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# Multiple choice question for engineering

## Set 1

1. At which temperature, the centigrade and Fahrenheit scales are equally?
a) 40°
b) -40°
c) 37°
d) -80°

Answer: b [Reason:] C/5=(F-32)/9 C/5=(C-32)/9 4C=-160 C=F=-40°

2. The volume of a gas at 20°C is 100cm3 at normal pressure. If it is heated to 100°C, its volume becomes 125cm3 at the same pressure, then volume coefficients of the gas (at normal pressure) is
a) 0.0033/°C
b) 0.0025/°C
c) 0.0030/°C
d) 0.0021/°C

Answer: a [Reason:] Vt=V0 (1+γt) V100/V20 =(1+100γ)/(1+20γ )=125/100=3/4 γ=1/300=0.0033/°C

3. Density of substance at 0°C is g/cc and 100°C, its density is 9.7g/cc. The coefficient of linear expansion of the substance is
a) 10-1
b) 10-2
c) 10-3
d) 10-4

4. The coefficient of volumetric expansion of mercury is 18×10-5/°C. The thermometer bulb has a volume of 10-6 m3 and cross-section of the stem is 0.002cm2. Assuming that bulb is filled with mercury at 0°C, the increase in length of the mercury column at 100°C will be
a) 9cm
b) 9mm
c) 18cm
d) 18mm

Answer: a [Reason:] Let h be the length of mercury column at 100°C. Then Expansion in mercury = Volume of stem γV∆T=Ah h=γV∆T/A=(18×10-5×10-6×100)/(0.002×10-4) m h=9×10-2 m h=9cm

5. Amount of heat required to raise the temperature of a body through 1K is called
a) Specific heat
b) Thermal capacity
c) Water equivalent
d) Entropy

Answer: b [Reason:] The amount of heat required to raise the temperature of a body through 1K is called its thermal capacity.

6. If the temperature of a rod is increased by 10°C, its length increases by 1%. What is the percentage change in volume of the body of the same material for 10°C increase in temperature?
a) 9%
b) 1%
c) 5%
d) 3%

Answer: d [Reason:] ∆I/I×100=100α∆T ∆V/V×100=100γ∆T=100×3α×∆T Hence for the same rise of temperature, increase in volume is 3 times the increase in length.

7. In order that the heat flows from one part of a solid to another part, what is required?
a) Uniform density
d) Uniform temperature

Answer: b [Reason:] As heat flows from higher temperature to lower temperature, so a temperature gradient is required.

8. A body A of mass 0.5kg and specific heat 0.85 is at a temperature of 60°C. Another body B of mass 0.3kg and specific heat 0.9 is at a temperature of 90°C. When they are connected to a conducting rod, heat will flow from
a) A to B
b) Heat can’t flow
c) B to A
d) First A to B and then B to A

Answer: c [Reason:] Heat always flows from a body at higher temperature to a body at lower temperature.

9. Two rods having thermal conductivity in the ratio of 5:3 having equal lengths and equal cross-sectional area are joined end to end. If the temperature of the free end of the first rod is 100°C and free end of the second rod is 20°C, then the temperature of the junction is
a) 50°C
b) 70°C
c) 60°C
d) 90°C

Answer: b [Reason:] Let T be temperature of the junction. In the steady state, Q1/t=Q2/t (K1 A(100-T))/d=(K2 A(T-T2))/d 5(100-T)=3(T-20) 8T=560 or T=70°C

10. Mud houses are cooler in summer and warmer in winter because
a) Mud is a good conductor of heat
b) Mud is a superconductor of heat
c) Mud is a bad conductor of heat
d) Mud can adapt according to temperature

Answer: c [Reason:] Mud is a ad conductor of heat. It does not allow heat to come in from outside in summer and it does not allow heat to go out from house in winter.

11. A perfectly black body is one whose
a) Absorptive power is 1
b) Absorptive power is 0
c) Emissive power is 1
d) Absorptive power is 0.5

Answer: a [Reason:] A black body is one which absorbs the entire radiation incident upon it. Its absorptive power is unity.

