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# Multiple choice question for engineering

## Set 1

1. The instantaneous speed of the point of contact during rolling is zero. True or false?
a) True
b) False

### View Answer

Answer: a [Reason:] A rolling body can be imagined to be rolling about an axis passing through the point of contact of the body and the ground. Hence the instantaneous speed of the point of contact is zero.

2. A mass m is moving with a constant velocity along a line parallel to the x-axis, away from the origin. Its angular momentum with respect to the origin
a) Is zero
b) Remains constant
c) Goes on increasing
d) Goes on decreasing

### View Answer

Answer: b [Reason:] Angular momentum = Mass of momentum L = mv×h = constant As the particle moves, m, v and h all remain unchanged.

3. A particles undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particles remain conserved?
a) Centre of the circle
b) On the circumference of the circle
c) Inside the circle
d) Outside the circle

### View Answer

Answer: a [Reason:] In uniform circular motion, centripetal force acts towards the centre. Torque due to such a force about the centre is zero. Hence the angular momentum is conserved about the centre of the circle.

4. If the resultant of all the external forces acting on a system of particles is 0, then from an inertial frame, one can surely say that
a) Linear momentum of the system does not change in time.
b) Kinetic energy of the system does not change in time.
c) Angular momentum of the system does not change in time.
d) Potential energy of the system does not change in time.

### View Answer

Answer: a [Reason:] According to the law of conservation of linear momentum if external force is 0 then the linear momentum of the system does not change in time. There may be external forces acting due to which kinetic energy or potential energy or both may change. Also net force is 0 does not mean net torque is 0. So angular momentum may change. Hence only linear momentum of the system does not change in time.

5. Statement 1: If there is no external torque on the body about its centre of mass, then the velocity of the centre of mass remains constant.
Statement 2: The linear momentum of the isolated system remains constant.
a) Statements 1 and 2 are true and statement 2 is the correct explanation of statement 1
b) Statement one and two are true and statement2 is not the correct explanation of statement1
c) Statement 1 is true, statement 2 is false
d) Statement 2 is true, statement 1 is false

### View Answer

Answer: d [Reason:] The absence of external torque does not ensure the absence of external force. If external force is present, then the velocity of centre of mass will not remain constant. Thus statement 1 is false.

6. If a person standing on a rotating disc stretches out his hands, the angular speed will
a) Increase
b) Decrease
c) Remains same
d) Increases and then decreases

### View Answer

Answer: b [Reason:] As the person stretches out his hands, his moment of inertia increases. To conserve angular momentum, his angular speed increases.

7. Analogue of mass in rotational motion is
a) Moment of inertia
b) Angular momentum
c) Gyration
d) Angular acceleration

### View Answer

Answer: a [Reason:] Analogue of mass in rotational motion is the angular momentum

8. Moment of inertia of an object does not depend upon
a) Mass of object
b) Mass of distribution
c) Angular velocity
d) Axis of rotation

### View Answer

Answer: c [Reason:] Moment of inertia does not depend on the angular velocity of the object but depends on all factors given in other options.

9. Statement 1: If polar ice melts, days will be longer.
Statement 2: Moment of inertia decreases and thus angular velocity increases.
a) Both statement 1 and 2 are true and statement2 is the correct explanation of the statement1
b) Both statement 1 and 2 are true but the statement2 is not the correct explanation of the statement1
c) Statement 1 is true but the statement 2 is false
d) Statement 1 and 2 are false

### View Answer

Answer: a [Reason:] As the polar ice melts, water so formed flows towards the equator. The moment of inertia of the earth increases. To conserve angular momentum, angular velocity decreases. This increases the length of the day.

