Work and Energy Test

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Work and Energy Test - 15

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Weekly Quiz Competition

Question 1

1 / -0

Use the following information to answer the next question.

The following table lists the power ratings of different appliances used by a family and the daily operating time of each appliance.
Device	Power rating (W)	Time of operation (h)
Bulb	40	10
Fan	50	9
TV set	120	6
Electric iron	750	1

How many units of energy are consumed by these devices in the month of July?

67.31 units

69.49 units

71.92 units

73.24 units

Solution

The relationship between power and energy is:
Energy consumed = Power × Time

For bulb:

Power rating = 40 W = 40 × 10⁻³ kW

Time = 10 h

∴Energy consumed in a day = 400 × 10⁻³ kWh = 400 × 10⁻³ units

For fan:

Power rating = 50 W = 50 × 10⁻³ kW

Time = 9 h

∴Energy consumed in a day = 50 × 10⁻³ × 9 = 450 × 10⁻³ units

For TV set:

Power rating = 120 W = 120 × 10⁻³ kW

Time = 6 h

∴Energy consumed in a day = 120 × 10⁻³ × 6 = 720 × 10⁻³ units

For electric iron:

Power rating = 750 W = 750 × 10⁻³ kW

Time = 1 h

∴Energy consumed in a day = 750 × 10⁻³ × 1 = 750 × 10⁻³ units

Total energy consumed by all the appliances in a day

= (400 + 450 + 720 + 750) × 10⁻³

= 2320 × 10⁻³ unit = 2.32 units

The month of July comprises 31 days. Therefore, the total energy consumed by all the given appliances in the month of July is (31 × 2.32) = 71.92 units.

The correct answer is C.

Question 2

1 / -0

Use the following information to answer the next question.

Three essential criteria for something to qualify scientifically as work done:

I A force must act on a body.

II The body must be displaced.

III Directions of the applied force and the displacement must be the same.

With reference to the scientific definition of work done,

only II is inessential

only III is inessential

both I and II are inessential

both I and III are inessential

Solution

Scientifically, work is done only when a force is applied on a body and it causes some displacement of the body along the line of direction of the applied force.

Therefore, the directions of the applied force and the displacement of the body can be opposite. Criterion III suggests that the direction of the applied force and that of the displacement must remain the same. However, this is not an essential criterion for something to qualify scientifically as work done.

The correct answer is B.

Question 3

1 / -0

Use the following information to answer the next question.

Three statements regarding work done:

I A person reading a book is not doing any work as per the scientific definition of work.

II The amount of work done can be expressed in Nm (Newton metre).

III Work done can be positive or negative.

With reference to work done,

only II is true

only III is false

all three statements are true

all three statements are false

Solution

Scientifically, work is done only when a force is applied on a body and it causes some displacement of the body along the line of direction of the applied force.

While reading a book, no force is applied and there is no displacement in the body of the reader. Hence, this case does not satisfy the scientific definition of work.

Work done is given by the relation:

Work done = Force × Displacement

The SI unit of force is Newton (N) and that of displacement is metre (m). Therefore, the SI unit of work done is Nm.

The value of work done depends on the directions of the applied force and the displacement caused by that force. Depending on the directions of these quantities, work done can be either positive or negative. When the displacement is in the direction of the applied force, the value of work done becomes positive. When the displacement is in the direction opposite to the applied force, the value of work done becomes negative.

Hence, with reference to work done, all three statements are true.

The correct answer is C.

Question 4
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A force of 2.4 N is acting on an object, causing the object to be displaced by 1.6 metres in the direction of the force. What is the work done by the force?

A
1.23 J

B
2.56 J

C
3.84 J

D
6.14 J

Solution

Work done = Force × Displacement

Applied force = 2.4 N

Displacement = 1.6 m

∴Work done = 2.4 × 1.6 = 3.84 J

The correct answer is C.
Question 5
1 / -0

Scientifically, work is done when a person

A
reads a book for a long time

B
climbs a staircase slowly

C
stands with a heavy load

D
pushes a huge rock

Solution

Scientifically, work is done only when a force is applied on a body and it causes some displacement of the body along the line of direction of the applied force.

