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# Multiple choice question for engineering

## Set 1

1. A motion can be periodic and not oscillatory. True or false?
a) True
b) False

Answer: a [Reason:] A motion can be periodic and not oscillatory. For example, uniform circular motion is periodic but not oscillatory.

2. A simple pendulum of length l and with a bob whose mass is m is moving along a circular arc of angle θ in a vertical plane. A sphere of mass m is placed at the end of the circle. What momentum will be given to the sphere by the moving bob?
a) Infinity
b) Constant
c) Unity
d) Zero

Answer: d [Reason:] The momentum given to the sphere by the moving bob is zero because the velocity of the bob at the end of the arc will be zero.

3. When a 2 kg body is suspended by a spring, the spring is stretched. If the body is pulled down slightly and released, it oscillates up and down. What force is applied on the body by the spring when it passes through the mean position?
a) Force equal to the gravity
b) Force equal to the pull
c) Conservative force
d) Force equal to the weight of the body

Answer: d [Reason:] At the mean position, there is no acceleration in the body, hence the resultant force applied by the spring will be exactly equal to the weight of the body.

4. The displacement of an object attached to a spring and executing simple harmonic motion is given by
x=2×10-2 cosπt(in m)
The time at which the maximum speed first occurs is
a) 0.5s
b) 0.75s
c) 0.125s
d) 0.25s

Answer: a [Reason:] Displacement, x = 2×10-2 cosπt Velocity, v = dx/dt=-2×10-2 πsinπt Velocity becomes maximum when Sinπt=1 πt=π/2 T=0.5s

5. The maximum velocity of a particle, executing simple harmonic motion with amplitude 7mm, is 4.4m/s. The period of oscillation is
a) 0.01s
b) 0.1s
c) 10s
d) 100s

Answer: a [Reason:] vmax=ωA=2π/T×A T=2πA/vmax =(2×22×7×10-310-3)/(7×4.4)=.01s

6. If the frequency of oscillation of a particle doing simple harmonic motion is n, the frequency of kinetic energy is
a) 2n
b) n
c) n/2
d) 2/n

Answer: c [Reason:] In one oscillation, the energy of the oscillation twice becomes kinetic and twice potential. Frequency of kinetic energy = 2n

7. Natural length of spring is 60 cm and its spring constant is 4000 N/m. A mass of 20 kg is hung from it. The extension produced in the spring (take g=9.8m/s2) is
a) 4.9cm
b) 0.49cm
c) 9.4cm
d) 0.94cm

Answer: a [Reason:] In equilibrium, kx=mg x=mg/k=(20×9.8)/9000=0.049m=4.9cm

8. The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is
a) 0.5π
b) π
c) 0.707 π
d) 0.61 π

Answer: a [Reason:] In simple harmonic motion, instantaneous acceleration is ahead of instantaneous velocity in phase by π/2 rad

9. A horizontal platform with an object placed on it is executing simple harmonic motion in the vertical direction. The amplitude of oscillation is 3.92×10-3 m. What must be the least period of these oscillations, so that the object is not detached from the platform?
a) 0.1256s
b) 0.1356s
c) 0.1456s
d) 0.1556s

Answer: a [Reason:] For an object to get detached from the platform, amax ≤g or ω2 A≤g (2π/T)2 A≤g Tmin=2π√(A/g)=2π√((3.92×10-3)/9.8) Tmin=2π×2×10-2=0.1256s

10. Statement: The amplitude of an oscillating pendulum decreases gradually with time [Reason:] The frequency of the pendulum decreases with time
a) Both statement and reason are true and reason is the correct explanation of the statement
b) Both statement and reason are true but reason is not the correct explanation of the statement
c) Statement is true, but reason is false
d) Statement and reason are false

Answer: c [Reason:] The statement is true but the reason is false. Due to friction of air, the amplitude gradually decreases with time

## Set 2

1. 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

Answer: c [Reason:] vH/vO =√(MO/MH) =√(32/2)=4:1

2. It takes 2 seconds for a sound 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) 1.9s
b) 2s
c) 2.1s
d) 2.2s

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

3. The disc of a siren containing 60holes rotates at a constant speed of 360rpm. The emitted sound is in unison with a tuning fork of frequency
a) 10Hz
b) 360Hz
c) 216Hz
d) 60Hz

Answer: b [Reason:] Frequency of revolution of disc=360rpm=360/60rps=60rps Frequency of emitted sound=6×No.of holes =6×60=360Hz

4. The quantity which does not change, when sound enters from one medium to another
a) Wavelength
b) Speed
c) Frequency
d) Velocity

