WBBSE Solutions For Class 9 Physical Science Chapter 5 Work

Chapter 5 Work Synopsis

1. When on object is displaced from its initial position under the action of a force, then work is said to be done. Work is a scalar quantity.
2. If d is the displacement of the object and F is the force applied, then work done, W=Fd.
3. During application of force on a body, if the body gets displaced in the direction of the applied force, then work is said to be done by the force. This is also called positive work.
4. During application of force on a body, if the body gets displaced in the direction opposite to that of the applied force, then work is said to be done against the force. This is also called negative work.
5. When the displacement of an object is at an angle of 90° with the direction of force, then no work is done by the applied force. This type of force is called no-work force.
6. The dimensional formula of work is ML²T^-2.
7. In CGS system and SI, the absolute units of work are erg and joule or 1 respectively.
8. 1J = 1N x1m= 10⁵ dyn . 100 = 10⁷ erg.

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Chapter 5 Work Short And Long Answer Type Questions

Question 1. Define work. How is the quantity of work measured?

Answer:

Work And Its Quantity Measurements :-

1. When an object is displaced from its initial position under the action of a force, then work is said to be done.
2. If applying a force F on a body displaces it by a distance d in the direction of the force, then work done, W = Fd.

Question 2. Define absolute units of work in CGS system and SI. Establish a relationship between the two units.

Answer:

Absolute Units Of Work In CGS System And SI And Its Relationship:-

The absolute unit of work in CGS system and SI are erg and joule, respectively.

1 erg: 1 erg is defined as the work done when a force of one dyne (dyn) applied to a body displaces it by 1cm in the direction of the force.

1 erg = 1 dyn x 1 cm = 1 dyn • cm

1 Joule: 1 joule is defined as the work done when a force of 1 N (newton) applied to a body displaces it by 1 metre (m) in the direction of the force.

1J = 1N x lm = 1N • m

Relationship Between Joule (J) And Erg:

1J = 1N x 1 m = 10⁵ dyn x 10² cm = 10⁷ erg

Question 3. What do you mean by work done by a force or positive work? Explain with examples.

Answer:

Work Done By A Force Or Positive Work Means:-

During the application of force on a body, if the body gets displaced in the direction of the applied force, then work is said to be done by the force. Since force and displacement are in the same direction, the value of this work is positive. Hence, it is called positive work.

For example, when a book is raised upward from the ground, work is said to be done by the force and is positive as the displacement of the book takes place in the same direction as that of the applied force.

Question 4. What do you mean by work done against a force or negative work? Explain With examples.

Answer:

Work Done Against A Force Or Negative Work Means:-

During application of force on a body, if the body gets displaced in the direction opposite to that of the applied force, then work is said to be done against the force. Since applied force and displacement are in the opposite directions, the value of this work is negative. Hence, it is called negative work.

For example, when a book is lowered slowly with constant velocity, an upward force is applied on the book at every moment. In this case, work is said to be done against the force and it is negative work as the displacement of the book takes place in the opposite direction as that of the applied force.

Question 5. What is a no-work force? Give two examples of no-work force.

Answer:

No-Work Force And Its Example:-

When the displacement of an object takes place in a direction perpendicular to the direction of the force, then no work is done by the applied force. This type of force is called no-work force.

Examples:

A man walks along a horizontal path with a suitcase in his hands. Force of gravity acts downward on the suitcase, but in a direction perpendicular to the displacement of the suitcase. Here, force of gravity is a no-work force.

Let us assume that due to the gravitational force of the sun, the earth is moving in circular orbits around the sun. At any position of the earth, the gravitational force acts along the radius towards the centre of the orbit and the direction of displacement is along the tangent at that point of the circular path.

This force of the sun on the earth is a no-work force since the direction of displacement of the earth at every point of its orbit is perpendicular to the force.

