**Important Questions for CBSE Class 9 Science Chapter 11 Work, Power and Energy**

**IMPORTANT QUESTIONS**

**1-MARK QUESTIONS**

**Question.1 Does work done depend upon the velocity of the body. [SAII-2014]**

** Answer.** No.

**Question.2 State the law of conservation of energy. [SAII-2014]**

** Answer.** It states that energy can neither be created nor destroyed. It can only change its form.

**More Resources for CBSE Class 9**

- NCERT Solutions
- NCERT Solutions Class 9 Maths
- NCERT Solutions Class 9 Science
- NCERT Solutions Class 9 Social Science
- NCERT Solutions Class 9 English
- NCERT Solutions Class 9 Hindi
- NCERT Solutions Class 9 Sanskrit
- NCERT Solutions Class 9 IT
- RD Sharma Class 9 Solutions

**Question.3 In a tug-of-war one team gives way to the other. What work is being done and by whom ? ****[SAII-2014]**

** Answer.**

The winning team does work. The work is equal to the product of the resultant force and the displacement undergone by the losing team.

**Question.4 What will cause greater change in kinetic energy of a body? Changing its mass or changing its velocity ?**

** Answer.** Changing its velocity.

**Question.5 List two essential conditions for work to be done. [SAII-2010]**

** Answer.** (i) A force must act and (ii) There should be displacement in the body.

**Question.6 When is 1 joule of work said to be done ?**

** Answer.** When a force of 1 newton acting on a body displaces it in its own direction.

**Question.7 What is the SI unit of work done and power ?**

** Answer.** Joule and Watt.

**Question.8 What is power? What is its SI unit ?**

** Answer.** It is defined as the rate of doing work. Its unit is watt.

**Question.9 Find the energy in kWh consumed in 10 hours by a machine of power 500 W. [SAII-2011]**

** Answer.** W = P x t = 500 x 10 = 5000 Wh – 5 kWh.

**Question.10. When is work said to be done against the force of gravity ?**

** Answer.** When a body lifted the work is done against the force of gravity.

**Question.11 Write an expression for the work done in lifting a body of mass ‘m’ through a vertical height ‘h’. [SAll-2012]**

** Answer.** Work done W = mgh, where g is acceleration due to gravity.

**Question.12 When a book is lifted from a table, against which force work is done ?**

** Answer.** Work is done against the force of gravity.

**Question.13 Will work be done by a man who pushes a wall ?**

** Answer.** No.

**Question.14 What is the work done when the force acting on the body and the displacement produced in the body are at right angles to each other ?**

** Answer.** Zero.

**Question.15 Is it possible that some force is acting on a body but still the work done is zero ?**

** Answer.** Yes, when force acts at an angle of 90° with the displacement.

**Question.16 What is the work done on a body moving in a circular path ?**

**Answer.** Zero, because force and displacement are perpendicular to each other.

**Question.17 Does every change in energy of the body involve work ?**

** Answer.** Yes.

**Question.18 What is the work done in the situation shown below ?**

**Answer.** Zero.

**Question.19 A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force. Let us take it that the force acts on the object through the displacement. What is the work done in this case ?**

** Answer.**

Given, displacement = 8 m,

Force = 7N

Now, Work done = Force x Displacement

= 7 x 8 = 56 J

**Question.20 When do we say that work is done ? ~**

** Answer.**

Work is said to be done when a force causes displacement of an object in the direction of applied force.

**Question.21 Write an expression for the work done when a force is acting on an object in the direction of its displacement.**

** Answer.**

Work done = Force x Displacement

**Question.22 A pair of bullocks exert a force of 140 N on a plough. The field being ploughed is 15 m long. How much work is done in ploughing the length of the field ?**

** Answer.**

Work done = Force x Displacement = 140 x 15 = 2100 J

**Question.23 What is the kinetic energy of an object?**

** Answer.**

The energy possessed by a body by virtue of its motion is called kinetic energy.

**Question.24 Write an expression for the kinetic energy of an object.**

** Answer.**

The expression is KE = 1/2 mv^{2}, where ‘m’ is the mass and V is the velocity of the body.

