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Updated 6 August 2026

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Work, Energy, and Simple Machines

CBSE · Class 9 · Science

NCERT Solutions for Work, Energy, and Simple Machines — CBSE Class 9 Science.

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58 Questions Solved · 4 Sections

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Think It Over

1What will be the magnitude of velocity of the child at the bottom of the blue slide?Show solution

By conservation of mechanical energy (neglecting friction), the child's potential energy at the top converts into kinetic energy at the bottom:

\frac{1}{2}mv^2 = mgh

Cancelling

m

and solving for

v

v = \sqrt{2gh}

So the magnitude of velocity at the bottom of the slide is

\sqrt{2gh}

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2Will two children of different masses reach the bottom of the same slide with the same velocity?Show solution

The book states that the child's speed at the bottom depends only on the height of the slide, not on the child's mass. Since

m

cancels in

\frac{1}{2}mv^2 = mgh,

two children of different masses will reach the bottom with the same velocity if they start from the same height and friction is neglected.

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3Which of the slides will result in the largest magnitude of velocity for the child at its bottom?Show solution

From Example 7.8, the velocity at the bottom is

v = \sqrt{2gh}

So the largest velocity will be for the slide with the greatest height

h

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Ready to Go Beyond

1If a force acts in a direction perpendicular to the displacement of an object, the work done by that force is zero (Fig. 7.6) because there is no displacement in the direction of the force. For example, when a girl carries a box while walking, she applies an upward force to balance its weight, while the box moves horizontally. Since, the force and displacement are perpendicular to each other, no work is done by this force on the box. In higher grades, you will learn how to calculate the work done when force and displacement are at an angle to each other.Show solution

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2Doing mechanical work is one way of transferring energy from one object to another. But that is not the only way! Energy can also be transferred as heat. When two objects at different temperatures come in contact, energy flows from the hotter one to the colder one. Energy can also move without direct contact. For example, the Sun's energy reaches the Earth through radiation. Energy is transferred in electric circuits, as well as via sound waves, and even in nuclear reactions that power the Sun.Show solution

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3You need to apply an external force to overcome the internal forces in the spring to deform it. Once you remove this external force, the internal forces undo the deformation, and in the process, it can carry out work. Thus, internal forces allow energy to be stored in a deformed object.Show solution

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4Expression (Eq. 7.8) for the potential energy of an object at height

h

is valid only near the Earth's surface. Further away from the Earth's surface, the gravitational acceleration

g

decreases. You will learn about the gravitational potential energy of objects far from the Earth in higher grades.Show solution

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5Work done on a system against its internal forces, such as gravitational, electric or magnetic forces, can result in a gain of the potential energy of the system. But this is not true for all internal forces. For example, work done against friction does not lead to a storage of energy. You will learn how to identify such forces in higher grades.Show solution

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6Mechanical energy is just one part of a bigger picture. In nature, energy can appear in many different forms. Scientists have discovered that the total energy of an object or system of objects which is not acted upon by any external forces, stays constant.Show solution

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7Movable pulleys or a system of pulleys (Fig. 7.25) can have a mechanical advantage greater than 1 and can lift much heavier objects with much smaller effort. In a movable pulley system, the load is attached to the movable pulley. One end of the rope is fixed to a point, while the other end is free to apply effort. Pulleys are widely used in real life, such as in elevators and cranes given the convenience they provide us.Show solution

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8The work done, that is the product of force and displacement, is the same in all cases. If the force decreases, the displacement increases, thereby the work done remains constant.Show solution

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9Levers can be of three classes depending upon the relative positions of effort, fulcrum and load, as shown in Table 7.2.Show solution

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10In all cases, the conservation of mechanical energy holds. The work we put in is equal to the useful work done on the load, ignoring friction. Machines do not create energy, they only help us use it more effectively.Show solution

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11What if it were possible to build a perpetual motion machine, which once started, could continue doing useful work forever, without any fuel or electricity?Show solution

A perpetual motion machine would mean a machine that keeps doing useful work forever without any fuel or electricity. The chapter says that real machines eventually slow down and stop because some energy is lost, mainly due to friction. So such a machine is not possible in reality.

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12You may have heard about another unit called horsepower (hp) used to measure power, especially for car engines, or pumps used to lift water. One horsepower is equal to

746\mathrm{W}

. In the early days, when engines were newly discovered, the powers of engines were compared to the power of actual horses which were used to drive carriages.Show solution

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13it were possible to build a perpetual motion machine, which once started, could continue doing useful work forever, without any fuel or electricity?Show solution

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Revise, Reflect, Refine

1(i)Work is said to be done when a force is applied, even if the object does not move.Show solution

The chapter says work is done only when a force causes displacement in the direction of the force. If the object does not move, then displacement is zero, so work done is zero.

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1(ii)Lifting a bucket vertically upward results in positive work done on the bucket.Show solution

When a bucket is lifted vertically upward, the applied force and the displacement are in the same direction. Therefore, the work done on the bucket is positive.