Question 6. A stone attached to a thread, is rotated around a finger in a horizontal plane. Which force is working in which direction due to this rotation? What is the direction of the displacement of the stone at any moment? Give reasons in favour of your answer. Explain how much work is done by you due to this rotation.

Answer:

A strong pull is felt by the finger due to rotation of the stone. The faster this stone is rotated, the more this pull is experienced. The stone rotates due to the pull toward the centre along the radius of the circle (along the thread in this case). This I force is called centripetal force.

It can be said from experience that if the thread breaks during rotation by any means, then no force is applied on the stone through the thread. The stone is dislodged tangentially from the circular path. This means that during revolution, the direction of displacement of the stone is always tangential to the circle.

The pull of the thread is along the radius of the circle and the displacement of the stone is tangential to the circle. This means that applied force and displacement are perpendicular to each other. Hence, this force on the stone is a no-work force.

Question 7. A man is walking up an inclined plane with a box in his hand. Is the gravitational force doing any work on the box?

Answer:

Given

A man is walking up an inclined plane with a box in his hand.

It is shown how gravity attracts the box in a straight downward direction.

As a result, a component of gravity, W₂ works downward along the inclined plane. But the displacement of the box takes place in upward direction along the inclined plane. So, gravity is doing positive work in this case.

Question 8. In a tug-of-war game, both the sides pull the rope with equal strength in opposite directions. What is the amount of work done by each side?

Answer:

In a tug of war game, both the sides pull the rope with equal strength but there is no displacement of the rope towards either side. As there is no displacement of the point of application of force, no work is done by the applied force and hence, the work done by each side is zero.

Question 9. In a tug-of-war game between teams A and B, team A which applies a force of 10 N is defeated by team B which applied a force of 12 N. In this case, which team has done positive work and which team has done negative work?

Answer:

In a tug-of-war game, team B has won. This means that team B has applied comparatively more force than team A. So, displacement of team A has taken place towards team B.

In this case, point of application of force i.e., displacement of team A has taken place towards direction of force applied by team B . Hence, team B has done positive work.

On the other hand, team A has also applied a force of 10 N on team B. In spite of that, displacement has taken place towards team B. Actually, team B has slide backwards in the game.

Hence, it may be said that displacement of team B was brought about by team A against the direction of force. So, team A has done negative work.

Question 10. A motor car is running on a horizontal road with uniform velocity. Is the engine of the car doing work in this condition?

Answer:

Given

A motor car is running on a horizontal road with uniform velocity.

Friction of the ground works against the motion of the car when it moves on a horizontal plane. To maintain the uniform velocity of the car, its engine applies a force equal to the frictional force in the direction of movement and for the displacement of the car against friction, the engine of the car works.

If the velocity of car=v; is frictional force = F, then work done by the engine per second = Fv.

Question 11. A man walks to the top of a hill along a steep path. Another man having the same mass as the first one goes to the top via a complex route. Which individual does greater amount of work?

Answer:

Given

A man walks to the top of a hill along a steep path. Another man having the same mass as the first one goes to the top via a complex route.

Work done by an object or an individual is the product of the force applied on it and the displacement of the object or individual.

As the masses of the two men are the same in this case, so their weights are also same. This means that each man has applied the same force against his weight to climb the hill.

Again, displacement is defined as the linear distance between the initial and final positions of the moving object or individual. In this case, displacements for both the men are the same as they have climbed the top of the hill from the ground level. As a result, both have done the same work.

[Note: Frictional force has not been taken into account in the given case. In reality, different amounts of frictional forces act on them while climbing the hill. Hence, the amount of work done by the two men is different in that case.]

Question 12. A man is swimming against the current in such a way that he is stationary with respect to the shore. Is he doing any work?

Answer:

Given

A man is swimming against the current in such a way that he is stationary with respect to the shore.

As there is no displacement with respect to the shore, no work is done with respect to the shore. But there is displacement with respect to the river water, so work done by the man is not zero with respect to water.