12. A black body radiates energy at the rate of 1×105 J/(sm)2 at a temperature of 227°C. The temperature to which it must be heated so that it radiates energy at the rate of 1×109 J/(sm)2
a) 5000 K
b) 5000°C
c) 500 K
d) 500°C

Answer: a [Reason:] From Stefan’s law, T2=(E2/E1)(1/4) T1=10×500=5000K

13. A black body at 200 K is found to emit maximum energy at a wavelength 14μm. When its temperature is raised to 1000K, then wavelength at which maximum energy emitted it
a) 14mm
b) 7μm
c) 2.8μm
d) 28mm

Answer: c [Reason:] By Wien’s law, 200×14=100×T T=2.8μm

14. The triple point of water is
a) 273.16°C
b) 273.16K
c) 273.16°F
d) 0.15K

Answer: b [Reason:] Triple point of water corresponds to a temperature of 273.16K and a pressure of 0.46cm of Hg

15. During constant temperature, we feel colder on the day when the humidity is
a) 85%
b) 40%
c) 60%
d) 25%

Answer: d [Reason:] If relative humidity is low, we feel colder because of rapid evaporation of sweat from our body.

## Set 2

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) 3.5lg
c) 1.5kg
d) 0.5kg

Answer: c [Reason:] By conservation of momentum, MV = mv M = mv/V = (0.05×30)/1 = 1.5kg

2. Rocket engines lift a rocket from the earth surface, because hot gases with high velocity
a) Push against the air
b) Push against the earth
c) React against the rocket and push it up
d) Heat up the air which lifts the rocket

Answer: c [Reason:] Rocket engines life a rocket from the earth surface, because hot gases with high velocity react against the rocket and push it up. Hot gases with high velocity react against the rocket and push it up.

3. The motion of a rocket is based on the principle of conservation of
a) Linear momentum
b) Angular momentum
c) Kinetic energy
d) Mass

Answer: a [Reason:] A rocket works on the principle of conservation of linear momentum.

4. A bullet is fired from the rifle. If the rifle recoils freely, then the kinetic energy of the rifle is
a) Less than the kinetic energy of the bullet
b) More than the kinetic energy of the bullet
c) Same as the kinetic energy of the bullet
d) Equal or less than the kinetic energy of the bullet

Answer: a [Reason:] By conservation of momentum, MV = mv or V = mv/M Kinetic energy of the rifle is Kr = 1/2MV2 = 1/2M(m2 v2)/M2 Kr = m/M Kb As m is lesser than M, Kr is lesser than Kb‘=m(g-a) is lesser than W(=mg)

6. A person with a spring balance with a body hanging from it goes up in an aeroplane, then the reading of the weight of the body as indicated by the spring balance, will
a) Go on increasing
b) Go on decreasing
c) First increases and then decreases
d) Remains the same

Answer: b [Reason:] As the person goes above the earth’s surface, the value of g decrease. Hence the reading in the spring balance will go on decreasing.

7. Assertion: On a rainy day, it is difficult to drive at high speed. [Reason:] The value of coefficient of friction is lowered due to wetting of the surface
a) If both assertion and reason are true and reason is the correct explanation of the assertion
b) If both assertion and reason are true but reason is not correct explanation of the assertion
c) If assertion is true, but reason is false
d) If both assertion and reason are false

Answer: a [Reason:] Both assertion and reason are true. Due to wetting, friction decreases between tyres and road. This may lead to skidding of the vehicle.

8. A monkey of mass 20 kg is holding a vertical rope. The rope will not break when a mass of 25 kg is suspended from it but will break if the mass exceeds 25kg. What is the minimum acceleration with which the monkey can climb up along the rope? (g= 10m/s2)
a) 5m/s2
b) 10m/s2
c) 25m/s2
d) 2.5m/s2

Answer: d [Reason:] When the monkey climbs up the rope with acceleration a, T = m(g+a) Mg = mg+ma 25×10=20×10+20a a = 2.5m/s2

9. A block has been placed on an inclined plane with the slope angle θ, block slides down the plant at constant speed. The coefficient of kinetic energy is equal to
a) sinθ
b) cosθ
c) g
d) tanθ

Answer: d [Reason:] As the block slides down the inclined plane with a constant speed, the angle of inclination is equal to the angle of response. μ = tangent of the angle of response μ = tanθ

10. A man is standing on a spring platform. Reading of spring balance is 60kg wt. If man jumps outside from the platform, then the reading of spring balance will
a) Increase
b) Become zero
c) Remain same
d) First increases and then becomes zero

Answer: d [Reason:] To jump outside the platform, the man pushes the platform, so the reading of the spring balance first increases and then becomes zero.

