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CLASS IX & X

PHYSICS

FORMULA SHEETS

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CLASS – IX

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CHAPTER – 1: MOTION

Speed and Velocity

distance travelledSpeed

time taken

sv

t

displacement Velocity

time

sv

t

Acceleration

change in velocity

Accelerationtime taken

v ua

t

Unit of acceleration = ms2, cm/s2, km/h2

Equations of Uniformly Accelerated Motion

(a) 1st Equation of Motion:

v = u + at …..(i)

(b) 2nd Equation of Motion:

21

2s ut at … (ii)

(c) 3rd Equation of Motion:

2as = v2 – u2 or v2 = u2 + 2as ….(iv)

Motion Under Gravity (Uniform Accelerated Motion)

(i) If a body moves upwards (or thrown up) ‘g’ is taken negative (i.e. motion is against gravitation

of earth). So we can form the equation of motion like,

v = u – gt, s = ut 1

2 gt2, v2 – u2 = – 2gh.

(ii) If a body travels downwards (towards earth) then ‘g’ is taken positive. So equations of motion

becomes

v = u + gt, s = ut + 1

2gt2, v2 – u2 = 2gh.

(iii) If a body is projected vertically upwards with certain velocity then it returns to the same point

of projection with the same velocity in the opposite direction.

(iv) The time for upward motion is the same as for the downward motion.

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Angular Displacement and Angular Velocity

;Angular displacement

Angular velocityTime taken t

t

Relation between Linear Velocity and Angular Velocity

v r

Linear Velocity = radius × Angular velocity

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CHAPTER – 2: FORCE

Force

A force is an external agency that displaces or tends to displace a body from its position of rest. The

direction in which the object is pushed or pulled is called the direction of the force. Force has both

magnitude and direction. It is a vector quantity.

“Force is the cause which can produce acceleration in the body on which it acts”.

Effects of Force:

The force or a set of forces acting on a body can do three things:

(i) A force or a set of forces can change the speed of the body.

(ii) A force or a set of forces can change the direction of motion.

(iii) A force can change the shape of the body.

Units of Force

(a) In C.G.S. System:

∴ F = ma → gm × cm/s2 = Dyne

(b) In S.I. System:

F = ma → kg × m/s2 = Newton

Linear Momentum: p mv

Newton’s first law : Inertial frame.

Newton’s second law: ,dp

Fdt

F ma

Newton’s third law: AB BAF F

Frictional force: fstatic, max = μsN, fkinetic = μkN

Banking angle: 2 2 tan

tan ,1 tan

v v

rg rg

Centripetal force: 2

,c

mvF

r

2

c

va

r

Pseudo force: 0 ,pseudoF ma 2

centrifugal

mvF

r

Minimum speed to complete vertical circle

min, bottom 5 ,v gl min, topv gl

Conical Pendulum: cos

2l

Tg

mg

T

l

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Conservation of Linear Momentum Formula

The principle of conservation of momentum states that if two objects collide, then the total momentum

before and after the collision will be the same if there is no external force acting on the colliding

objects.

Initial momentum = Final momentum

i fP P

Angular Momentum Formula

Angular momentum can be experienced by an object in two situations. They are:

Point object:

The object accelerating around a fixed point. For example, Earth revolving around the sun. Here the

angular momentum is given by:

L r p

Where,

L is the angular velocity

R is the radius (distance between the object and the fixed point about which it revolves)

p is the linear momentum.

Extended object

The object, which is rotating about a fixed point. For example, Earth rotates about its axis. Here the

angular momentum is given by:

L I

Where,

L is the angular momentum.

I is the rotational inertia.

is the angular velocity.

Impulses of Force

Impulse = Force × Time

or I = F. t

The S.I. unit of impulse is Newton-second (N-s) and the C.G.S unit is dyne - second (dyne -s).

Impulse and Momentum:

From Newton’s second law of motion

Force, 2 1p pF

t

or 2 1.F t p p

i.e., Impulse = Change in momentum

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CHAPTER – 3: GRAVITATION

1. Newton’s Universal Law of Gravitation

F = 2

1 2 G m m

d

2. Unit of Gravitational Constant:

G = 2

1 2

Fd

m m

SI unit of G = 2

Nm

kg kg=

2

2

Nm

kg= Nm2 kg–2

CGS unit of G is dyne cm2 g-2

The value of G = 6.67 × 10-11 N m2 kg-2 or 6.67 × 10-8 dyne cm2 g-2

= The value of G was found by Henry Cavendish.