Chapter 5 Work Very Short Answer Type Questions Choose The Correct Answer

Question 1. Which of the following vehicles does more work to traverse a fixed distance in the same path carrying the same weight?

1. Bullock cart
2. Bicycle
3. Horse cart
4. Same work is done by all the vehicles

Answer: 4. Same work is done by all the vehicles

Question 2. Unit of work in SI is

1. Watt
2. Erg
3. Joule
4. Dyne

Answer: 3. Joule

Question 3. In a tug of war,

1. The defeated team does positive work
2. The defeated team does negative work
3. The victorious team does negative work
4. No work is done by either of the teams

Answer: 2. The defeated team does negative work

Question 4. A body makes a complete round in a circular path and during its journey, average applied force on it was F, r being the radius of the circular path. What is the total amount of work done by the body?

1. Zero
2. 2πrF
3. 2πF
4. πrF

Answer: 1. Zero

Question 5. Gravitational force is a no-workforce. This is because

1. Displacement of the body does not occur in the direction of gravitational force
2. Displacement of the body occurs in a direction perpendicular to the direction of gravitational force
3. Displacement of the body occurs in the direction opposite to that of gravitational force
4. There is no displacement of the body

Answer: 2. Displacement of the body occurs in a direction perpendicular to the direction of gravitational force

Question 6. A body starts its journey from point A, traverses a path ACB and reaches point B. Average applied force, F acts on the body during the entire course of its journey. If the path ACB is semicircular with a radius r, the amount of work done by the body is

1. Zero
2. πrF
3. 2πrF
4. 2rF

Answer: 4. 2rF

Question 7. A body held in hand is brought downward. Here, work is done against the force because

1. The direction of applied force is downward
2. The direction of gravitational force on the body is downward
3. The direction of displacement of body is downward
4. The direction of force applied on the body is upward but displacement of the body is downward

Answer: 4. The direction of force applied on the body is upward but displacement of the body is downward

Question 8. Dimensional formula of work is

1. MLT^-2
2. ML²T^-3
3. ML²T^-2
4. MLT^-3

Answer: 3. ML²T^-2

Question 9. Application of 200 dyn force displaces a body 4 m along the direction of force. Work done is

1. 0.004 J
2. 0.008 J
3. 0.08 J
4. 800 J

Answer: 2. 0.008 J

Question 10. Work done to raise a mass of 4 kg to a height of 2 m against gravity (g = 9.8 m/s²) is

1. 79.4J
2. 39.2J
3. 72.4J
4. 78.4J

Answer: 4. 78.4J

Question 11. Example of no-work force is

1. Frictional force
2. Centripetal force
3. Surface tension
4. All of the above

Answer: 2. Centripetal force

Question 12. Work done by winding the spring of a manual-winding watch is stored in the watch as

1. Sound energy
2. Kinetic energy
3. Potential energy
4. Light energy

Answer: 3. Potential energy

Question 13. The relationship between joule and erg is

1. 1J = 10⁵erg
2. 1J = 10⁷erg
3. 1J = 10¹⁰erg
4. 1J = 10 erg

Answer: 2. 1J = 10⁷erg

Question 14. Suppose you start racing from a fixed position in a field and come back to the same place. What is the total work done?

1. Zero
2. Positive quantity
3. Negative quantity
4. None of these

Answer: 1. Zero

Question 15. Two teams P and Q participate in a tug of war contest and pull the rope with the same force. Which team does more work?

1. TeamP
2. TeamQ
3. No work is done by either team
4. None of the above

Answer: 3. No work is done by either team

Question 16. A man drags a block 4 m on the floor. Friction force being 100 N, work done against friction is

1. 40 J
2. 0.4 J
3. 400 J
4. 4000 J

Answer: 3. 400 J

Question 17. A man weighing 40 kg, carrying a box of mass 10 kg, climbs up 10 steps of a staircase. If the height of each step is 20 cm, what is the amount of work done? [g = 10m/s²]

1. 1000J
2. 980J
3. 900J
4. 1100J

Answer: 1. 1000J

Question 18. Suppose you start racing from a fixed position in a field and come back to the some place. What is the total work done?