**Question.25 Define 1 watt of power.**

** Answer.**

When a work of 1 joule is done in 1s, the power is said to be one watt.

**Question.26 A lamp consumes 1000 J of electrical energy in 10 s. What is its power ?**

** Answer.**

Given, W = 1000 J, t = 10 s, R = ?

Using p = W/t = 1000/10 = 100 W

**Question.27 Define average power.**

** Answer.**

When a machine or person does different amounts of work or uses energy in different intervals of time, the ratio between the total work or energy consumed to the total time is average power.

**Question.28 Define energy.**

** Answer.**

Energy is the ability of a body to do work. It is also defined as the capacity to do work.

**Question.29 A body performs no work. Does it imply that the body possesses no energy ?**

** Answer.**

When a body does not perform any work, it never implies that the body has no energy. The body may have energy but still does not perform any work, e.g., a book placed on a table has potential energy but is not performing any work.

**Question.30 What is the SI unit of energy?**

** Answer.**The SI unit of energy is joule.

**Question.31 Does a body at rest possess any kinetic energy ?**

** Answer.**No.

**Question.32 What will happen to the kinetic energy of a body if its mass is doubled ?**

** Answer.** Its kinetic energy will be doubled.

**Question.33 What will happen to the kinetic energy of a body if its velocity is halved ? [SAII-2012]**

** Answer.** The kinetic energy of the body will become one-fourth.

**Question.34 By how much will the speed of a body, of fixed mass, increase if its kinetic energy becomes four times its initial kinetic energy ?**

** Answer.** The speed is doubled.

**Question.35 Can a body possess energy even if it is not in motion ?**

** Answer.** Yes, it can possess potential energy.

**Question.36 Define potential energy.**

** Answer.** It is defined as the energy possessed by a body by virtue of its position or change in shape.

**Question.37 Name the energy possessed by a stretched rubber band lying on the table.**

** Answer.** Potential energy.

**Question.38 Give the SI unit of potential energy.**

** Answer.** The SI unit of potential energy is.joule.

**Question.39 What do you mean by trans- formation of energy ?**

** Answer.** It is the change of energy from one form of energy into another form of energy.

**Question.40 Can energy be destroyed? Can energy be created ?**

** Answer.** No,

**Question.41 A cell converts one form of energy into another. Name the two forms.**

** Answer.**

It converts chemical energy into electrical energy.

**Question.42 Name one unit of power bigger than watt.**

** Answer.** A unit bigger than watt is kilowatt.

**Question.43 When an arrow is shot from its bow, it has kinetic energy. From where does it get the kinetic energy ? [SAll-2010]**

** Answer.**

A stretched bow possesses potential energy on account of a change in its shape. To shoot an arrow; the bow is released. The potential energy of the bow is converted into the kinetic energy of the arrow.

**Question.44 Name at least three commonly used units of energy.**

** Answer.** (i) Joule (ii) Erg (iii) Kilowatt hour.

**Question.45 Name the practical unit of power in engineering.**

** Answer.** Horsepower.

**Question.46 Name at least six forms of energy.**

** Answer.**

(i) Chemical energy

(ii) Heat energy

(iii) Light energy

(iv) Electrical energy

(v) Sound energy

(vi)Solar energy

**Question.47 How many watt are there in 1 horse – power ?**

** Answer.** 746 watt.

**Question.48 What is horsepower ?**

** Answer.** It is a unit of power.

**Question.49 A light and a heavy body have equal kinetic energy. Which one is moving fast ? [SAII-2011]**

** Answer.** The lighter body is moving fast.

**2 MARKS QUESTIONS**

**Question.1 State the relation between kW h and joule. Define 1 watt. [SAII-2014]**

** Answer.**

1 kW h – 1000 W h = 1000 Js^{-1} x 60 x 60 s = 3.6 x 10^{6} J

1 watt is the power of an agent which can do one joule of work in one second.

**Question.2 Is it possible that a body be in accelerated motion under a force acting on the body, yet no work is being done by the force? Explain your answer giving a suitable example. [SAII-2012]**

** Answer. **Yes, it is possible, when the force is perpendicular to the direction of motion. The moon revolving round the earth under the centripetal force of attraction of the earth but earth does not do any work on the motion of The moon.

