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S.K. GUPTAANUBHUTI GANGAL

S. CHAND & COMPANY PVT. LTD.(AN ISO 9001: 2008 COMPANY)

RAM NAGAR, NEW DELHI-110 055

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CLASS – VII

S.Chand’s IIT Foundation Series

(Physics and Chemistry)

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Reprint with Corrections 2013

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Here is the book especially designed to motivate you, to sharpen your intellect and develop the rightattitude and aptitude and lay solid foundation for your success in various entrance examinations likeIIT, AIEEE, EAMCET, WBJEE, MPPET, SCRA, Kerala PET, OJEE, Raj PET, AMU, etc.

SALIENT FEATURES1. Content based on the curriculum of the classes for CBSE, ICSE, Andhra Pradesh and Boards of School

Education of other states.2. Full and comprehensive coverage of all the topics.3. Detailed synopsis of each chapter at the beginning in the form of ‘Key Concepts’. This will not only facilitate

thorough ‘Revision’ and ‘Recall’ of every topic but also greatly help the students in understanding and masteringthe concepts besides providing a back-up to classroom teaching.

4. The books are enriched with an exhaustive range of hundreds of thought provoking objective questions in theform of solved examples and practice questions in Question Banks which not only offer a great variety andreflect the modern trends but also invite, explore, develop and put to test the thinking, analysing and problemsolving skills of the students.

5. Answers, Hints and Solutions have been provided to boost up the morale and increase the confidence level.6. Self Assessment Sheets have been given at the end of each chapter to help the students to assess and

evaluate their understanding of the concepts and learn to attack the problems independently.7. Concept maps and crossword puzzles have been given to help the students gain mastery over the

fundamentals of each topic.We hope the series will be able to fulfil its aims and objectives and will be found immensely useful bythe students aspiring to become top class engineers.Suggestions for improvement and also the feedback from various sources would be most welcome andgratefully acknowledged.

AUTHORS

ARE YOU ASPIRING TO BECOME AN ENGINEERAND BECOME AN IIT SCHOLAR ?

(v)

Disclaimer : While the authors of this book have made every effort to avoid any mistake or omission and have used theirskill, expertise and knowledge to the best of their capacity to provide accurate and updated information. The author andS. Chand does not give any representation or warranty with respect to the accuracy or completeness of the contents of thispublication and are selling this publication on the condition and understanding that they shall not be made liable in anymanner whatsoever. S.Chand and the author expressly disclaim all and any liability/responsibility to any person, whether apurchaser or reader of this publication or not, in respect of anything and everything forming part of the contents of thispublication. S. Chand shall not be responsible for any errors, omissions or damages arising out of the use of the informationcontained in this publication.Further, the appearance of the personal name, location, place and incidence, if any; in the illustrations used herein is purelycoincidental and work of imagination. Thus the same should in no manner be termed as defamatory to any individual.

CCCCCOOOOONNNNNTTTTTENENENENENTTTTTSSSSS

Topics in Physics

Chapter 1. Motion and Time 1 – 3 to 1 – 26

Chapter 2. Density 2 – 1 to 2 – 6

Chapter 3. Heat 3 – 1 to 3 – 14

Chapter 4. Light 4 – 1 to 4 – 19

Chapter 5. Introduction to Electricity 5 – 1 to 5 – 8

Chapter 6. Current Electricity (Electric Current and its Effects) 6 – 1 to 6 – 17

Chapter 7. Sound 7 – 1 to 7 – 19

Topics in Chemistry

Chapter 8. Elements, Compounds and Mixtures 8 – 3 to 8 – 11

Chapter 9. Structure of Atom, Physical and Chemical Changes 9 – 1 to 9 – 12

Chapter 10. Acids, Bases and Salts 10 – 1 to 10 – 10

(vi)