10. The moment of inertia of a body about a given axis is 1.2kgm2. Initially, the body at rest. In order to produce a rotational kinetic energy of 1500 joule, an angular acceleration of 25radian/sec2 must be applied about the axis for duration of
a) 4s
b) 2s
c) 8s
d) 10s

### View Answer

Answer: b [Reason:] Rotational kinetic energy = 1/2 Iω2 1500=1/2×1.2×ω2 ω=√(3000/1.2)=50rad/s t=(ω-ω0)/α=(50-0)/25 t=2sec

## Set 2

1. If fundamental frequency is 50 and next successive frequencies are 150 and 250, then it is
a) A pipe closed at both ends
b) A pipe closed at one end
c) An open pipe
d) A stretched string

### View Answer

Answer: b [Reason:] For a pipe closed at one end, higher frequencies are odd multiples of the fundamental frequency

2. A stone thrown into still water creates a circular wave pattern moving radially outwards. If r is the distance measured from the centre to the pattern, the amplitude of the wave varies as
a) r(-1/2)
b) r(-1)
c) r(-3/2)
d) r(-2)

### View Answer

Answer: a [Reason:] For a circular wave, I∝1/r But A∝√I A∝1/√r A∝r(-1/2)

3. A siren emitting sound of frequency 800Hz is going away from a static listener with a speed of 30m/s. Frequency of the sound to be heard by the listener is (Take velocity of sound as 330m/s)
a) 733.3Hz
b) 644.8Hz
c) 481.2Hz
d) 286.5Hz

### View Answer

Answer: a [Reason:] γ=v/(v+vs)×γ=330/(330+30)×800 =733.3Hz

4. An observer standing by the side of a road hears the siren of an ambulance, which is moving away from him. If the actual frequency of the siren is 2000Hz, then the frequency heard by the observer will be
a) 1990Hz
b) 2000Hz
c) 2100Hz
d) 4000Hz

### View Answer

Answer: a [Reason:] γ=1990 Apparent frequency decreases when the source moves away from the observer.

5. Statement: Sound wave cannot propagate fastest in solids [Reason:] Sound wave can propagate slightly in vacuum
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) Both statement and reason are false

### View Answer

Answer: c [Reason:] The statement is true but the reason is false. Sound waves, being mechanical waves, cannot propagate through vacuum.

6. With the propagation of a longitudinal wave through a material medium, the quantities transmitted in the propagation direction are
a) Energy, momentum and mass
b) Energy
c) Energy and mass
d) Energy and linear momentum

### View Answer

Answer: b [Reason:] In wave propagation, energy is transmitted in the direction of propagation of the wave.

7. Which of the following statements is true?
a) Both light and sound waves can travel in vacuum
b) Both light and sound waves in air are transverse
c) The sound waves in air are longitudinal while the light waves are transverse
d) Both light and sound waves in air are longitudinal

### View Answer

Answer: c [Reason:] The sound waves in air are longitudinal while the light waves are transverse

8. The velocity of sound in any gas depends upon
a) Wavelength of sound only
b) Density and elasticity of gas
c) Intensity of sound waves only
d) Amplitude and frequency of sound

### View Answer

Answer: b [Reason:] The velocity of sound in a gas depends on density and elasticity of the gas.

9. A 5.5 metre length of string has a mass of 0.035kg. If the tension in the string in 77N, the speed of a wave on the string is
a) 110m/s
b) 165m/s
c) 77m/s
d) 102m/s

### View Answer

Answer: a [Reason:] Here m=0.035/5.5 kg/m T=77N v=√(T/m)=√((77×5.5)/0.035)=110m/s

10. Standing waves are produces in 10m long stretched string. If the string vibrates in 5 segments and wave velocity in 20m/s, the frequency is
a) 5Hz
b) 10Hz
c) 2Hz
d) 4Hz

### View Answer

Answer: a [Reason:] Frequency of standing waves in a stretched string, vp=p/2l×√(T/m)=p/2l×v vp=5/(2×10)×20=5Hz

11. A stretched string resonates with tuning fork of frequency 512Hz when length of the string is 0.5m. The length f the string required to vibrate resonantly with a tuning fork of frequency 256Hz would be
a) 0.25m
b) 0.5m
c) 1m
d) 2m

### View Answer

Answer: c [Reason:] For a stretched string, v∝1/l v1/v2 =l2/l1 l2=v1/v2 ×l1=512/250×0.5=1m

## Set 3

1. In incompressible fluid flows steadily through a cylindrical pipe which had a radius 2R at point A and R at a point B further along the flow direction. If the velocity at A is v, then that at B is
a) v/2
b) v
c) 2v
d) 4v

### View Answer

Answer: d [Reason:] Using equation of continuity, a1 v1=a2 v2 π(2R)2 v=πR2 v2 v2=4v

2. When the temperature is increased, the angle of contact of a liquid
a) Increase
b) Decrease
c) Remains the same
d) First increases and then decreases

### View Answer

Answer: a [Reason:] The angle of contact of a liquid increases with the increase of temperature.