**Question.3 Define work. How is work measured ? When is work done by a force negative? [SAII-2013]**

** Answer. **Work is said to be done if force acting on an object displaces it through a certain distance.

It is measured as the product of force and displacement.

Work done is negative if force and displacement are in the opposite direction.

**Question.4 What is the work done by the force of gravity in the following cases ?**

** (a) Satellite moving around the earth in a circular orbit of radius 35000 km.**

** (b) A stone of mass 250 g is thrown up through a height of 2.5 m. [SAII-2013]**

** Answer.**

(a) Zero, as the displacement in one complete revolution is zero.

(b) Given m = 250 g = 0.25 kg, h = 2.5 m, g = 10 ms^{-2}, W = ?

Now, W = FS = mg x h = 0.25 x 10 x 2.5 = 6.25 J

**Question.5 A mass of 10 kg is at a point A on a table. It is moved to a point B. If the line joining A and B is horizontal, what is the work done on the object by the gravitational force? Explain your answer.**

** Answer. **The work done is zero. This is because the gravitational force and displacement are perpendicular to each other.

**Question.6 The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why? [SAII-2010]**

** Answer. **It does not violate the law of conservation of energy. Whatever, is the decrease in PE due to loss of height, same is the increase in the KE due to increase in velocity of the body.

**Question.7 What are the various energy transformations that occur when you are riding a bicycle?**

** Answer. **The chemical energy of the food changes into heat and then to muscular energy. On paddling, the muscular energy changes into mechanical energy.

**Question.8 Does the transfer of energy take place when you push a huge rock with all your might and fail to move it? Where is the energy you spend going?**

** Answer. **Energy transfer does not take place as no displacement takes place in the direction of applied force; the energy spent is used to overcome inertia of rest of the rock.

**Question.9 An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the work done by the force of gravity on the object ? [SAll-2011 ]**

** Answer. **Since the body returns to a point which is on the same horizontal line through the point of projection, no displacement has taken place against the force of gravity; therefore, no work is done by the force due to gravity.

**Question.10 A battery lights a bulb. Describe the energy changes involved in the process.**

** Answer. **Within the electric cell of the battery the chemical energy changes into electrical energy. The electric energy on flowing through the filament of the bulb, first changes into heat energy and then into the light energy.

**Question.11 What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.**

** Answer. **The work done by the force of gravity on the satellite is zero because the force of gravity acts at right angles to the direction of motion of the satellite. Therefore, no displacement is caused in the direction of applied force. The force of gravity only changes the direction of motion of the i satellite.

**Question.12 Can there be displacement of an object in the absence of any force acting on it? Think;**

** discuss this question with your friends and teacher. [SAII-2012]**

** Answer. **The answer is. both Yes and No. Yes, because when an object moves in deep space from one

point to another point in a straight line, the displacement takes place, without the application of

force. No, because force cannot be zero for displacement on the surface of earth. Some force is i essential.

**Question.13 A person holds a bundle of hay over his head for 30 minutes and gets tired. Has he done some work or not ? justify your answer.**

** Answer. **The person does not do work because no displacement takes place in the direction of applied force as the force acts in the vertically upward direction.

**Question.14 An object of mass, m is moving with a constant velocity, v. How much work should be done on the object in order to bring the object to rest ?**

** Answer. **Work done to bring the object to rest is equal change in kinetic energy of the object.

**Question.15 Soni says that the acceleration in an object could be zero even when several forces are acting on it. Do you agree with her ? Why ?**

** Answer. **Yes, we do agree when the number of forces act on a body, such that they constitute balanced forces, then net force acting on the body is zero. In such a situation no acceleration acts on the object.

**Question.16 A freely falling object eventually stops on reaching the ground. What happens to its kinetic ****energy ? [SAI1-2011]**

** Answer. **The KE on reaching the ground changes into heat energy, sound energy etc. and, therefore, gets dissipated in air.

**Question.17 What kinds of energy transformations take place at a thermal power station ?**

** Answer. **At a thermal power station, the chemical energy of coal is changed into heat energy which is further changed into electrical energy with the help of an electric generator.