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1(iii)The SI unit for both work and energy is joule (J).Show solution

The chapter states that the SI unit of work and the SI unit of energy is the same, namely the joule (J).

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1(iv)A motionless stretched rubber band has kinetic energy.Show solution

A motionless stretched rubber band has potential energy due to its deformation, not kinetic energy, because kinetic energy is the energy due to motion.

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1(v)Energy can change from one form to another.Show solution

The chapter clearly states that energy can be converted from one form to another, such as electrical energy to light or thermal energy.

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2(i)Work done

=

（20x）in the direction of force).Show solution

From the definition in the chapter:

\text{work done} = \text{force applied} \times \text{displacement in the direction of the force}

So the blank is force × displacement.

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2(ii)1 joule of work is done when a force of newton displaces an object by 1 metre in the direction of the force.Show solution

The chapter defines:

1\,\text{J} = 1\,\text{N} \times 1\,\text{m}

So 1 joule of work is done when a force of 1 newton displaces an object by 1 metre in the direction of the force.

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2(iii)The expression for kinetic energy of a body of mass

m

and velocity

v

isShow solution

The chapter gives the expression for kinetic energy as

K = \frac{1}{2}mv^2

where

m

is mass and

v

is velocity.

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2(iv)The potential energy of an object of mass

m

at a small height

h

from the Earth's surface isShow solution

For an object at height

h

near the Earth's surface, the potential energy is given by

U = mgh

where

m

is mass,

g

is acceleration due to gravity, and

h

is height.

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2(v)Power is defined as the at which work is done.Show solution

Power is defined as the rate at which work is done:

P = \frac{W}{t}

So the blank is rate.

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3When a ball thrown upwards reaches its highest point, tick which of the following statement(s) are correct?Show solution

At the highest point of a ball thrown upward:

- The force acting on the ball is zero — false, gravity still acts downward.
- The acceleration is zero — false, acceleration due to gravity is still downward.
- The kinetic energy is zero — true at the highest point because the velocity becomes zero momentarily.
- The potential energy is maximum — true because the ball is at the greatest height.

So the correct statements are (iii) and (iv).

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4For each of the following situations, identify the energy transformation that takes place:Show solution

The energy transformations are:

1. Truck moving uphill: kinetic energy → potential energy
2. Unwinding of a watch spring: potential energy of spring → kinetic energy
3. Photosynthesis in green leaves: solar energy → chemical energy
4. Water flowing from a dam: potential energy → kinetic energy
5. Burning of a matchstick: chemical energy → heat and light energy
6. Explosion of a fire cracker: chemical energy → heat, light, sound, and kinetic energy
7. Speaking into a microphone: sound energy → electrical energy
8. A glowing electric bulb: electrical energy → light energy and heat energy
9. A solar panel: solar energy → electrical energy

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5A student is slowly lifted straight up in an elevator from the ground level to the top floor of a building. Later, the same student climbs the staircase, all the way to the top. Given that the height of the building is

h = 72.5 \, \text{m}

, acceleration due to gravity is

g = 10 \, \text{m} \, \text{s}^{-2}

, and student’s mass is

m = 50 \, \text{kg}

.Show solution

Potential energy gained on being lifted is

U = mgh

Given

m = 50\,\text{kg}

g = 10\,\text{m s}^{-2}

h = 72.5\,\text{m}

U = 50 \times 10 \times 72.5 = 36250\,\text{J}

So:

1. When the student is lifted straight up, gain in potential energy = 36250 J.
2. When the student climbs the stairs to the same top, gain in potential energy is also 36250 J.
3. Therefore, potential energy depends only on height, not on the path taken.

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6A crane lifts a mass

m

to the 10th floor of a building in a certain time. It then raises the same mass to the 20th floor of the same building in double the time. How much more energy and power are required? Assume that the height of all floors is equal.

7Which factors determine the energy required to raise a flag from the ground to the top of a tall flagpole using a pulley? Does raising the flag slowly or quickly change the amount of work done? If the speed at which the flag is raised is doubled, how does the power requirement change? Explain your answers.

8A man of mass

60\mathrm{kg}

rides a scooter of mass

100\mathrm{kg}

. He accelerates the scooter to a velocity

\nu

. The next day, his son with a mass of

40\mathrm{kg}

joins him as a passenger. If the scooter reaches the same speed on both days in the same time interval, what is the ratio of the fuel of the tank used on the two days? Assume that the energy transfer to the scooter happens entirely due to fuel, and no other losses occur due to air resistance and friction.

9On a seesaw with sliding seats, a child is sitting on one side and an adult on the other side. The adult weighs twice that of the child. The seesaw however is balanced. Draw a figure which depicts this situation showing the distances from the fulcrum where the child and the adult are seated.

10A ball of mass 2 kg is thrown up with a velocity of 20 m s⁻¹.

11A 10.0 kg block is moving on horizontal floor with negligible friction. As shown in the Fig. 7.37, a variable force is applied on the block in its direction of motion from its position at 0 m till 4 m. If the block had a kinetic energy of 180 J when it was at 0 m, find the block's speed (i) at 0 m, and (ii) at 4 m. Does the block have negative acceleration in any portion of its motion?