3. Gravitational acceleration: 2

GMg

R

4. Variation of g with depth: inside

1 hg g

R

5. Variation of g with height: outside

1 2hg g

R

6. Effect of non-spherical earth shape on g

g at pole > g at the equator (since Re – Rp ≈ 21 km)

7. Orbital velocity of the satellite: 0

GMV

R

8. Relation between Escape Velocity and Orbital Velocity

02eV V

9. Kepler’s Law

First Law: Eliptical orbit with the sun at one of the focus.

Second Law: Areal velocity is constant 0dA

dt

Third Law: 2 3T R

10. LAW OF FLOATATION

Weight of the floating solid = weight of the liquid displaced.

i.e. 1 21 1 2 2

2 1

VV g V g

V

or Density of solid Volumeof theimmersed portionof the solid

Density of liquid Total volumeof the solid

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CHAPTER – 4: WORK POWER & ENERGY

WORK, POWER AND ENERGY

Work:

. cos ,W F S FS .W F dS

Kinetic energy: 2

21

2 2

pK mv

m

Potential energy:

/F U x for conservative forces.

gravitational ,U mgh 2

spring

1

2U kx

Work done by conservative forces is path independent and depends only on initial and final points:

conservative. 0.F dr

Work-energy theorem: W K

Mechanical energy: E = U + K. Conserved if forces are conservative in nature.

Power: ,av

WP

t

instP F v

Some manmade devices which convert one form of energy into another are given as follows.

DEVICE INPUT ENERGY OUTPUT ENERGY

1. Fan Electrical energy Kinetic energy

2. Electric lamp Electrical energy Light energy

3. Electrical heaters Electrical energy Heat energy

4. Radio Electrical energy Sound energy

5. Water pump Electrical energy to kinetic energy of impeller

to potential energy of water

6. Cell Chemical energy Electrical energy

7. Microphone Sound energy Electrical energy

8. Rechargeable cell (a) During discharging

Chemical energy

(b) During charging

Electrical energy

(a) Electrical energy

(b) Chemical energy

9. Loudspeaker Electrical energy Sound energy

10. Elevator moving up Electrical energy Potential energy

11. Television Electrical energy Sound energy, light energy

12. Thermal power plant Chemical energy of coal Electrical energy

13. Car Chemical energy of

petrol/diesel

Mechanical energy

14. Nuclear power plant Nuclear energy Electrical energy

15. Solar cell Solar energy Electrical energy

16. Watch Potential energy of

wounded spring

K.E. of hands or watch

17. Generator Kinetic energy Electrical energy

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CHAPTER – 5: SOUND

SOUND

Sound is mechanical energy, which produces sensation of heating.

Sound is produced due to vibration of different objects.

A material medium is essential for the propagation of sound as it cannot travel in vacuum.

A region of compressed air (increased density of pressure) is called a compression and that of

rarefied air (decreased density or pressure) is called a rarefaction.

LONGITUDINAL AND TRANSVERSE WAVES

A wave motion is a form of disturbance (a mode of momentum and energy transfer) which is

due to repeated vibrations of the particles about their mean positions and the motion is

transferred from one particle to the other without any net movement of the medium. A wave

motion is of two types:

(i) Longitudinal (ii) Transverse

Sound waves are longitudinal waves. Light waves, on the other hand, are transverse waves.

Sound wave propagates as compressions and rarefactions. (i.e., as variation in density of

pressure) in the medium.

As sound propagates, it is the sound energy that travels in the medium and not the medium

itself.

The change in density (or pressure) from the maximum value to the minimum value and again

to the maximum value is called an oscillation.

The number of complete oscillations per second is called the frequency (v) of the sound wave.

The unit of frequency is called hertz (Hz).

The time taken for one complete oscillation in density (or pressure) of the medium is called the

time period (T) of the wave.

The distance between two consecutive compressions (or crests) or two consecutive rarefactions

(or troughs) is called the wavelength. The unit of wavelength is meter (m).

The distance travelled by a sound wave in its periodic time is also called wavelength (λ) of the

wave.

The relation between frequency (v) and time period (T) is 1 1

,v TT V

or v T = 1.

The speed of sound depends mainly on its nature and the temperature of the medium through

which its propagates.

The relation between speed of the sound wave (v), its frequency (v) and wavelength (λ) is v = vλ.

The sound wave is described by: (i) Its speed, (ii) Its frequency (or wavelength) and

(iii) Its amplitude.

In general, speed of sound in solids > speed of sound in liquids > speed of sound in gases.

However, this relation is not always valid.

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Sources that move faster than the speed of sound are said to have supersonic speeds. Bullets,

jet aircrafts etc. travel at supersonic speeds.

