‘}/T=2 T

^{‘}=2T=2×2=4 sec

13. A simple pendulum is executing simple harmonic motion with a time period T. If the length of the pendulum is increased by 21%, the increase in the time period of the pendulum of increased length is

a) 10%

b) 30%

c) 21%

d) 50%

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14. A hollow spherical pendulum is filled with mercury has time period T. If mercury is thrown out completely, then the new time period

a) Increases

b) Decreases

c) Remains the same

d) First increases and then decreases

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15. A simple pendulum is vibrating in an evacuated chamber. It will oscillate with

a) Constant amplitude

b) Increasing amplitude

c) Decreasing amplitude

d) First increasing amplitude and then decreasing amplitude

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16. Two simple pendulum, whose lengths are 100cm and 121cm, are suspended side by side. Their bobs are pulled together and then released. After how many minimum oscillations of the longer pendulum, will the two be in phase again?

a) 11

b) 10

c) 21

d) 20

### View Answer

_{1}=(n+1) T

_{2}n√(l

_{1})=(n+1) √(l

_{2}) n√121=(n+1)√100 n×11=(n+1)10 n=10