**Question.18 Name the transformation of energy involved in the following cases :**

** (a) When a body is thrown upwards.**

** (b) When a body falls from the top of a hill.**

** (c) When coal burns.**

** (d) When a gas bums.**

** (e) When water falls from a height.**

** Answer.**

(a) Kinetic energy into potential energy.

(fa) Potential energy into kinetic energy.

(c) Chemical energy into heat energy.

(cf) Chemical energy into heat energy.

(e) Potential energy into kinetic energy.

**Question.19 What are the factors on which the work done depends ? [SAII-2010]**

** Answer.**The work done by a force depends upon:

(i) The magnitude of the force.

(ii) The magnitude of the displacement and

(iii) The angle between force and displacement.

**Question.20 How are kinetic energy and momentum related ?**

** Answer.**

**Question.21 What is the work done by a coolie walking on a horizontal platform with a load on his head ?**

** Answer. **In order to balance the load on his head, the coolie applies a force on it in the upward direction, equal to its weight. His displacement is along the horizontal direction. Thus, the angle between force F and displacement is 90°. Therefore, work done W = FS cos θ = FS cos 90° =0.

**Question.22 We wind our watch once a day, what happens to the energy ?**

** Answer. **When we wind our watch, we wind the spring inside the watch. As a result, energy is stored in the spring in the form of elastic potential energy. This elastic potential energy is used to make the watch work the whole day. .

**Question.23 What is the amount of work done by a force when a body moves in a circular path ? ****[SAll-2012]**

** Answer. **Work done is given by the expression W = FS cos θ. When a body moves in a circular path, then the displacement (S) is zero. Therefore, work done is W = F x 0 = 0.

**3 MARKS QUESTIONS**

**Question.1 Look at the activities listed below.**

** Reason out whether or not work is done in the light of your understanding of the term ‘work’**

** (i) Suma is swimming in a pbnd.**

** (ii) A donkey is carrying a load on its back.**

** (iii) A wind-mill is filling water from a well.**

** (iv) A green plant is carrying out photosynthesis.**

** (v) An engine is pulling a train.**

** (vi)Food grains are getting dried in the sun.**

** (vii) A sailboat is moving due to wind energy.**

** Answer.**

(i) Work is done because the displacement of swimmer takes place in the direction of applied force.

(ii) If the donkey is not moving, no work is done as the displacement of load does not take place in the direction of applied force.

(iii) Work is done, as the displacement takes place in the direction of force.

(iv) No work is done, because no displacement takes place.

(v) Work is done, because displacement takes place in the direction of applied force.

(vi)No work is done, because displacement does not take place.

(vii)Work is done because displacement takes place in the direction of the force.

**Question.2 Illustrate the law of conservation of energy by discussing the energy changes which occur when we draw a pendulum bob to one side and allow it to oscillate. Why does the bob eventually come to rest ? What happens to its energy eventually ? Is it a violation of the law of conservation of energy ?**

** Answer. **When the pendulum bob is pulled (say towards left), the energy supplied is stored in it is the form of PE on account of its higher position. When the pendulum is released so that it stars moving towards right, then its PE changes into KE, such that in mean position, it has maximum KE, and zero PE. As the pendulum moves towards extreme right, its -KE changes into PE such that at the extreme position, of has maximum PE and zero KE. When it moves from this extreme position to mean position, its PE again changes to KE. This illustrates the law of conservation of energy. Eventually, the bob comes to rest, because during each oscillation a part of the energy possessed by it transferred to air and- m overcoming friction at the point of suspension. Thus, the energy of the pendulum is dissipated in air.

The law of conservation of energy is not violated because the energy merely changes its form and is not destroyed.

**Question.3 ****In each of the following a force, F is acting on an object of mass, m. The direction of displacement is from west to east shown by the longer arrow. Observe the diagrams carefully and state whether the work done by the force is negative, positive or zero.**

**Answer.**

**Question.4 Distinguish between work, energy and power. State the SI units for each of these quantities.**

** Answer.**

**Work:** It is defined as the product of force applied and the distance moved by the body on the application of the force. In SI it is measured in joule.