TOPICS IN PHYSICS

Motion and TimeMotion and TimeMotion and TimeMotion and TimeMotion and Time DensityDensityDensityDensityDensity HeatHeatHeatHeatHeat LightLightLightLightLight Introduction to ElectricityIntroduction to ElectricityIntroduction to ElectricityIntroduction to ElectricityIntroduction to Electricity Current Electricity (Electric Current andCurrent Electricity (Electric Current andCurrent Electricity (Electric Current andCurrent Electricity (Electric Current andCurrent Electricity (Electric Current and

its Effects)its Effects)its Effects)its Effects)its Effects) SoundSoundSoundSoundSound

IIT Foundation Science Class – VII1–2Ch

q

Motion and Time 1–3Ch

I. Motion1. What is motion? When an object changes position over time relative to a reference point, the

object is in motion. A reference point is an object that appears to stay in place as a non-movingobject such as a tree or a building. The object is said to be at rest if it does not change its position relativeto reference point.

2. Types of motion. You have learnt in class 6 that there are four important types of motion.(a) Translatory motion. If every point of a moving object moves through the same distance in the same time,

then the motion is called a translatory motion.Translatory motion is of two types:

(i) Rectilinear motion. If an object moves in a straight line, it is called rectilinear motion.(ii) Curvilinear motion. It is motion of an object along a curve or circular path. Motion along a circular

path may be called circular motion.Ex. A car moving along a curved path; a javeline thrown by an athlete. Motion of a child in a merry-go-round and motion of pedals of a moving bicycle are circular motions.

(b) Rotational motion. When an object turns (or spins) about a fixed axis, it is called rotational motion.Ex. Turning of the blades of a fan, motion of earth about its axis, spinning of a top on its axis, spinningwheel or charkha, potter’s wheel.

(c) Oscillatory motion. The back and forth motion of a body as a whole about its mean position is calledoscillatory motion.Ex. Motion of the pendulum of a wall clock; motion of a swing; motion of the piston of an engine.

(d) Vibratory motion. In this kind of motion all the parts of the body do not move. Only a part of the bodymoves back and forth about its mean position.Ex. The plucked string of a guitar, vibrating membrane of a drum.

(e) Periodic motion. The motion which repeats itself after regular intervals of time is called periodic motion.If the body does not repeat its motion, then it is called non-periodic motion.

Ex. Revolution of the earth. It gets repeated after every 13654 days, the heartbeat of a normal

person, the needle of a sewing machine, the swinging pendulum of a wall clock are all periodicmotions. The motion of a falling leaf and that of a car on a rough road are non-periodic motions.

(f) Random motion. If a body keeps changing its motion from one type to another, then it is said to beundergoing random motion.Ex. A flying mosquito, a flying bird.

Chapter

1 MOTION AND TIME

Ch1-3

IIT Foundation Science Class – VII1–4Ch

(g) Multiple motion. A body is said to be having multiple motion if it possesses more than one motion at thesame time.Ex. (i) A drilling machine has rotatory as well as rectilinear motion.(ii) The earth has two types of motion-rotation and revolution.(iii) Wheels of a vehicle rotate and carry the vehicle forward. Then, they have both rotatory and translatory

motion.II. Scalar and vector quantities. Those physical quantities which are completely described by

magnitude (size) alone are known as scalar quantities, e.g., length or distance, mass, time, area andvolume etc.Those physical quantities which are completely described only if their magnitudes as well asdirections are known, are called vector quantities, e.g., displacement, velocity, acceleration, force and weight etc.A vector quantity is completely represented by a straight line with an arrow-head, where length of the linerepresents the magnitude of the vector quantity and direction of arrow indicates the direction of the vectorquantity.

A B

III. Distance. The distance travelled by a body is the actual length of the path covered by a moving bodyirrespective of the direction in which the body travels. It is a scalar quantity having magnitude only.

A

B D

C E

F

Distance travelled = AB + BC + CD + DE + EFIV. Displacement. When a body moves from one position to another, the shortest distance between the initial

position and final position of the body along with direction is known as its displacement.

A

B D

C E

F

Displacement = AF

Whenever a body travels along a zig-zag path, the final displacement is obtained by joining the starting pointand the finishing point of the body by a straight line.