1. Zero
2. Positive quantity
3. Negative quantity
4. Unity

Answer: 1. Zero

Question 19. The angle between the applied force and displacement in the case of no work force is

1. 0°
2. 45°
3. 90°
4. 180°

Answer: 3. 90°

Question 20. The work done on an object does not depend upon the

1. Force applied
2. Initial velocity
3. Displacement
4. Angle between force and displacement

Answer: 2. Initial velocity

Chapter 5 Work Answer In Brief

Question 1. Product of two vector quantities is a scalar quantity. Give an example.

Answer: Force and displacement are vector quantities but their product, work is a scalar quantity.

Question 2. Give an example of no-work force.

Answer:

Example of no-work force

Centripetal force is a no-work force.

Question 3. What is the dimensional formula of work?

Answer: Dimensional formula of work is ML²T^-2.

Question 4. What is the absolute unit of work in SI?

Answer: The absolute unit of work in SI is joule (J).

Question 5. What is the absolute unit of work in CGS system?

Answer: The absolute unit of work in CGS system is erg.

Question 6. 1J = how many erg?

Answer: 1J = 10⁷erg

Question 7. What is the angle between force and displacement in case of no-work force?

Answer: In case of no-work force, angle between force and displacement is 90°.

Question 8. How much work is done by a weight-lifter when he stands with a weight above his head?

Answer: As the weight-lifter stands still with the weight above his head without any displacement, no work is done by him.

Question 9. The earth moves around the sun due to the force exerted by the sun on the earth. Is any work being done by the sun due to this motion of the earth?

Answer: No, force of attraction or gravitational force of the sun on earth is a centripetal force which is a no-work force.

Question 10. Does work depend on the speed with which a body is raised upward?

Answer: No, work done depends on displacement of the body and not on the speed with which the body is raised upward.

Question 11. Apart from no-work force, is it possible for the value of work done to be zero in any other case?

Answer: Yes, if the displacement of a body is zero even after the application of force, amount of work done is zero.

Question 12. What is the value of work related to potential energy in a place where gravity is zero?

Answer: Value of work related to potential energy in a place of zero gravity, is zero.

Question 13. In a tug of war game, which side does work when the rope remains motionless?

Answer: As there is no displacement of the rope, none of the sides is doing any work.

Question 14. A book is raised upward with uniform velocity. In this case, is work being done against the force or by the force?

Answer: As the displacement of the book is in the direction of the applied upward force, work is being done in favour of the force.

Question 15. A book is lowered downward with uniform velocity. In this case, is work being done against the force or by the force?

Answer: As the displacement of the book is downward but the book is held using an upward force, work is done against the force.

Question 16. A book held in hand, is displaced horizontally with uniform velocity. What is the relationship between force and work in this case?

Answer: In this case, the applied force is a no-work force.

Question 17. Can we recover the work done under a force?

Answer: Work done can be recovered if it is done under a force where mechanical energy is conserved.

Question 18. A stone is thrown upward. Is work being done by or against the force of gravity?

Answer: In this case, work is done against the force of gravity since displacement of the stone is upward but gravitational force acts downward.

Question 19. When is work done by a force positive?

Answer: Work done by a force is positive when the displacement of the body is in the direction of the force.

Question 20. When is work done by a force negative?

Answer: Work done by a force is negative, when the displacement of the body is in the direction opposite to the direction of the force.

Question 21. How much work is done by a weight-lifter when he stands with a weight above his head?

Answer: If the weighter-lifter stands still with the weight above his head without any displacement, no work is done by him.

Question 22. Does work depend on the speed with which a body is displaced?