**Energy :** It is defined as the capacity of a body to do work. In SI it is measured in joule.

**Power:** It is defined as the rate of doing work. It measures how fast or slow the work is done. In SI it is measured in watt.

**Question.5 A girl sits and stands repeatedly for 5 minutes. Draw a graph to show variation of potential energy with time.**

** Answer.**

**5 MARKS QUESTIONS**

**Question.1 Calculate the electricity bill amount for a month of 31 days, if the following devices are used as specified :**

** (a) 3 bulbs of 40 W for 6 hours.**

** (b) 4 tubelights of 50 W for 8 hours,**

** (c) A TV of 120 W fro 6 hours.**

** Give the rate of electricity is Rs 2.50 per unit. [SAll-2014]**

** Answer.**

**Question.2**

** (a) What is meant by mechanical energy ? State its two forms. State the law of conservation of energy. Give an example in which we observe a continuous change of one form of energy into another and vice-versa.**

** (b) Calculate the amount of work required to stop a car of 1000 kg moving with a speed of 72 km h”1. [SAII-2013]**

** Answer.**

(a) It is the sum of KE and PE of an object. It states that energy can neither be created nor be destroyed. We observe a continuous change in energy in a simple pendulum and its : explanation. At the mean position, the energy is wholly kinetic while at the extreme position it is wholly potential. As the pendulum oscillates its energy continuously changes between kinetic and potential.

**Question.3 State the law of conservation of energy? Show that when a body falls from a certain height the total mechanical energy remains conserved.**

** Answer.**

**AT POINT B :**

**Question.4**

** (a)Derive an expression for kinetic energy of a body having mass m and moving with a velocity v.**

** (b)When velocity of a body is increased 5 times, what is the change in its kinetic energy ?**

** (c)Two masses m and 2m are dropped from heights h and 2h. On reaching the ground, which will have greater kinetic energy and why ? [SAII-2013]**

** Answer.**

(a)For derivation see above questions.

(b)Kinetic energy is given by the expression

KE = 1/2 mv^{2}, therefore, if velocity is made 5 times KE will increase by 25 times.

(c)More the potential energy more will be the kinetic energy of the body when it falls. Hence, the body with mass 2m will have greater kinetic energy as it has more potential energy.

**Question.5**

** (a)State the law of conservation of energy.**

** (b)What is the work done to increase the velocity of a car from 36 km h-1 to 72 km h~1 if the mass of the car is 1500 kg ? Does the work done by the force have a negative or a positive magnitude ?**

** (c)Where does an oscillating pendulum have maximum PE and KE ? [SAII-2013]**

** Answer.**

**APPLICATION BASED QUESTIONS**

**Question.1 A light body and a heavy body have the same kinetic energy. Which one will have the greater momentum ?**

** Answer.**

**Question.2 A light and a heavy body have the same momentum. Which one will have greater kinetic energy ?**

** Answer.**

**Question.3**

** (a) Can a body have energy without having momentum ? Explain.**

** (b) Can a body have momentum without having energy ? Explain.**

** Answer.**

**Question.4 When an arrow is shot from its bow, it has kinetic energy. From where does it get the kinetic energy ?**

** Answer. **A stretched bow possesses potential energy on account of a change in its shape. To shoot an arrow; the bow is released. The potential energy of the bow is converted into the kinetic energy of the arrow.

**Question.5 A spring which has been kept compressed by tying its ends together is allowed to be dissolved in an acid. What happens to the potential energy of the spring ?**

** Answer. **The PE of the spring gets converted into KE of acid molecules whose temperature rises.

**Higher Order Thinking Skills (HOTS) Questions**

**Question.1 justify giving proper reasoning whether the work done in the following cases is positive or negative :**

** (a) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.**

** (b) Work done by gravitational force in the above case.**

** (c) Work done by friction on a body sliding down an inclined plane.**

** (d) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity.**

** (e) Work done by resistive force of air on a vibrating pendulum in bringing it to rest.**

** Answer.**

(a) Work done is positive as the bucket moves in the direction of force applied by the man.

(b) Work done by the gravitational force is negative, as the bucket moves upwards i.e., opposite to the gravitational force.