V. Speed is defined as the distance travelled by an object in unit time. Thus, the formula for calculating speed is

Speed =

Distance travelled =Time taken

dt

The SI unit for speed is metre per second (m/s). We also use other units such as kilometre per hour(km/h) and kilometre per minute.

VI. Average speed. Most of the times, object do not travel at a constant speed, so it is useful to calculateaverage speed using the following formula:

Average speed = Total distance

Total timeVII. The speed of a body is uniform, if it covers equal distances in equal intervals of time. Motion of a body is

said to be non-uniform motion when an object keeps changing its speed while moving along a straight line.VIII. Velocity

1. Velocity is the speed of an object in a particular direction. It is vector quantity. The terms speed and velocitydo not have the same meaning. Velocity must have direction.

Motion and Time 1–5Ch

2. An object’s velocity is constant only if its speed and direction don't change. Therefore, constant velocity isalways motion along a straight line.

3. An object’s velocity changes if either its speed or direction or both change.4. Velocity is found by using the relation :

Velocity = Change in displacement

Time TakenVelocity will be zero if the displacement (distance between the final and initial positions of a body) is zero.

5. Uniform velocity. If a body travels with a uniform speed in a constant direction, then it is said to haveuniform or constant velocity.Ex. An aeroplane moving at a constant speed of 300 km/h in the north-east direction has aconstant velocity of 300 km/h N–E.

6. When speed or direction or both change, the body is said to have a variable or non-uniform velocity.15m/s

15m/s

15m/s

Direction is changing(variable velocity)

IX. Acceleration1. Acceleration is the rate at which velocity changes. Velocity changes if speed changes, if direction changes,

or if both change. So, an object accelerates if its speed, its direction or both change.2. An increase in velocity is commonly called positive acceleration. A decrease in velocity is commonly called

negative acceleration, or retardation or deceleration. Keep in mind that acceleration is not only how muchvelocity changes but also how fast velocity changes. The faster the velocity changes, the greater theacceleration isWe can write

Acceleration = Change in velocity

Time Taken

= Final velocity – Initial velocity

Time takenA body with constant velocity has zero acceleration (Because in this case, change in velocity = 0).

3. Uniform acceleration. The table shows that the speed at every second keeps increasing by 1 m/s withno change in direction.

Time Speed Direction(in sec) (in m/s)

1 sec 1 m/s South2 sec 2 m/s South3 sec 3 m/s South4 sec 4 m/s South

When the velocity of a body changes uniformly, then we say that the body has uniform acceleration.

In this case, acceleration = Change in velocity

Time taken

4 m/s – 1 m/s=

4 sec = 2 23 m/s 0.75 m/s4

South.

IIT Foundation Science Class – VII1–6Ch

We use different units for acceleration as per the situation or our convenience, such as km/h2.km/min2 and cm/sec2 but in SI unit it is m/s2.Suppose the velocity of a body moving towards, North, decreases from 150 km/h to 30 km/h at the rate of15 km/h, then there is retardation which is given by

Acceleration = Final velocity – Initial velocityTime taken

= 30 km/h 150 km/h 1208h 8 km/h2 North

= –15 km/h2 North or Retardation = 15 km/h2 North

4. Acceleration can be shown on a graph of velocity versus time. The graph shows thatduring the first 8 seconds, there is uniform increase in the velocity while during the last 2 seconds the movingbody gradually slows down. Thus, there is positive acceleration during the first 8 seconds and negativeaccleration, i.e., retardation, during the last 2 seconds.

Vel

ocity

(m

/s)

Time(s)

5

10

15

20

25

1 2 3 4 5 6 7 8 9 100

Velocity-time graphX. Time-distance graph. 1. Suppose the distances covered by a bus at intervals of 5 minutes are as shown

in the following table.

Time Start(in minutes) 0 5 10 15 20 25 30

Distance covered(in kilometre) 0 6 12 18 24 30 36

This information can be displayed on a graph as shown below.