Answer: No, work done depends on displacement of the body, not on the speed with which the body is displaced.

Question 23. What is the work done by the force of gravity on a satellite moving round the earth?

Answer: The force of gravity acts at right angle to the displacement of the satellite, so work done is zero.

Chapter 5 Work Fill In The Blanks

Question 1. Work is a ______ quantity.

Answer: Scalar

Question 2. The applied force does not do any work if the angle between force and displacement is ________

Answer: 900

Question 3. Centripetal force is _______ force.

Answer: No Work

Question 4. Any car traversing the same path carrying the same weight does the same amount of ______

Answer: Work

Question 5. Negative work denotes that work is done ________ the force.

Answer: Against

Question 6. A boy fails to lift a water-filled bucket in spite of his attempts. Amount of work done by the boy is ________

Answer: Zero

Question 7. Work done by the string of a simple pendulum during oscillation is _______

Answer: Zero

Question 8. _________ work is done when a mass is taken up with constant velocity by holding it in hand.

Answer: Positive

Chapter 5 Work State Whether True Or False

Question 1. It is said that work has been done when there is displacement of an object due to the application of an external force on a body.

Answer: True

Question 2. Negative work is done when the point of application of force moves in a direction opposite to that of the applied force.

Answer: True

Question 3. It is said that work has been done when there is displacement of an object due to the application of an external force on a body.

Answer: True

Question 4. Positive work is done when the point of application of force moves in a direction of the applied force.

Answer: True

Question 5. When an airplane takes off the work done by its weight is positive.

Answer: False

Question 6. Work is a vector quantity.

Answer: False

Question 7. In a tug-of-war the stronger team does positive work.

Answer: True

Chapter 5 Topic A Work Numerical Examples

If applying a force F on a body displaces it by a distance d in the direction of the force, then work done, W = Fd

The absolute units of work in CGS system and SI are erg and joule (J) respectively.

Question 1. A body is displaced 2 m in the direction of an applied force of 400 dyn. Calculate the work done.

Answer:

Given

A body is displaced 2 m in the direction of an applied force of 400 dyn.

Applied force, F= 400 dyn

Displacement of the body in the direction of force, d = 2 m = 200 cm

∴ work done,W = Fd = 400 dyn x 200 cm = 8 x 10⁴ erg

Question 2. A body of mass 10kg is raised upward by 5 m. Calculate the work done.

Answer:

Given

A body of mass 10kg is raised upward by 5 m.

Mass of the body, m = 10 kg

∴ applied force,

F = mg – 10 kg x 9.8 m/s² = 98 N

Displacement of the body, d = 5 m

∴ W = Fd = 98N x 5m = 490J

Question 3. A man drags a .box 10 m on the floor. What is the work done against friction, if frictional force of the floor is 200 N?

Answer:

Given

A man drags a .box 10 m on the floor.

Frictional force of the floor = 200 N Displacement of the box against friction, s = 10 m

∴ work done against friction, W = Fs = 200 N x 10 m = 2000 J

Question 4. The mass and the length of a uniform chain are M and L respectively. This chain is kept on a smooth table, 1/4th length of the chain is hanging from the side of the table. What is the work done to raise this hanging , chain on the table, if acceleration due to gravity is g?

Answer:

Given

The mass and the length of a uniform chain are M and L respectively. This chain is kept on a smooth table, 1/4th length of the chain is hanging from the side of the table.

Mass of the hanging portion = \(\frac{M}{4}\) and its weight = \(\frac{Mg}{4}\)

As the chain is uniform, we may assume that the mass of the hanging chain is centred around its mid-point.

That point is situated at \(\frac{L}{4}\) x \(\frac{1}{2}\) = \(\frac{L}{8}\) below the surface of the table.

∴ work done to raise this hanging portion on the table,

W = \(\frac{Mg}{4}\) X \(\frac{L}{8}\) = \(\frac{MgL}{32}\)