(c) Work done is negative, as frictional force acts opposite to the direction of motion of the body.

(d) Work done is positive because applied force acts along the same direction as the direction of motion of the body.

(e) Work done is negative because the resistive force of air always acts opposite of the direction of motion of the vibrating*pendulum.

**Question.2 What is the work done by a coolie walking on a horizontal platform with a load on his head? ****[SAII-2010]**

** Answer. **In order to balance the load on his head, the coolie applies a force on it in the upward direction, equal to its weight. His displacement is along the horizontal direction. Thus, the angle between force F and displacement is 90°. Therefore, work done W = FS cos θ = FS cos 90° = 0.

**Question.3 The work done in lifting a box on to a platform does not depend upon how fast it is lifted up.**

** Explain your answer giving proper reasoning. [SAll-2013]**

** Answer. **The work done (W) in lifting a box through a distance (S) against the gravitational force (F) is given by W = FS. Hence, it is obvious that it is independent of the rate at which the box is lifted.

**Question.4 Is it possible that a body be in accelerated motion under a force acting on the body, yet no work is being done by the force ? Explain your answer giving a suitable example.**

** Answer. **Yes, it is possible, when the force is perpendicular to the direction of motion. The moon revolving round the earth under the centripetal force of attraction of the earth, but earth does no work on the motion.

**Question.5 A body moves along a circular path. How much work is done in doing so? Explain.**

** Answer. **In case of a body moving along a circular path, the force (centripetal) is always along the radius while displacement is tangential. Hence, work done W = FS cos 90° = 0 as angle between F and S is 90°.

**Question.6 A man rowing a boat upstream is at rest with respect to the shore. Is he doing work ? ****[SAII-2012]**

** Answer. **The man is doing work relative to the stream because he is applying force to produce relative motion between the boat and the stream. But he does zero work relative to the shore as the displacement relative to the shore is zero.

**Question.7 What type of energy is stored in the spring of a watch? [SAII-2013]**

** Answer. **When we wind a watch, the configuration of its spring is changed. The energy stored in the spring is obviously potential in nature (elastic potential energy to be more accurate).

**Question.8 What happens to the kinetic energy when :**

** (i) the mass of the body is doubled at constant velocity?**

** (ii)the velocity of the body is doubled at constant mass?**

** (iii)the mass of thesbody is doubled but the velocity is reduced to half?**

** Answer.**

**Question.9 When a constant force is applied to a body moving with constant acceleration, is the power of the force constant ? If not, how would force have to vary with speed for the power to be constant ?**

** Answer.**

**Question.10 A spring which is kept compressed by tying its ends together is allowed to be dissolved in an acid. What happens to the potential energy of the spring ?**

** Answer. **The potential energy of the spring gets converted into heat energy (kinetic energy of acid molecules). Due to this heat, the temperature of the acid rises.

**Reasoning Questions**

** Question.1**

** (a) Define power. Give its SI unit.**

** (b) Taking the example of a simple pendulum, explain the variations in the forms of energy and the; inter-conversions involved. [SA II-2011]**

** Answer.**

(a) Power is defined as the rate of doing work. Its SI unit is watt.

(b) For a simple pendulum, the inter-conversion of energy is as shown in the table below :

**Question.2**

** (a) How much work is done when a force of 1 N moves a body through a distance of 1 m in its direction?**

** (b) Is it possible that a force is acting on a body but still the work done is zero? Explain**

** giving one example. [SA II – 2011]**

** Answer.**

(a) 1 J of work is done.

(b) Yes, it is possible when force acts at right angles to the direction of motion of the body. Example Gravitational force of earth acts on a satellite at right angles to its direction of motion.

**Question.3**

** (a) What is meant by potential energy? Is potential energy vector or scalar quantity?**

** (b) Give one example of a body having potential energy. [SA II – 2011]**

** Answer.**

(a) The energy possessed by a body by virtue of its position or configuration. It is a scalar

quantity.

(b) Stretched string of a bow.