A shock wave is produced when sound producing source moves with a speed higher than the

speed of sound.

It is not necessary for an object to be a vibrating source of sound to produce a shock wave.

A shock wave carries a large amount of energy.

Sonic boom is a very sharp and loud sound produced by pressure variation associated with a

shock wave.

ECHO

Like light waves, sound waves are also reflected from a surface on which they fall. The laws of

reflection of sound are the same as those of light.

The echo is the phenomenon of repetition of sound of a source by reflection from an obstacle.

The time interval between the incident sound and the reflected sound for hearing a distinct

echo is 0.1 s and this property is called persistence of hearing.

For hearing a distinct echo the minimum distance of the obstacle from the source of sound

should be 17.2 m. This distance changes with change of temperature.

MULTIPLE ECHO

Multiple echoes are heard when sound is repeatedly reflected from a number of obstacles at

suitable distances.

REVERBERATION

Reverberation is the phenomenon of persistence or prolongation of audible sound after the

source has stopped emitting sound.

Reverberation is reduced by (i) carpeting the floor (ii) upholstering furniture and (iii) creating

false ceilings with a suitable sound absorbing material.

The ceilings of concert halls are curved to enable the sound in reaching all corners of the hall.

A sound board is used to evenly spread the sound throughout the width of the hall.

The audible range of hearing for average human beings is in the frequency range of 20 Hz to

20kHz. Children under the age of five can hear upto 25 kHz whereas aged people become less

sensitive to higher frequencies.

INFRASOUND AND ULTRASOUND

Infrasound (or infrasonic) has a frequency below 20 Hz.

Ultrasound (or ultrasonic) has a frequency above 20 kHz.

APPLICATIONS OF ULTRASOUND

(i) Industry (ii) Medical Science

(iii) Communication (iv) SONAR

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In industry, ultrasound is used in:

(i) Cleaning instruments and electronic equipments

(ii) Plastic welding

(iii) Detecting flaws and cracks in metal blocks used in constructing big structures.

In medical science, ultrasound is used in:

(i) Echo-cardiography (ii) Ultrasonography

(iii) Surgery (iv) The rapeutics.

SONAR is Sound Navigation and Ranging and is used to measure distance, direction and

speed of objects lying under sea. It is also used in ship-to-ship communication.

HUMAN EAR

The human ear can be divided into three parts:

(i) The outer ear which collects sound waves

(ii) The middle ear which amplifies the sound waves about 60 times and

(iii) The inner ear which converts the amplified sound energy into electrical energy and

conveys to the brain as nerve impulses for interpretation.

DISTANCE BETWEEN THE SOURCE OF SOUND AND OBSTACLE:

Let the distance between observer and the obstacle = d

Speed of sound (in the medium) = v

Time after which echo is heard = t

Then, t = 2 v

v 2

d tor d

The minimum distance (in air at 25oC) between the observer and the obstacle for the echo to be heard

clearly should be 17.2m.

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CLASS - X

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CHAPTER – 1: ELECTRICITY

ELECTRICITY AND ITS EFFECT (NOTATIONS)

Physical Quantity Symbols SI Unit

Voltage (potential difference) V Volt (V)

Power P Watt (W)

Charge Q Coulomb (C)

Work or Energy W Joule (J)

Resistance R Ohm (Ω)

Current I Ampere (A)

Resistivity ρ Ohm metre (Ω m)

CURRENT

The rate of flow of charges (Q) through a conductor is called current (I) and is given by.

ChargeCurrent = or I= .

Time

Q

t The SI unit of current is ampere (A).

1 coulomb1 Ampere =

1 second

ELECTROMOTIVE FORCE

The potential difference at the terminals off cells in an open circuit is called electromotive force (emf)

and is denoted by letter E.

Potential difference is the work done in bringing a unit charge from one place to another.

WorkPotential Difference = ,

Charge

1 Joule1 Volt

1 Coulomb

JV

C

OHMS LAW

AT any constant temperature the current (I) flowing through a conductor is directly proportional to the

potential difference (V) across it. Mathematically.

I ∝ V vice-versa V ∝ I

or V = RI ,V V

R II R

Where R – Resistance, V – Voltage (P. D.), I – Current

SYMBOLS OF A FEW COMMMONLY USED COMPONENTS IN CIRCUIT DIAGRAM

Component Symbol Component Symbol

An electric cell Electric Bulb

Battery of Cells

A resistance

Plug key or switch (open) or

Variable

Resistance

(Rheostat) or

l

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A closed plug or switch or

Ammeter A+ –

A wire joint

Voltmeter V+ –

RESISTANCE

Resistance is a property of a conductor by virtue of which it opposes the flow of electricity through it.