6

12

18

24

30

36

Dis

tanc

e in

kilo

met

res

5 10 15 20 25 30

Time in minutes

Time-Distance GraphFOR UNIFORM SPEED

Time-Distance Graph

Motion and Time 1–7Ch

2. The slope of the distance-time graph (the measure of steepness) gives the speed of the object.3. The distance-time graph having higher slope (i.e., which is more steep) indicates higher speed than the

distance-time graph having lower slope (i.e., which is less steep). Thus, the graph OB represents a higherspeed than the speed represented by OA.

Y

XTime

Dis

tanc

e

B

A

O

4. The distance-time graph for an object moving with non-uniform speed (i.e., changing speed) is a curved line.

Y

0 X

TimeDistance-time graph for

non-uniform motion

Dis

tanc

e

5. The distance-time graph for an object having zero speed, i.e., which is not moving is a straight line parallelto the time-axis (or X-axis).

Y

0 X

Distance-time graph for astationary object

Dis

tanc

e

Time

XI. Velocity-time graph. The relation between velocity and time of the motion of an object is given by theequation 2 5 .= + tv The picture shows the graph of the motion of this object.

t 1s 2s 3s 4sv 7 m/s 12 m/s 17 m/s 22 m/s

IIT Foundation Science Class – VII1–8Ch

Acceleration (a) is given by

a = 2 1

2 1t t

v v

So, for t1 = 0, 1v = 2 m/s; for t2 = 1s, 2v = 7 m/s

So, acceleration from A to B = 2 1

2 1t t

v v =

7 21 0 = 5 m/s2.

Similarly, from A to C,

v 2 = 12 m/s, t2 = 2 s

v1 = 2 m/s, t1 = 0 s

a = 12 22 0 = 5 m/s2.

Observe that (1) velocity-time graph for the relation v = 2 + 5t (type v = u + at), is a straight line witha constant equal to slope. (2) acceleration of the object is a constant equal to 5 m/s2. This type of motionis called uniformly accelerated motion.

XII. Interpretation of graphs(a) The velocity of the object is equal to the slope of displacement-time graph.(b) The acceleration of the object is equal to the slope of the velocity-time graph.(c) The displacement of the object during a time interval is equal to the area under velocity-time graph.

XIII.Equations of motion. Suppose a body starts with velocity u m/s. This velocity increases at the rate of am/s per second till the body finally attains the velocity v m/s after time t. Then,

Initial velocity Final velocity

u m/s v m/s

Time tThe velocity keeps on increasing by a m/s during this period.

Acceleration = Final velocity – Initial velocity

Time

or a = – ut

v = u + at …(1)

This is the equation of motion containing four quantities u, a, t, v. Any three of these being known, the fourthcan be found out.For uniformly acelerated motion, Average velocity = Average of initial and final velocities

= 2u v

Displacement (s) = Average velocity × Time

or s = + ×2

tvu …(2)

5

0 1 2

Time (t) in secondsvelocity-time graph

10

15

20

25

3 4

Vel

ocity

()

inm

/sv

A

B

C

E

D

Motion and Time 1–9Ch

Substituting v = u + at in equation (2), we get

s = 1 1 1( ) 22 2 2

u u at t ut at t

s = ut + 212

at …(3)

Also, from (1), t = uav . Substituting in eq. (2),

2s = (u + v ) . u

av

2 2 2u as v

or v2 = u2 + 2as …(4)XIV. Centripetal acceleration. An object in circular motion is always changing its direction. Therefore, its

velocity is always changing so it is accelerating. The acceleration that occurs in circular motion is known ascentripetal acceleration. Centripetal acceleration occurs on a Ferris wheel of an amusement park or as themoon orbits earth.

XV. Acceleration due to gravity. If an object is dropped from a height, its velocitykeeps on increasing due to the gravitational pull of the earth. Thus the body has anaccelerated motion. The acceleration with which the bodies fall freely towards the earthis called acceleration due to gravity and is denoted by the letter 'g'. Its average valueis 9.8 m/s2 which is sometimes taken as 10 m/s2 for approximate calculations. The valueof g changes from place to place and with altitude. On the moon the value of ‘g’ is aboutone-sixth of that on the earth.