3. Assertion: A hydrogen filled balloon stops using after it has attained a certain height in the sky [Reason:] The atmospheric pressure decreases with height and becomes zero when maximum height is attained
a) Both assertion and reason are true and reason is the correct explanation of the assertion
b) Both assertion and reason are true but reason is not the correct explanation of the assertion
c) Assertion is true but reason is false
d) Assertion and reason is false

### View Answer

Answer: c [Reason:] The assertion is true but the reason is false. When the atmospheric pressure becomes equal to the pressure inside the balloon, the balloon stops rising.

4. A cube of wood floating in water supports a 200g mass at the centre of its top face. When the mass is removed, the mass rises by 2cm. Determine the volume of cube.
a) 1000cm3
b) 100cm3
c) 10cm3
d) 1cm3

### View Answer

Answer: a [Reason:] Let the side of the cube be l cm. As the mass 200g is removed, the cube rises by 2 cm. So by law of floatation, Upthrust on cube due to displaced volume of water = 200gf l×l×2×l×g=200×g l2=100 So, l=10cm Therefore, volume of the cube =103=1000cm3

5. A solid weight 6kg in air. If its density is 2000kgm-3, what will be its apparent weight in water?
a) 6kg
b) 2kg
c) 3kg
d) 5kg

### View Answer

Answer: c [Reason:] Volume of solid=mass/density=6/2000 m3=Volume of water displaced Mass of water displaced=Volume×Density=6/2000×1000=3kg Apparent weight in water = 6-3 = 3kg

6. A boat having a length of 3m and breadth 2m is floating on a lake. The boat sinks by one cm, when a man gets on it. What is the mass of the man?
a) 6kg
b) 60kg
c) 16kg
d) 600kg

### View Answer

Answer: b [Reason:] Fraction of volume above water surface = 1 – 0.90 = 0.10 Weight of man = Weight of water displaced by boat when the man gets in m×9.8=(3×2×0.01)×103×9.8 Hence, m = 60kg

7. It is difficult to cook food at the mountain. True or false?
a) True
b) False

### View Answer

Answer: a [Reason:] The pressure inside the pressure cooker is very high. This rises the boiling point of water and the temperature inside the cooker is higher than 100°C which results in faster cooking of food. At the mountains, the pressure is less, so the boiling point of water is less than 100°C. This makes the cooking of food difficult.

8. Spherical balls of radius R are falling in a viscous fluid of viscosity Ƞ with a velocity v. The retarding viscous force acting on the spherical ball is
a) Directly proportional to R but inversely proportional to v
b) Directly proportional to both radius R and velocity v
c) Inversely proportional to both radius R and velocity v
d) Inversely proportional to R but directly proportional to velocity v

### View Answer

Answer: b [Reason:] F = 6πȠRv, that is retarding viscous force is directly proportional to both R and v.

9. A wooden block is taken to the bottom of a deep, calm lake of water and then released. It rises up with a
a) Constant acceleration
b) Decreasing acceleration
c) Constant velocity
d) Decreasing velocity

### View Answer

Answer: a [Reason:] The wooden block rises up with acceleration, a=(Upthrust-weight of block)/(Mass of block)

10. The water droplets in free fall are spherical due to
a) Gravity
b) Viscosity
c) Surface tension
d) Intermolecular attraction

### View Answer

Answer: c [Reason:] Freely falling water droplets assume spherical shape due to surface tension of water.