Resistance is measured in Ohms (Ω). Resistance is a scalar quantity.

CONDUCTOR

Low-resistance material which allows the flow of electric current through it is called a conductor. All

metals are conductors except Hg and Pb etc.

RESISTOR

High-resistance materials are called resistors. Resistors become hot when current flows through them

(nichrome wire is a typical resistor).

INSULATOR

A material which does not allow heat and electricity to pass through it is called an insulator. Rubber,

dry wood etc., are insulators.

IMPORTANT FORMULAE:

1. Coulomb’s Law

1 2

2

k q qF

r

(k is constant of proportionally)

q1 and q2 = two electric changes

r = distance between two electric charges

F = Force

2. ; ;W W

V W V Q QQ V

V = p.d., W = Work done, Q = Quantity of charge transferred

3. ; ;V V

V R I R II R

V = p.d., R = Resistance, I = Current

4. ;l R A

RA l

R = Resistance; l = length, A = Area of cross section; ρ = rho, a constant known as resistivity.

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5. Series combination R = R1 + R2 + R3 …. + Rn

6. Parallel combination 1 2 3

1 1 1 1....

nR R R R R

For equal resistances

Rs = nR (For series connection)

R

Rpn

(For parallel connection)

2Rsn

Rp

Rs = Effective resistance in series

Rp = Effective resistance in parallel

n = number of resistors

R = Resistance of each resistor

7. Work Energy consumed

; Power = Time Time

WP

t

8. ;W V I t Power = potential difference × current × time

2

2 V tW I Rt W

R

9. P = V × I; Power = potential difference × current

10. P = I2 × R; Power = (current)2 × resistance

11.

22 potential difference; Power =

resistance

VP

R

12. Electric energy = P × t; electric energy = power × time

13. Heating Effects of Current: H = I2Rt

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CHAPTER – 2: LIGHT

LAW OF REFLECTION

1. Incident ray, reflected ray and normal at the point of

incidence lie in the same plane.

2. The angle of incidence is equal to the angle of

reflection i.e., ∠i = ∠r.

REFLECTION FROM A PLANE MIRROR

1. The image is virtual. The image and the object are

equidistant from the mirror.

2. The object size is equal to the image size i.e.,

magnification is 1.

REFLECTION FROM A SPERICAL MIRROR

1. Focal length is equal to half of radius of curvature i.e., f = R/2.

2. The object distance u, image distance v and focal length f are related by the mirror formula:

1 1 1

v u f

3. The magnification is the ratio of image height to the object height and it is given by

v

mu

IMAGE FORMATION FROM CONCAVE MIRROR

S.

No.

Position of

the object

Position of

the image

Nature & size of

the image Ray diagram

(

1) At infinity At focus F

Real, inverted

and highly

diminished.

(point size)

(

2)

Between

infinity

and C

Between C

& F

Real, inverted

and smaller than

the object

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(

3) At C At C

Real, inverted

and same size.

(

4)

Between

C & F

Between C

and infinite

Real, inverted

and enlarged.

(

5) At F At infinity

Real, inverted

and infinitely

large.

(

6)

Between

focus

and pole

Behind the

mirror

Virtual, erect and

enlarged.

IMAGE FROM A CONVEX MIRROR

S. No. Position of the

object

Position of the

image Size of image

Nature of the

image

(i) At infinity At F, behind mirror Highly diminished Virtual and erect.

(ii) Between infinity

and pole of mirror

Between P & F

behind the mirror

Smaller than object Virtual and erect.

SIGN CONVENTION OF SPHERICAL MIRROR

(i) Whenever and wherever possible, the ray of light is taken to travel from left to right.

(ii) The distances above principal axis are taken to be positive while below it, negative.

(iii) Along principal axis, distances are measured from the pole and in the direction of light are taken

to be positive while opposite to it is negative.

FORMULAS ON REFRACTION OF LIGHT

Refractive Index

speed of light in vacuum c

speed of light in medium v

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Laws of Refraction

1. Incident ray, refracted ray and normal at the point of incidence lie in the same plane.

2. The angle of incidence is related to the angle of refraction by Snell’s Law:

2

1

sin

sin

i

r

Lens Formula

The object distance u, image distance v and focal length f of a lens are related by the lens formula

1 1 1

v u f

The magnification by a lens is given by

vm

u

Power of a Lens

The power of a lens is related to its focal length by

P = 1/f

The power P in diopter if f in metre.