12The gravitational attraction on the surface of the Moon (lunar surface) is about 1/6th of that on the surface of the Earth. An astronaut can throw a ball up to a height of 8 m from the surface of the Earth. How far up will the ball thrown with the same upward velocity travel from the surface of the Moon?

14The potential energy-displacement graph of a 0.5 kg ball moving along a frictionless track is shown in Fig. 7.39. At O, the velocity of the ball is 0 m s⁻¹ and potential energy is 30 J. Calculate the velocity of the ball at P, Q and R.

15A coconut of mass 1.5 kg falls from the top of a coconut tree onto the wet sand on a beach. The height of the tree is 10 m. On impact, the coconut comes to rest by making a depression in the sand.

1State whether True or False.

2Fill in the blanks.

4For each of the following situations, identify the energy transformation that takes place: (i) a truck moving uphill, (ii) unwinding of a watch spring, (iii) photosynthesis in green leaves, (iv) water flowing from a dam, (v) burning of a matchstick, (vi) explosion of a fire cracker, (vii) speaking into a microphone, (viii) a glowing electric bulb, and (ix) a solar panel.

Pause and Ponder

1In the previous chapter, a weightlifter is shown holding a barbell steady in her hands (Fig. 6.8). Is she doing any work on the barbell while holding it steady?

2Is the work done by friction on the stack of coins that travels on a rough surface (Fig. 6.13c) — positive, negative or zero?

3When you pedal a bicycle on a flat road, your muscles supply energy. In what forms does this muscular energy appear as you ride?

4Two objects A and B of mass m and 4 m have the same kinetic energy. What is the ratio of the magnitude of velocities of A and B?

5Does the kinetic energy of an object which moves with constant velocity change with its position?

6Does the potential energy of an object near the surface of the Earth change if it moves with constant velocity in the horizontal direction? What if the object is gradually raised in the vertical direction?

7For the situation depicted in Fig. 7.19, calculate the mechanical energy of the ball just before it hits the ground and show that even at this position, it is

mgh

8You may have seen an exhibit like that in Fig. 7.22 in a science park, where a ball is released from the highest point. Describe how the kinetic energy and potential energy change at points A, B and C. Why do subsequent points, such as C, D and E, usually have lower heights compared to the previous ones? Could it have anything to do with the energy lost due to friction?

9Explain why roads on hills are built to wind around in gentle slopes rather than going straight up (Fig. 4.26)?

10To reach a higher floor, we find climbing an inclined ladder easier in comparison to climbing a vertical ladder (Fig. 7.30). Explain why.

11Why is it easier to open the lid of a can by using a spoon as shown in Fig. 7.35?

12Why do you push an object closer to scissors fulcrum when you want to cut an object which is hard?

13Throughout history, many designs of perpetual machines (using wheels, weights or magnets) have been proposed but none actually work.

Why do all real machines eventually slow down and stop? Explain in terms of work and energy.

10A ball of mass 2 kg is thrown up with a velocity of 20 m s⁻¹.

(i) Identify the sign of the work done by gravity on the ball during its upward motion and its downward motion.
(ii) If the ball reaches a height of 19.4 m, how much work was done by air resistance (assume g = 10 m s⁻²).

13A 1000 kg car is moving along a road at a constant speed. Suddenly, the driver notices some obstruction ahead and applies the brakes to come to a complete stop. The graphical representation of motion of the car starting from the instant the driver spots the traffic ahead is shown in Fig. 7.38.

(i) Describe how the car moves between positions A and B.
(ii) Calculate the kinetic energy of the car at A.
(iii) State the work done by the brakes in bringing the car to a halt between B and C.
(iv) What does the kinetic energy of the car transform into?

15A coconut of mass 1.5 kg falls from the top of a coconut tree onto the wet sand on a beach. The height of the tree is 10 m. On impact, the coconut comes to rest by making a depression in the sand.

(i) Calculate the velocity of the coconut just before it hits the sand.
(ii) Assume that the average resistive force of sand is 3000 N and all of the coconut's energy is used to create the depression in the sand. Calculate the depth of the depression the coconut makes in the sand. Assume g = 10 m s⁻².

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Frequently Asked Questions

What are the important topics in Work, Energy, and Simple Machines for CBSE Class 9 Science?

Key topics in Work, Energy, and Simple Machines include Distance vs Displacement: The Correct Decision Path, Motion - Complete Chapter Concept Overview, Chapter 7 Motion – Complete Concept Map. These are the concepts CBSE Class 9 examiners draw on most — study them first, then practise related questions.

How to score full marks in Work, Energy, and Simple Machines — CBSE Class 9 Science?

Understand the core concepts first, then work through the 80 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Where can I get free NCERT Solutions for Work, Energy, and Simple Machines Class 9 Science?

This page has free step-by-step NCERT Solutions for every exercise question in Work, Energy, and Simple Machines (CBSE Class 9 Science) — written the way examiners award marks: given, formula, working, answer.

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Work, Energy, and Simple Machines

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Think It Over

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