XVI. When motion takes place under gravity, the equations of motion given under point XIII above become v = u – gt v = u + gt

h = ut – 12

gt2 h = ut + 12

gt2

v2 = u2 – 2gh v2 = u2 + 2gh(when body is (when body is cominggoing upward) downward)

u = initial velocity, v = final velocity, g = acceleration due to gravity, t = duration of motion, h = height attained.XVII. All objects accelerate toward Earth at a rate of 9.8 m/s2. So, every second that an object falls, the object’s

downward velocity increases by 9.8 m/s.Thus, we have(i) For motion during the 1st second,

20 m/s 9.8 m/s 1s v (using v = u + gt) = 9.8 m/s

AB = 0 + 12 × 9.8 × 12 (using s = ut +

12 gt2)

= 4.9 m.(ii) For motion for 2 seconds,

2v = 0 + 9.8 × 2 = 19.6 m/s

AC = 210 9.8 22

= 19.6 m

Distance fallen during 2nd sec = BC = AC – AB = 19.6 m – 4.9 m = 14.7 m

Earth

A

Dv = 29.4 m/s downward3

v = 19.6 m/s downward2

u = 0 m/s downward

v = 9.8 m/s downward1AB = 4.9 m B

2nd S14.7 m

3rd S24.5 m

1st S

C

Body movingupward

–g

Body movingdownward

+ g

IIT Foundation Science Class – VII1–10Ch

Alternatively, 2v = 1v + gt = 9.8 + 9.8 × 1 = 19.6 m/s

BC = 21

12

t gtv = 219.8 1 9.8 12

= 14.7 m

Similarly, you can calculate the velocity at the end of 3rd second and the distance CD that is covered inthe 3rd second.

A falling object accelerates at a constant rate. The object falls faster and farther each second than itdid the second before.

XVIII. Simple pendulum. A simple pendulum consists of a mass called a bob,which is attached to a fixed string. If the bob is pulled a little to the right sideto position B and then released, it will move on to position C, at an equaldistance on the other side of the mean position A, and then go on repeating thisback and forth movement between the two extreme positions B and C. We saythat the simple pendulum is oscillating or vibrating. The path of the bob is anarc of a circle.The movement of the bob from one extreme position B to another extremeposition C and then back to B is considered one complete cycle of motion andis taken as one oscillation (or one vibration).Galileo discovered that every swing or oscillation is completed in exactly the same time, provided its lengthis kept constant.

XIX. Time period. The time taken by the pendulum bob to make one complete oscillation (or vibration) is calledtime-period of the pendulum. It is also called 'periodic time' or just ‘period’ of the pendulum. It depends on(i) length of the pendulum

(ii) accleration due to gravity and is given by the formula

T = 2 Lg

where T = Time-period of simple pendulum,

L = Length of the pendulum, g = Acceleration due to gravity, = 227 or 3.14 (approx).

Bob

String

Meanor

Central Position

C

A

B

Solved Examples

Ex. 1. Sameer takes 20 minutes from his house to reach his office on a bicycle. If the bicycle has a speedof 2 m/s, calculate the distance between his house and the office.

Sol. Speed = 2 m/s, time = 20 minutes = 20 × 60 seconds = 1200 s

Distance = speed × time = 2 m/s × 1200 s = 2400 m = 2 km 400 m.

Ex. 2. A car moves with a speed of 40 km/h for 15 minutes and then with a speed of 60 km/h for the next15 minutes. The total distance covered by the car is :(a) 100 km (b) 25 km (c) 15 km (d) 10 kmChoose the correct option.

Sol. Ans. (b)

Case (1): Time = 15 minutes = 15 1h h,60 4

speed = 40 km/h

Distance covered at the above speed = speed × time = 40 km/h × 1 h4 = 10 km

Case (2) : Time = 15 minutes = 1 h4

, speed = 60 kmh

A Compact And Comprenensive BookOf IIT Foudation Science (Physics And

Chemistry) Class VII

Publisher : SChand Publications ISBN : 9788121939034Author : S K Gupta AndAnubhuti Gangal

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