11. Assertion: A needle placed carefully on the surface of water may float, whereas a ball of the same material will always sink. [Reason:] The buoyancy of an object depends both on the material and shape of the object
a) Both assertion and reason are true and reason is the correct explanation of the assertion
b) Both assertion and reason are true but reason is not the correct explanation of the assertion
c) Assertion is true but reason is false
d) Assertion and reason is false

### View Answer

Answer: c [Reason:] The assertion is true but the reason is false. The needle floats because the force of surface tension on it is enough to balance its weight. In case of ball, the resultant of the force of surface tension and buoyancy is enough to balance the weight of the ball.

## Set 4

1. In stable equilibrium, a body has maximum potential. True or false?
a) True
b) False

### View Answer

Answer: b [Reason:] A body is said to be in stable equilibrium if it tends to regain its equilibrium position after being slightly displaced and released. In stable equilibrium, a body has minimum potential energy.

2. On being displaced, the centre of mass of unstable equilibrium goes
a) Higher
b) Neither higher nor lower
c) First higher and then lower
d) Lower

### View Answer

Answer: d [Reason:] A body is said to be in unstable equilibrium if it gets further displaced from its equilibrium position after being slightly displaced and released. In unstable equilibrium, a body possesses maximum potential energy and its centre of mass goes lower on being slightly displaced.

3. Which of the following stays in equilibrium even after being slightly displaced?
a) Stable equilibrium
b) Unstable equilibrium
c) Neutral equilibrium
d) Rigid body

### View Answer

Answer: c [Reason:] If a body stays in equilibrium position even after being slightly displaced and released, it is said to be in neutral equilibrium. When a body is slightly displaced, its centre of mass is neither raised nor lowered and its potential energy remains constant.

4. Moment of inertia can be regarded as the measure of rotational inertia of the body. True or false?
a) True
b) False

### View Answer

Answer: a [Reason:] The mass of a body resists change in its state of linear motion, it is a measure of its inertia in linear motion, Similarly, the moment of inertia of a body about an axis of rotation resists a change in its rotational motion. The greater the moment of inertia of body, the greater is the torque required to change its state of rotation. Thus moment of inertia of a body can be regarded as the measure of rotational inertia of the body.

5. The flying wheel attached to the shaft of steam engine works on the principle of
a) Centripetal action
b) Moment of inertia
c) Newton’s third law of motion
d) Conservation of momentum

### View Answer

Answer: b [Reason:] A flywheel is attached to the shaft of an engine. Because of its large moment of inertia, the flywheel opposes the sudden increase or decrease of the speed of the vehicle. It allows a gradual change in the speed and prevents jerky motions and hence ensures smooth ride for the passengers.

6. A wheel of mass 8kg and radius of gyration 25cm is rotating at 300rpm. What is its moment of inertia?
a) 0.5 kgm2
b) 10 kgm2
c) 5 kgm2
d) 0.25 kgm2

### View Answer

Answer: a [Reason:] M = 8kg, K = 25cm = 0.25m Therefore, l = MK2 = 8×0.252 = 0.5 kgm2

7. The moment of inertia of a uniform circular disc about its diameter is 100gcm2. What is its moment of inertia about its tangent?
a) 200 gcm2
b) 100 gcm2
c) 900 gcm2
d) 500 gcm2

### View Answer

Answer: d [Reason:] By the theorem of parallel axes, moment of inertia about a tangent parallel to the diameter, I = Id+MR2 = 1/4 MR2+MR2=5/4 MR2 I = 5×100 = 500 gcm2

8. The moment of inertia of a uniform circular disc about its diameter is 100 gcm2. What is its moment of inertia about an axis perpendicular to its plane.
a) 500 gcm2
b) 100 gcm2
c) 200 gcm2
d) 700 gcm2

### View Answer

Answer: c [Reason:] By theorem of perpendicular axes, moment of inertia of the disc about an axis perpendicular to its plane, I = Sum of the moments of inertia about two perpendicular diameters I = Id+Id=2×1/4×MR2=2×1000= 200 gcm2

9. Calculate the moment of inertia of the earth about its diameter, taking it to be a sphere of 1025kg and diameter 12800km.
a) 1.64 kgm2
b) 16.4×1038 kgm2
c) 1.64×1038 kgm2
d) 0