When a person climbs the steps of a staircase, he actually applies his own muscular force. This force helps him to undergo a certain displacement on the stairs. Moreover, as the person climbs up, a work is done against the force of gravity (which acts downward).

The correct answer is B.

Question 6

1 / -0

Use the following information to answer the next question.

Hydroelectricity is generated by storing a large amount of water at a height and then allowing this water to run over some rotating turbines. These turbines eventually generate electricity.

Which of the following conservation principles is used in a hydropower plant?

Conservation of mass

Conservation of charge

Conservation of energy

Conservation of momentum

Solution

The law of conservation of energy states that energy can neither be created nor destroyed. Energy, however, can change from one form to another.

A body or a substance possesses mechanical energy by virtue of its motion or position. A water dam is constructed to harness the mechanical energy of water by storing it in huge amounts at a height. When this stored water is allowed to run over some rotating turbines installed in a hydropower plant, the mechanical energy of water helps rotate the turbines, which eventually generate electricity. Hence, a hydropower plant converts mechanical energy into electrical energy. Thus, the principal of conservation of energy is utilised in a hydropower plant.

The correct answer is C.

Question 7
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A car of mass 1200 kg starts from rest and acquires a uniform velocity of 18 m/s. What is the work done on the car?

A
184400 J

B
188400 J

C
194400 J

D
198400 J

Solution

Change in kinetic energy of the car is given by the relation:

Where,

m = Mass of the car = 1200 kg

v = Final velocity of the car = 18 m/s

u = Initial velocity of the car = 0

= 600 × 324 = 194400 J

Hence, the work done on the car is 194400 J.

The correct answer is C.

Question 8

1 / -0

Use the following information to answer the next question.

Puneet constructs a portable power plant, similar to those used in hydropower plants.

As he opens the tap, the running water rotates the blades of the turbine, as shown in the figure. As a result, a small amount of electricity is generated. This generated electricity makes the torch bulb glow.

What are the energy transformations taking place in the given power plant?

Electrical energy → Mechanical energy → Light energy

Mechanical energy → Electrical energy → Light energy

Heat energy → Electrical energy → Light energy

Chemical energy → Mechanical energy → Light energy

Solution

The law of conservation of energy states that energy can neither be created nor destroyed. Energy, however, can change from one form to another.

A body or a substance possesses mechanical energy by virtue of its motion or its position. In the given case, the water falling from the tap possesses energy because of its height and motion. Water (possessing mechanical energy) falls on the blades of the turbine and rotates it. The rotation of the turbine blades is used to generate electricity. In this process, mechanical energy is converted into electrical energy. The generated electric energy is used to make the bulb glow. Here, electrical energy is converted into light energy.

The correct answer is B.

Question 9
1 / -0

Use the following information to answer the next question.

A wooden block of mass, m is given a constant force, f for time, t. The block is initially at rest.

What is the kinetic energy acquired by the block?

A

B

C

D

Solution

Mass of the block = m

Force applied = f

Time = t

Initial velocity = u = 0 (Since the block is at rest)

From Newton’s second law of motion:

f = ma

(i)

From the first equation of motion:

v = u + at

v = at

(ii)

The kinetic energy acquired by the block is:

The correct answer is B.

Question 10

1 / -0

Use the following information to answer the next question.

Cars I and II, having masses m and 2m respectively, are moving with velocities 2v and v respectively. They are brought to rest by the application of breaks. The cars take the same time and cover the same distance before coming to rest.

What is the ratio of change in kinetic energy of car I to that of car II?

1 : 2

2 : 1

1 : 4

4 : 1

Solution

Change in kinetic energy of a body is given by the relation:

Where,

m = Mass of the body

v = Final velocity of the body

u = Initial velocity of the body

For car I: For car II:

Mass = m Mass = 2m

Initial velocity = 2v Initial velocity = v

Final velocity = 0 Final velocity = 0

(Since both the cars come to rest)

Change in K.E. of car I,

(i)

Change in K.E. of car II,

(ii)

The correct answer is B.

Question 11
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An object of mass four kilograms is raised to a height of 20 metres from the ground. What is the amount of potential energy stored in the object?