Answer: c [Reason:] Frequency remains unchanged when sound travels from one medium to another

5. The equation of a simple harmonic wave is given by
y=5sin⁡(π/2) (100t-x)
Where x and y are in metre and time is in second. The period of the wave in second will be
a) 0.04
b) 0.01
c) 1
d) 5

Answer: a [Reason:] y=5sin⁡(π/2) (100t-x) y=Asin(ωt-kx) ω=2π/T=π/2×100 T=2/50=0.04s

6. If wave y=Acos(ωt+kx) Is moving along x-axis, the shapes of pulse at t=0 and t=2s
a) Are different
b) Are same
c) May not be the same
d) Unpredictable

Answer: b [Reason:] The shapes of y-x graph remains same at t=0 and t=2s

7. y1=4sin⁡(ωt+kx), y2=-4cos⁡(ωt+kx), the phase difference is
a) π/2
b) 3π/2
c) π
d) Zero

Answer: b [Reason:] y1=4sin⁡(ωt+kx) y2=-4cos⁡(ωt+kx) =-4sin⁡(ωt+kx+3π/2) ∆φ=3π/2

8. A wave equation is y=0.1sin[100πt-kx] and wave velocity is 100m/s, its number is equal to
a) 1/m
b) 2/m
c) π/m
d) 2π/m

Answer: c [Reason:] y=0.1sin⁡[100πt-kx] y=Asin(ωt-kx) ω=100π Wave number=ω/v=100π/100=π/m

9. A particle on the trough of a wave at any instant will come to the mean position after a time (T=time period)
a) T/2
b) T/4
c) T
d) 2T

Answer: b [Reason:] Time taken by a particle to move from trough to the mean position=T/4

10. A string is tied on a sonometer, second end is hanging downward through a pulley with tension T. The velocity of the transverse wave produced is proportional to
a) 1/√T
b) √T
c) T
d) 1/T

11. The fundamental frequency of a sonometer wire is n. If the tension is made 3 times and length and diameter are also increased 3 times, the new frequency will be
a) 3n
b) n/3√3
c) n/3
d) √3 n

Answer: b [Reason:] n=1/LD×√(T/πρ) n=1/(3L×3D)×√(3T/πρ)=√3/9×n=1/(3√3) n

## Set 3

1. What is the process of producing electric dipoles inside the dielectric by an external electric field?
a) Polarisation
b) Dipole moment
c) Susceptibility
d) Magnetisation

Answer: a [Reason:] When an external magnetic field is applied to the dielectrics, the field exerts a force on each positive charges in its own direction while negative charges are pushed in the opposite direction. Consequently, an electric dipole is created in all the atoms. Thus the process of producing electric dipoles inside the dielectrics by an external electric field is called polarisation.

2. Which of the following easily adapt itself to store electrical energy?
a) Passive dielectric
b) Superconductor
c) Active dielectric
d) Polar molecules

Answer: c [Reason:] When dielectric is subjected to external electric field, if the dielectric actively accepts electricity, then they are termed as active dielectrics. Thus active dielectrics are the dielectrics which can easily adapt itself to store the electrical energy in it.

3. Which of the following restricts the flow of electrical energy?
a) Superconductors
b) Passive dielectrics
c) Polar molecules
d) Active dielectric

Answer: b [Reason:] Passive dielectric acts as an insulator; conduction will not take place though this dielectrics. Thus passive dielectrics are the dielectrics which restrict the flow of electrical energy in it.

4. For non-polar molecules, there is no absorption or emission in the range of infrared. True or false?
a) True
b) False

Answer: a [Reason:] These molecules posses centre of symmetry and hence the centres of positive and negative charges coincide. Therefore the net charges and net dipole moment of these molecules will be zero and hence these non-polar molecules will not posses any dipole moment in it. Hence there is no absorption or emission in the range of infrared.

5. How does ionic polarisation occur?
a) Splitting of ions
b) Passing magnetic field
c) Displacement of cations and anions
d) Never occurs

Answer: c [Reason:] Ionic polarisation occurs due to the displacement of cations and anions from its original position in the opposite directions, in the presence of electric field.

6. Polar molecules have permanent dipole moments even in the absence of an electric field. True or false?
a) False
b) True

Answer: b [Reason:] In the absence of electric field the polar molecules posses some dipole moment. These dipoles are randomly arranged and they cancel each other. Hence the net dipole moment is very less.

7. Which of the following polarisations is very rapid?
a) Electronic polarisation
b) Ionic polarisation
c) Space charge polarisation
d) Orientation polarisation

Answer: a [Reason:] Electronic polarisation is very rapid and will complete at the instant the voltage is applied. The reason is that the electrons are very light particles. Therefore even for high frequency this kind of polarisation occurs.