For Convergent or Convex Lens

S. No. Object Image Magnification

1 At At F m << - 1

2 - 2F F – 2F m < - 1

3 2F At 2F m = - 1

4 At F – 2F - 2F m > - 1

5 At F At m >> -1

6 F – O In front of lens m > + 1

Combinations of Lenses

If two thin lens are placed in contact to each other then,

power of combination, P = P1 + P2

1 2

1 1 1

F f f

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CHAPTER – 3: MAGNETIC EFFECTS OF ELECTRIC CURRENT

1. Magnetic field due to a moving point charge:

0

34

q v rB

r

7 2 2

0 4 10 /N s C is called the permeability of free space.

2. Biot-savart’s Law:

This law states that tahe magnetic field (dB) at point P due to small current element Idl of the

current-carrying conductor is directly proportional to the Idl (current) element of the conductor

2

. . sinI dldB

r

3. Magnetic field due to a straight wire

I r

P

01 2sin sin

4

IB

r

4. Magnetic field due to an infinite straight line

rP

0 1

2B

r

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5. Magnetic field due to a circular loop

r

I

(i) At centre

B = μ0NI/2r

(ii) At axis

2

0

32 2 2

2

NIRB

R x

6. Magnetic field on the axis of a solenoid

B = (μ0NI/2) (cosθ1 – cosθ2)

7. Amperes Law

0.B d I

8. Magnetic field due to a long cylinder

(i) B = 0, r < R (ii) 0 ,2

IB r R

r

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9. Magnetic force acting on a moving point charge

r

B

V

F q v B

10. Magnetic force acting on a current-carrying wire

F I B

11. Magnetic Moment of a current carrying loop

M NIA

12. The torque acting on a loop

M B

13. Magnetic field due to single pole

0

22

mB

r

14. Magnetic field on the axis of the magnet

0

3

2

4

MB

r

15. Magnetic field on the equatorial axis of the magnet

0

34

MB

r

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CHAPTER – 4: THE HUMAN EYE & COLOURFUL WORLD

REFRACTION BY A PRISM

The incident ray suffers a deviation (or bending) through an angle due to refraction through the

prism. The angle is called the angle of deviation.

Note:

1. The prism is in the position of the minimum deviation when angle of emergence e = angle

of incidence i .

2. The refractive index of the material of prism is given as

mAsin

2

Asin

2

DISPERSION OF WHITE LIGHT BY A GLASS PRISM

Dispersion of light

The process of splitting of white light into its

seven constituent colours is called dispersion of

white light. The band of seven colours formed on

a screen due to the dispersion of white light is

called spectrum of visible light or spectrum of

white light.

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CHAPTER – 5: SOURCES OF ENERGY

NUCLEAR FISSION

Nuclear fission reaction is that in which a heavier nucleus breaks down into two or more

lighter nuclei of nearly equal size (mass) with the release of large amount of energy.

235 1 143 90 1

92 0 56 36 03 200 .U n Ba Kr n MeV

The above nuclear fission reaction was first observed by Hahn and strassman.

NUCLEAR FUSSION

The fusion of two lighter nuclei in a stable heavier nucleus with the release of large amount of

energy is called nuclear fusion.

1 4 0

1 2 14 2 27H He e MeV

UNIT OF RADIOACTIVITY

The SI unit for activity is becquerel, Henry Becquerel .Becquerel is simply equal to 1 disintegration or

decay per second. There is also another unit named “curie” that is widely used and is related to the SI

unit as:

1 curie = 1 Ci = 3.7 × 1010decays per second= 3.7 × 1010Bq

TYPES OF RADIOACTIVE DECAY

Alpha decay: An alpha particle (A = 4, Z = 2) is emitted from the nucleus, resulting in a

daughter nucleus (A -4, Z - 2).

Proton emission: The parent nucleus emits a proton, resulting in a daughter nucleus (A -1, Z - 1).

Neutron emission: The parent nucleus ejects a neutron, resulting in a daughter nucleus (A - 1, Z).

Spontaneous fission: An unstable nucleus disintegrates into two or more small nuclei.

Beta minus (β−) decay: A nucleus emits an electron and electron antineutrino to yield a

daughter with (A, Z + 1).

Beta plus (β+) decay: A nucleus emits a positron and electron neutrino to yield a daughter with

(A, Z – 1).

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Number of particles emitted Mass number difference

4

Number of particles emitted

2 Atomic number difference

Number of particles 4

b d

Number of particles ( )

2

b dc a

HALF-LIFE

The term half-life was introduced by Rutherford.

The time required to decay exactly one half of the initial amount of a radioactive element is

called half-life of that element 1 0.5 50%

2

or or .T T T

1

2

0.693

decay constantT