### View Answer

Answer: c [Reason:] M = 1025kg, R = 6400km = 6.4×106 m Moment of inertia of the earth about its diameter I = 2/5 MR2 = 2/5×1025×(6.4×106)2 I = 1.64×1038 kgm2

10. A torque of 2×10-4 Nm is applied to produce an angular acceleration of 4rad/s2 in a rotating body. What is the moment of inertia of the body?
a) 0.5 kgm2
b) 5×104 kgm2
c) 0.5×10-4 kgm2
d) 0.5×104 kgm2

### View Answer

Answer: c [Reason:] Torque = Iα I = Torque/α = (2×10-4)/4=0.5×10-4 kgm2

## Set 5

1. What will happen with magnetic materials is kept in external magnetic field?
a) They will move
b) They will develop magnetic lines of force
c) They will create a permanent magnetic moment
d) They will be unaffected

### View Answer

Answer: c [Reason:] Magnetic materials are the materials which can behave as magnets. When these materials are kept in an external magnetic field, they will create a permanent magnetic moment in it.

2. Magnetism originates due to rotational motion of charged particles. True or false?
a) True
b) False

### View Answer

Answer: a [Reason:] Magnetism originates from magnetic moment of the magnetic materials due to the rotational motion of the charged particles. When an electron revolves around the positive nucleus, orbital magnetic moment arises.

3. What is the name of the continuous curve in magnetic field, the tangent of which gives the direction of magnetic intensity?
a) Magnetic lines of force
b) Magnetic lines of induction
c) Magnetic force
d) Magnetic dipole moment

### View Answer

Answer: a [Reason:] Magnetic lines of force are defined as the continuous curve in a magnetic field. The tangent drawn at any point on the curve gives the direction of resultant magnetic field at that point.

4. What is the name of the magnetic lines which forms a closed path?
a) Magnetic lines of force
b) Magnetic force between two poles
c) Magnetic field
d) Magnetic lines of induction

### View Answer

Answer: d [Reason:] The magnetic lines of force which originate from North Pole to South Pole doesn’t end there itself. They are supposed to continue through the magnet and reach the North Pole from where they started and forms a closed loop. Such lines are called magnetic lines of induction.

5. How is the residual magnetism from a material removed?
a) Retentivity
b) Coercivity
c) Magneton
d) Switching off magnetic field

### View Answer

Answer: b [Reason:] The residual magnetism can be completely removed from the material by applying a reverse magnetic field. Hence coercivity of magnetic material is the strength of reverse magnetic field which is used to completely demagnetise the material.

6. In which of the following magnetic moment is zero?
a) Dia-magnetic material
b) Parra-magnetic material
c) Ferromagnetic material
d) Ferrimagnetic material

### View Answer

Answer: a [Reason:] In a diamagnetic material, the electron orbits are more or less random, and mostly all the magnetic moments are cancelled. Similarly all the spins are almost paired. Hence the net magnetic moment in the diamagnetic material is zero.

7. Which of the following is a weak magnet?
a) Ferromagnetic material
b) Antiferromagnetic
c) Paramagnetic
d) Diamagnetic

### View Answer

Answer: d [Reason:] The diamagnets are called weak magnets because there is no permanent dipole moment. Their net magnetic moment is zero.

8. When does a diamagnetic material become normal material?
a) At critical temperature
b) Above critical temperature
c) Never
d) Below critical temperature

### View Answer

Answer: d [Reason:] Critical temperature is the temperature at which properties like magnetism changes. When the temperature is less than critical temperature, diamagnetic material becomes normal magnet.

9. Magnetic susceptibility is negative for paramagnetic material. True or false?
a) True
b) False

### View Answer

Answer: b [Reason:] Magnetic susceptibility is positive for paramagnetic material. It is given by Curie-Weiss law, Susceptibility = C/(T-θ) Where, C = Curie constant T = Absolute temperature θ = Curie temperature

10. When does a paramagnetic material become diamagnetic material?
a) At critical temperature
b) Above critical temperature
c) Below critical temperature
d) Never

### View Answer

Answer: c [Reason:] Critical temperature is the temperature at which properties like magnetism changes. When the temperature is less than critical temperature, diamagnetic material becomes normal magnet.