8. Which of the following is the slowest polarisation method?
a) Ionic polarisation
b) Orientation polarisation
c) Electronic polarisation
d) Space charge polarisation

Answer: d [Reason:] Space charge polarisation is very slow because in this case the ions have to diffuse over several interatomic distances. Also this process occurs at very low frequency.

9. When does a dielectric become a conductor?
a) At avalanche breakdown
b) At high temperature
c) At dielectric breakdown
d) In the presence of magnetic field

Answer: c [Reason:] When a dielectric is placed in an electric field and if the electric field is increased, when the electric field exceeds the critical field, the dielectric loses its insulating property and becomes conducting. This is called dielectric breakdown.

10. Which of the following breakdowns occur at higher temperature?
a) Avalanche breakdown
b) Thermal breakdown
c) Electrochemical breakdown
d) Dielectric breakdown

Answer: b [Reason:] When a dielectric is subjected to an electric field, heat is generated. This generated heat is dissipated by the dielectric. In some cases the generated heat will be very high compared to the heat dissipated. Under such conditions the temperature inside the dielectric increases and heat may produce breakdown. This is thermal breakdown.

11. When mobility increases, insulation resistance decreases and dielectric becomes conducting. True or false?
a) True
b) False

Answer: a [Reason:] If the temperature is increased, mobility of ions increases and hence electrochemical reaction may be induced to take place. Therefore when mobility of ions is increased, insulation resistance decreases and hence dielectric becomes conducting.

12. Which of the following materials exhibit Ferro-electricity?
a) Iron
b) Platinum
c) Hydrogen
d) Rochelle salt

Answer: d [Reason:] When a dielectric exhibits electric polarisation even in the absence of external field, it is known as ferro-elecricity and these materials are termed as Ferro-electrics. They are anisotropic crystals which exhibit spontaneous polarisation. Hence only Rochelle salt exhibits Ferro-electricity.

13. Calculate the electronic polarizability of an argon atom whose ɛr = 1.0024 at NTP and N = 2.7×1025 atoms/m3.
a) 0.0024 Fm2
b) 7.87 ×10-40 Fm2
c) 7.87 Fm2
d) 1.0024×10-40 Fm2

Answer: b [Reason:] Electronic polarisabilty αe = (ε0r-1))/N Electronic polarisability = 7.87 × 10-40 Fm2

14. Calculate the dielectric constant of a material which when inserted in parallel condenser of area 10mm × 10mm and distance of separation of 2mm, gives a capacitance of 10-9 F.
a) 8.854×10-12
b) 100
c) 2259
d) 5354

Answer: c [Reason:] C= (εr ε0 A)/d εr = Cd/(ε0 A) = 2259

15. Find the capacitance of layer of A13 O3 that is 0.5μm thick and 2000mm2 of square area εr = 8.
a) 1000μF
b) 0.283μF
c) 16μF
d) 2.83μF

Answer: b [Reason:] C = (εr ε0 A)/d Capacitance = 0.283μF

## Set 4

1. How does a semiconductor behave at absolute zero?
a) Conductor
b) Insulator
c) Semiconductor
d) Protection device

Answer: b [Reason:] A semiconductor is a solid which has the energy band similar to that of the insulator. It acts as an insulator at absolute zero.

2. Semiconductor acts as an insulator in the presence of impurities. True or false?
a) True
b) False

Answer: b [Reason:] When the temperature is raised or when impurity is added, their conductivity increases. Conductivity is inversely proportional to temperature.

3. How is the resistance of semiconductor classified?
a) High resistance
b) Positive temperature co-efficient
c) Negative temperature co-efficient
d) Low resistance

Answer: c [Reason:] Semiconductors have negative temperature co-efficient. The reason for this is, when the temperature is increased, a large number of charge carriers are produced due to breaking of covalent bonds and hence these electrons move freely and gives rise to conductivity.

4. What are the charge carriers in semiconductors?
a) Electrons and holes
b) Electrons
c) Holes
d) Charges

Answer: a [Reason:] In conductors, electrons are charge carriers. But in semiconductors, both electrons and holes are charge carriers and will take part in conduction.

5. Which of the following is known as indirect band gap semiconductors?
a) Germanium
b) Nickel
c) Platinum
d) Carbon

Answer: a [Reason:] The elemental semiconductor is made up of single element from the fourth column elements such as Germanium. Here recombination takes place takes place via traps. It is called indirect bad gap semiconductors.