**Question.4 When is the work done by a force said to be negative? Give one situation in which one of the forces acting on the object is doing positive work and the other is doing negative work. ****[SA II – 2012]**

** Answer. **We know that work done W = FS cos 0, where 0 is the angle between F and S. Clearly, W will be -ve, if 0 is between 90° and 180° because then cos 0 will be -ve. Consider the case of a body falling under gravity. The body experiences an upward frictional force and downward force due to gravity. Since the body is moving downwards, the work done by force to gravity will be +ve but that is against the upward thrust will be -ve.

**Question.5**

** (a) Is it possible that a body be in accelerated motion under the action of a force, yet no work is being done by the force? Explain with an example.**

** (b) Two bodies of masses m, and m2 have equal kinetic energies. What is the ratio of their**

** linear momenta? [SA II – 2012]**

** Answer.**

(a) Yes, it is possible in the case of a body moving in a circular path with a speed v. The body has a centripetal acceleration directed along the radius of the circular path. The

displacement is, however, tangential to the radius i.e., 0 = 90°. Thus, work done, W = FS cos 90° = 0.

**Important Topics/Areas/Questions which are**

** frequently asked in the examination**

**Question.1 An object of mass mwhen raised To height h possess a potential energy of 1200 J. Find the new potential energy :**

** (a) if the same object is raised to height h/4.**

** (b) if the same object is raised to height 4h. [SAll-2014]**

** Answer.**

**Question.2 Define 1 watt of power. A lamp consumes 1000 ] of electrical energy in 10 s. Calculate its power. [SAII-2013]**

** Answer.**

**Question.3 Explain that the flying bird has; potential and kinetic energy and give their expressions.**

** [SA1I-2013]**

** Answer.**

**Question.4**

** (a)An arrow moves forward when released from a stretched bow. Explain the transformation of energy in the process.**

** (b)A boy of mass 50 kg climbs up a vertical height of 100 m. Calculate the amount of potential energy he gains. [SAII-2013]**

** Answer.**

**Question.5**

** (a)What is the commercial unit of energy ? Give its relationship with SI unit of energy.**

** (b)An electric bulb of 60 W is lighted for 10 hours everyday. How many units of electrical energy is consumed by this bulb in one day ? [SAII-2013]**

** Answer.**

**Question.6 Define : (a) power (b) work done (c) kinetic energy. Give SI unit of each. [SAII-2014]**

** Answer.**

(a) The rate of doing work is called power. Its SI unit is watt.

(b) Work is the product of force and displacement. Its SI unit is joule.

(c) It is the energy possessed by a body by virtue of its motion. Its SI unit is joule.

**Question.7 Define power. Write commercial unit and SI unit of electrical energy. An electrical geyser of 1.5 kW works for 2 hours. Find the electrical energy units consumed in a day. [SAII-2014]**

** Answer.**

**Question.8 The masses of scooter and bike are in the ratio of 2 : 3 but moving with same speed of 108 km h~1. Compute the ratio of their kinetic energy. [SAII-2014]**

** Answer.**

**NUMERICAL PROBLEMS**

**Question.1 The kinetic energy of an object of mass ‘m’ moving with a velocity of 5 ms-1 is 25 J. What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times?**

** Solution.**

**Question.2 Certain force acting on a 20 kg mass changes its velocity from 5 ms ^{-1} to 2 ms^{-1}. Calculate the work done by the force. [SAII-2013]**

**Solution.**

**Question.3. A certain household has consumed 250 units of energy during a month. How much energy is this in joule? [SAU-2011]**

** Solution.**

**Question.4 An electric heater is rated 1500 W. How much energy does it use in 10 hours?**

** Solution.**

**Question.5 Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 kmh-1? [SAII-2010]**

** Solution.**

**Question.6 Find the energy in kWh consumed in 10 hours by four devices of power 500 W each.**

** Solution.**

**Question.7 Two bodies of equal masses move with the uniform velocities v and 3v respectively. Find the , ratio of their kinetic energies. [SAII-2013]**

** Solution.**

Thus, the kinetic energy of the second body is nine times the kinetic energy of the first body.