## Set 3

1. Can earth be regarded as a point object when describing its yearly journey around the sun?
a) Yes
b) No

Answer: a [Reason:] Earth can be regarded as a point object when describing its yearly journey around the sun because the size of the earth is much smaller than the distance from the sun.

2. Displacement can be greater than the distance travelled by an object. True or false?
a) True
b) False

Answer: b [Reason:] The displacement of an object can be either equal to or less than the distance travelled by the object. This is because displacement is shortest distance between the initial and final positions of the object while distance travelled is the length of the actual path traversed by the object.

3. Under what condition is the average velocity equal to the instantaneous velocity?
a) Varying velocity
b) Varying speed
c) Constant velocity
d) Constant speed

Answer: c [Reason:] When a body moves with a constant velocity, its average velocity over any time interval is same as instantaneous velocity.

4. How is the speed related to magnitude of velocity?
a) Greater
b) Lesser
c) Equal
d) Doesn’t vary

Answer: a [Reason:] Due to change in direction of motion, the length of the path traversed by a body is generally greater than the magnitude of its displacement. So the speed is greater than the magnitude of velocity.

5. Two balls of different masses (one lighter and one heavier) are thrown vertically upward with same initial speed. Which one will rise to a greater height?
a) The lighter one
b) The heavier one
c) Neither
d) Both the balls

Answer: d [Reason:] Both he balls will rise to the same height. It is because, for a body moving with given initial velocity and acceleration, the distance covered by the body does not depend on the mass of the body.

6. When rain falls vertically downwards, the front screen of a moving car gets wet while the back screen remains dry. True or false?
a) True
b) False

Answer: a [Reason:] When the rain is falling vertically downwards, the front screen of a moving car gets wet while back screen remains dry. This is because the rain strikes the car in a direction of relative velocity of rain with respect to car.

7. Two trains A and B of length 400m each are moving on twp parallel tracks with a uniform speed of 72km/h in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1m/s. If after 50s, the guard of B just brushes past the driver of A, what is the original distance between them?
a) 50m
b) 150m
c) 125m
d) 1250m

Answer: d [Reason:] Let x be the distance between then driver of train A and the guard of train B. Initially, both trains are moving in the same direction with the same speed of 72km/h. So relative velocity of B with respect to A = vB-vA = 0. Hence the train B needs to cover a distance with a= 1m/s, t= 50 s, u = 0 s = ut + 1/2at2 = 1250m

8. A player throws a ball upwards with an initial speed of 29.4m/s. What is the direction of acceleration during the upwards motion of the ball?
a) Upwards
b) Diagonal
c) Projectile motion
d) Vertically downwards

Answer: d [Reason:] The ball moves under the effect of gravity. The direction of acceleration due to gravity is always vertically downwards.

9. A particle in one dimensional motion with zero speed may have non-zero velocity. True or false?
a) True
b) False

Answer: b [Reason:] Speed is magnitude of velocity and the magnitude of non-zero velocity cannot be zero.

10. For a particle in one dimensional motion, which of the following is true?
a) Zero speed at any instant may have zero acceleration at the instant
b) Zero speed may have non-zero velocity
c) Constant speed must have zero acceleration
d) Positive value of acceleration must be speeding up

Answer: c [Reason:] When a particle moves with a constant speed in the same direction, neither the magnitude nor the direction of velocity changes and so acceleration is zero. In case a particle rebounds instantly with the same speed, its acceleration will be infinite which is physically not possible.

11. A bullet fired into a fixed target loss half of its velocity after penetrating 3cm. How much further will it penetrate before coming to rest assuming that it faces constant resistance in motion?
a) 1.5cm
b) 1cm
c) 3cm
d) 2cm

Answer: b [Reason:] If u is initial velocity then v=u/2 s=3cm As v2-u2=2as a= -u2/8 Now v=0 Initial velocity=u/2 s=1cm Thus the bullet will penetrate a further distance of 1cm before coming to rest.

12. From a building 2 balls A and B are thrown such that A is thrown upward and B is thrown downward. If vA and vB are their respective velocities on reaching the ground, then
a) vB is greater than vA
b) vB = vA
c) vB is lesser than vA
d) Their velocities depend on their masses.