A
776 J

B
778 J

C
784 J

D
790 J

Solution

Potential energy is the energy stored in an object by virtue of its position or shape. It is given by the relation:

E_P= mgh

Where,

m = Mass of the object = 4 kg

g = Acceleration due to gravity = 9.8 m/s²

h = Height up to which the object is raised = 20 m

∴E_P= 4 × 9.8 × 20

= 784 J

The correct answer is C.
Question 12
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Potential energy is the energy stored in a body by virtue of its

A
motion and/or temperature

B
position and/or shape

C
velocity

D
density

Solution

Potential energy is the energy stored in a body by virtue of its position and/or shape.

The correct answer is B.
Question 13
1 / -0

Use the following information to answer the next question.

Balls I and II are simultaneously dropped from a building. The masses of balls I and II are m and 2m respectively.

If air resistance is ignored, then what will be the ratio of the instantaneous velocity of ball I to that of ball II when they reach the halfway mark?

A
1 : 1

B
2 : 3

C
1 : 4

D
3 : 2

Solution

According to the law of conservation of energy, the total energy of a system always remains the same.

In the given case, the total energy of each ball, at any instant, is equal to the sum of its potential and kinetic energies

Total energy = Potential energy + Kinetic energy

Mass of ball I = m

Mass of ball II = 2m

Let the height of the building be h.

Acceleration due to gravity = g

When each ball is halfway down, its total potential energy will be equal to its total kinetic energy.

For ball I: At the halfway mark

= Instantaneous velocity of ball I

For ball II: At the halfway mark

= Instantaneous velocity of ball II

The correct answer is A.
Question 14
1 / -0

Use the following information to answer the next question.

A stone is dropped from a building of height, h. The stone falls freely under the action of gravity.

If the air resistance is ignored, then what will be the instantaneous velocity of the stone when it covers three-fourth of the total height?

A

B

C

D

Solution

According to the law of conservation of energy, the total energy of a system is always constant.

In the given case, the total energy of the stone at any instant will be equal to the sum of its potential and kinetic energies. That is,

Total energy = Potential energy + Kinetic energy

Mass of the stone = m

Acceleration due to gravity, g = 9.8 m/s²

Height of the building = h

Case I: When the stone is about to fall

Potential energy = mgh

Kinetic energy = 0 (Since velocity, v = 0)

Total energy = Potential energy = mgh (i)

Case II: When the stone covers three-fourth of the height

Height from the ground =

Potential energy =

Kinetic energy = (v = Instantaneous velocity)

Total energy (ii)

From (i) and (ii), we get:

The correct answer is B.
Question 15
1 / -0

Use the following information to answer the next question.

A car is accelerated from rest in such a way that it acquires a uniform velocity of 5 m/s after covering a distance of 20 m. The mass of the car is 1200 kg.

What is the power generated by the car’s engine?

A
1875 W

B
1500 W

C
1000 W

D
1375 W

Solution

Mass of the car, m= 1200 kg

Initial velocity, u= 0 (Since the car is at rest)

Final velocity, v= 5 m/s

Distance covered, s= 20 m

From the third equation of motion:

From the first equation of motion:

v = u+ at

From Newton’s second law of motion:

F = ma

= 1200 ×0.625 = 750 N

Work done by the engine, W= F × s

= 750 ×20 = 15000 J
Question 16
1 / -0

Use the following information to answer the next question.

Firoze drops a stone from the top of a building. The height of the building is 30 metres and the mass of the stone is 1.5 kg.

If air resistance is ignored, then what is the difference between the total energy of the stone at 20-m and at 10-m heights from the ground?

A
0 J

B
2 J

C
4 J

D
6 J

Solution

According to the law of conservation of energy, the total energy of a system always remains the same.

In the given case, the total energy of the stone at any instant is equal to the sum of its potential and kinetic energies. When it is at the top, it contains only potential energy. As it begins to fall, its potential energy gets converted into kinetic energy in such a way that the total energy of the system remains the same.

Hence, the total energy of the stone at 20-m and at 10-m heights from the ground will be the same. Therefore, the difference will be zero.

The correct answer is A.