**Question.8 A man of mass 60 kg runs up a flight of 30 steps in 40 seconds. If each step is 20 cm high, calculate the power of the man. [SAU-2012]**

** Solution.**

**Question.9 Calculate the amount of work done in moving a 50 kg block through a distance of 10 m by applying a force of 100 N.**

** Solution.**

**Question.10 A block of mass 5 kg is lying bn a frictionless table. A force of 20 N is applied on it for 10 seconds. Calculate its kinetic energy.**

** Solution.**

**Question.11 A girl of mass 40 kg climbs a rope 6 m long at constant speed in 15 seconds. What power she expands during the climb?**

** Solution.**

**Question.12 A man weighing 70 kg carries a weight of 10 kg to the top 6f a tower 100 m high. Calculate the work done.**

** Solution.**We know that work done is given by W = FS = mgh i.e., change in potential energy, therefore, we have W = mgh = (70 + 10) x 9.8 x100 = 78400 J

**Question.13 Calculate the kinetic energy of a body of mass 2 kg moving with a velocity of 0.1 ms-1.**

** Solution.**

**Question.14 Find the velocity of a body of mass 100 g having a kinetic energy of 20 J.**

** Solution.**

**Question.15 A man drops a 10 kg rock from the top of a 5 m ladder. What is its kinetic energy when reaches the ground? What is its speed just before it hits the ground?**

** Solution.**

**Question.16 Which would have greater effect on kinetic energy of an object – doubling the mass, or doubling the velocity?**

** Solution. **We .know that KE∝ m, KE ∝ v2

Therefore, by doubling the mass, the kinetic energy doubles, while by doubling the velocity, the kinetic energy increases four times. Therefore, doubling the velocity will have a greater effect on the kinetic energy of an object.

**Question.17 A body of mass 4 kg initially at rest is subjected to a force of I6 N. What is the kinetic energy acquired by the body at the end of 10 s? [SAII-2010]**

** Solution.**

**Question.18 A crane pulls up a car weighing 500 kg to a vertical height of 4 m. Calculate the work done by the crane.**

** Solution.**

In order to lift the car, the crane has to do work against the force of gravity.

Therefore, the force required = Mg = 500 x 9.8 = 4900 N

Now, displacement undergone by the car, S = 4 m

Hence, work done = FS = 4900 x 4 = 19600 J

**Question.19 A force of 10 N displaces a body by a distance of 2 m at an angle 60° to its own direction. Find the amount of work done. [SAII-2012]**

** Solution.**

By definition, Work = Force x Displacement in the direction of force = FD cos θ

Given, F = 10 N;S = 2m;θ = 60°. Therefore,

W = 10 x 2 x cos 60° = 10 x 2 x 1/2 =10J

**Question.20 A boy of mass 40 kg runs up flight of 50 steps each 10 cm high in 5 seconds. Find: (i) the work done by the boy. (ii) the power developed, (g = 9.8 ms ^{-2})**

**Solution.**

**Question.21 Calculate the power of an engine required to lift 10s kg of coal per hour from a mine 360 m deep, (Take g = 10ms ^{-2}).**

**Solution.**

**Question.22 A man whose mass is 50 kg climbs up 30 steps of a stair in 30 s. If each step is 20 cm high, calculate the power used in climbing the stairs. [Take g = 10 ms ^{-2}]**

**Solution.**

**Question.23 A mass of 10 kg is dropped from a height of 50 cm. Find its : (i) Kinetic energy (ii) Velocity just as it reaches the ground. Does the velocity depend upon the mass of the particle? Explain. [Take g = 10 ms ^{-2}] [SAll-2012]**

**Solution.**

**Question.24 If you apply 1 J of energy to lift a book of 0.5 kg, how high will it rise? [Take g = 10 ms ^{-2}]**

**Solution.**

We know that PE = mgh

1 = 0.5 x 10 x h

Therefore, h = 0.2 m = 20 cm

**Question.25 A woman pulls a bucket of water of total mass 5 kg from a well which is 10 m in 10 s. Calculate the power used by her. [Take g = 10 ms ^{-2}]**

**Solution.**

**Question.26 **

**(a) Define average power.**

** (b) A lamp consumes 1000 J of electrical energy in 10 s. What is its power?**

** (c) Give the commercial unit of energy in Joules. [SAll-2013]**

** Solution.**