Answer: b [Reason:] Suppose the ball A is thrown upward with velocity u and ball B is thrown downward with same velocity u. After reaching the highest point the ball A comes back to its position with the same velocity in downward direction. As the 2 balls fall from the same position with the same velocity, both attain the same velocity on reaching the ground.

13. The displacement of the body is given to be proportional to the cube of time elapsed. The magnitude of acceleration of body is
a) Increasing with time
b) Decreasing with time
c) Constant but not zero
d) Zero

Answer: a [Reason:] s=kt3 Velocity=ds/dt=3kt2 Acceleration=dv/dt=6kt Clearly acceleration increases uniformly with time.

14. When a ball is thrown vertically upwards, at the maximum height
a) The velocity is zero and therefore there is no acceleration acting in the particle
b) The acceleration is present and therefore the velocity is not zero
c) Acceleration depends on the velocity
d) Acceleration is independent of the velocity

Answer: d [Reason:] When a ball is thrown vertically upward, at the maximum height the acceleration becomes independent of the velocity

15. Tom and jerry are running forward with the same speed. They are following a rubber ball at a constant speed v as seen by the thrower. According to Sam, who’s standing on the ground, the speed of the ball is
a) Same as v
b) Greater than v
c) Less than v
d) Zero

Answer: b [Reason:] As they are moving in the same direction, the relative velocity of the ball with respect to Tom or Jerry will be vB=v+v(Tom or Jerry) For Sam, the speed of the ball will be greater than v

## Set 4

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

Answer: c [Reason:] 5× ʎ/2=10 orʎ=4m v=20m/s γ=v/ʎ=20/4=5Hz

2. If vibrations of a string are to be increased by a factor 2, tension in the string must be made
a) Half
b) Twice
c) Four times
d) Eight times

Answer: c [Reason:] γ=1/2π×√(T/m) To double γ, the tension must be made 4 times the original tension.

3. The tension in piano wire is 10N. What should be the tension in the wire to produce a note of double the frequency?
a) 5N
b) 20N
c) 40N
d) 80N

Answer: c [Reason:] As seen in the above problem, T=4T=4×10=40N

4. A string in a musical instrument is 50cm long and its fundamental frequency is 800Hz. If a frequency of 1000Hz is to be produced, then required length of string is
a) 62.5cm
b) 50cm
c) 40cm
d) 37.5cm

Answer: c [Reason:] γ∝1/l γ/γ=l/l l=γ/γ ×l=800/1000×50=40cm

5. The frequency of a tuning fork is 256. It will not resonate with a fork of frequency
a) 256
b) 512
c) 738
d) 768

Answer: c [Reason:] Tuning fork of frequency 256Hz will resonate with forks of integral multiple frequencies such as 256, 768, 1024 etc. It will not resonate with a fork of frequency 738Hz as it is not an integral multiple of 256Hz.

6. An organ pipe closed at one end has fundamental frequency of 1500Hz. The maximum number of overtones generated by this pipe, which a normal person can hear is
a) 12
b) 9
c) 6
d) 4

Answer: c [Reason:] Human year can hear frequencies upto 20000Hz. For a closed organ pipe, v=n×v/4L =n×fundamental frequency 20000=n×1500 n≅13 The possible harmonics are: 1, 3, 5, 7, 9, 11, 13 Maximum number of overtones=7-1=6

7. A tube closed at one end containing air produces fundamental note of frequency 512Hz. If the tube is open at both ends, the fundamental frequency will be
a) 256Hz
b) 768Hz
c) 1024Hz
d) 1280Hz

Answer: c [Reason:] Fundamental frequency of a closed pipe, γ=v/4L=512Hz Fundamental frequency of open pipe, γ=v/2L=2γ=2×512=1024Hz

8. A closed organ pipe and an open pipe of the same length produce four beats per second, when sounded together. If the length of the closed pipe is increased, then the number of beats will
a) Increase
b) Decrease
c) Remain the same
d) First decrease then remain the same

Answer: a [Reason:] γopenclosed=γ/(2Lopen)-γ/(4Lclosed) =Beat frequency Clearly, if the length of the closed pipe is increased, then the beat frequency will increase.