6. Which column elements are combined to make compound semiconductors?
a) First and fourth
b) Fifth and sixth
c) Second and fourth
d) Third and fifth

Answer: d [Reason:] The compound semiconductors are made by combining the third and fifth column elements. Such as GaAs are made by combining third and fifth column elements.

7. Compound semiconductors are also known as direct bad gap semiconductors. True or false?
a) True
b) False

Answer: a [Reason:] In compound semiconductors, recombination takes place directly and its energy difference is emitted in the form of photons in the visible or infrared range. Hence the compound semiconductors are also knows as direct band gap semiconductors.

8. How is charge carriers produced in intrinsic semiconductors?
a) By pure atoms
b) By electrons
c) By impure atoms
d) By holes

Answer: c [Reason:] Impure semiconductors in which the charge carriers are produced due to impurity atoms are called extrinsic semiconductors. They are obtained by doping an intrinsic semiconductor with impurity atoms.

9. What type of material is obtained when intrinsic semiconductor is doped with pentavalent impurity?
a) N-type semiconductor
b) Extrinsic semiconductor
c) P-type semiconductor
d) Insulator

Answer: a [Reason:] N-type semiconductor is obtained by doping an intrinsic semiconductor with pentavalent impurity atoms.

10. What type of material is obtained when an intrinsic semiconductor is doped with trivalent impurity?
a) Extrinsic semiconductor
b) Insulator
c) N-type semiconductor
d) P-type semiconductor

Answer: d [Reason:] P-type semiconductor is obtained by doping an intrinsic semiconductor with trivalent impurity.

## Set 5

1. If no external torque acts on a body, its angular velocity remains conserved. True or false?
a) True
b) False

Answer: b [Reason:] If no external torque acts on a body, its angular velocity is not conserved but angular momentum is conserved.

2. Which component of linear momentum does not contribute to angular momentum?
a) Horizontal component
b) Vertical component
d) Tangential component

Answer: c [Reason:] The radial component does not contribute to the angular momentum.

3. A heavenly body revolves around a massive star in a highly elliptical orbit. Ignoring mass loss of the heavenly body when it comes too close to the star, the angular momentum over the orbit is
a) Zero
b) Increasing
c) Decreasing
d) Constant

Answer: d [Reason:] The heavenly body revolves around the massive star under the effect of gravitational force, which is purely radial. The torque exerted by such a force is zero. Hence the angular momentum of the heavenly body remains constant over its entire orbit.

4. A body can be in equilibrium while it is in motion. True or false?
a) True
b) False

Answer: b [Reason:] A body can be in equilibrium while it is in motion. A body in motion will be in equilibrium if it has no linear and angular accelerations. Hence a body moving with uniform velocity along a straight line will be in equilibrium.

5. We can rise from a chair without bending a little forward. True or false?
a) True
b) False

Answer: b [Reason:] Our weight exerts a torque about our feet. This makes it difficult for us to rise from the chair. When we bend forward, the centre of gravity of our body comes above our feet. The torque due to our weight becomes zero and we can easily rise from the chair.

6. When a cat falls from a height
a) It sustains injury
b) It dies
c) It lands on its feet
d) It bounces back

Answer: c [Reason:] When a cat falls to the ground from a height, it stretches its body along with the tail so that its moment of inertia becomes high. The value of angular speed decreases and therefore the cat is able to land on the ground gently.

7. How many propellers are there in a helicopter?
a) One
b) No propellers
c) Three
d) Two

Answer: d [Reason:] If there were only one propeller in the helicopter then, due to conservation of angular momentum, the helicopter itself would have turned in the opposite direction.

8. If earth were to shrink suddenly, what would happen to the length of the day?
a) It increases
b) It remains the same
c) It decreases
d) It becomes unpredictable

Answer: When the earth shrinks, the moment of inertia (I=2/5 MR^2) decreases about its own axis due to the decrease in radius R. To converse angular momentum, the time period T decreases. That is, the length of the day decreases.

9. A child is sitting on a swing. Its minimum and maximum heights from the ground 0.75m and 2m respectively, its maximum speed will be
a) 10 m/s
b) 5 m/s
c) 8 m/s
d) 15 m/s

Answer: b [Reason:] Maximum kinetic energy = Drop in potential energy 1/2 mv2=mg(h2-h1) v=√(2g(h2-h1))=√(2×10(2-0.75))=5m/s

10. A moving body of mass m and velocity 3km/h collides with a rest body of mass 2m and strikes to it. Now the combined mass starts to move. What will be the combined velocity?
a) 3km/h
b) 4km/h
c) 1km/h
d) 2km/h