9. At resonance air column of length 20cm resonates with a tuning fork of frequency 450Hz. Ignoring end correction, the velocity of sound in air is
a) 720m/s
b) 820m/s
c) 920m/s
d) 360m/s

Answer: d [Reason:] ʎ/4=20cm,ʎ=80cm=0.80m, γ=450Hz v=γʎ=450×0.80=360m/s

10. Statement: Sound wave cannot propagate through vacuum but light can [Reason:] Sound wave cannot be polarised but light can
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

Answer: b [Reason:] Both the statement and reason are true but the reason is not a correct explanation of the statement. Sound waves, being mechanical waves, cannot travel through vacuum. Light waves being electromagnetic waves, can travel through vacuum.

## Set 5

1. A child sits stationary at one end of a long trolley moving uniformly with speed v on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, then what is the effect of the speed of the centre of mass of the (trolley+child) system?
a) The speed of the centre of mass increases
b) The speed of the centre of mass decreases
c) The speed of the centre of mass will not change
d) The speed of the centre of mass will first increase and then decrease

Answer: c [Reason:] The force involved in the given problem is the internal forces of the system. No external force acts on the system when the child runs So, there will be no change in the speed of the centre of mass of the (trolley+child) system.

2. A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In each case, the ball will reach the bottom
a) With the same speed
b) With different speed
c) With different speed but same time
d) Immediately

Answer: a [Reason:] Acceleration of the rolling sphere, a=gsinθ/((1+k2/R2) ) Velocity of the sphere at the bottom of the inclined plane, v=√(2gh/((1+k2/R2))) The sphere will reach the bottom with the same speed v because h is the same in both the cases.

3. A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In each case, the ball will
a) Reach the bottom at the same time
b) Will take longer time to roll down one plane
c) Reach the bottom at unpredictable time
d) Reach the bottom at same time and keeps rolling

Answer: b [Reason:] Acceleration of the rolling sphere, a=gsinθ/((1+k2/R2) ) Velocity of the sphere at the bottom of the inclined plane, v=√(2gh/((1+k2/R2))) The sphere will take longer time to roll down one plane than the other. It will take larger time in case if the plane with smaller inclination because the acceleration is proportional to sinθ.

4. A hook of radius 2m weighs 100kg. It rolls along a horizontal floor so that its centre if mass has a speed of 20cm/s. How much work has to be done to stop it?
a) 5 J
b) 6 J
c) 2 J
d) 4 J

Answer: d [Reason:] vcm=20cm/s = 0.20ms Work required to stop the hoop = Rotational kinetic energy+Traslational kinetic energy Work required = 1/2 Iω2+1/2 M(vcm)2 = 4J

5. During rolling, the force of friction acts in the same direction as the direction of motion of the centre of mass of the body. True or false?
a) True
b) False

Answer: a [Reason:] When a body rolls, the force if the friction acts in the same direction as the direction of motion of the centre of mass of the body.

6. Where does the centre of mass of two particles of equal mass lie?
a) Inside the body
b) Outside the body
c) Near the first body
d) Midway between them

Answer: d [Reason:] The centre of mass of two particles of equal masses lies midway between them. Its position vector is the average of the position vectors of the two particles.

7. Two particles A and B, initially at rest, move towards each other under mutual force of attraction. At the instant when the speed of A is v and the speed of B is 2v, the speed of mass of the system is
a) 3v
b) v
c) Zero
d) 1.5v

Answer: c [Reason:] No external force is acting on the centre of mass. It remains at rest. The speed of centre of mass is zero.

8. A smooth sphere A is moving on a frictionless horizontal plane with angular speed ω and the centre of mass velocity u. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision, their angular speeds are ω(A) and ω(B) respectively. Then,
a) ωA is lesser than ωB
b) ωAB
c) ωA
d) ωB

Answer: c [Reason:] Only their linear velocities are exchanged. The two spheres cannot exert torques on each other, as their surfaces are frictionless, and so that angular velocities of the sphere do not change.

9. Moment of inertia of a circular wire of mass M and radius R about its diameter is
a) 1/2 MR2
b) 1/4 MR2
c) 2MR2
d) MR2

Answer: b [Reason:] A circular wire behaves like a ring. By perpendicular axes theorem, ID+ID=1/2 MR2 Therefore, 1/4 MR2

10. One solid sphere ‘A’ and another hollow sphere ‘B’ are of same mass and same outer radii. Their moments of inertia about their diameters are respectively IA and IB, such that
a) IA=IB
b) IA is greater thab IB
c) IA is lesser than IB
d) IA/IBAB