HANDBOOK OF PHYSICS

S. No. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

12.

13.

14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

E

26.

CONTENTS Basic Mathematics used in Physics Vectors Unit, Dimension, Measurements & Practical Physics Kinematics Laws of Motion and Friction Work, Energy and Power Circular Motion Collision and Centre of Mass Rotational Motion Gravitation Properties of Matter and Fluid Mechanics (A) Elasticity (B) Hydrostatics (C) Hydrodynamics (D) Surface Tension (E) Viscosity Thermal Physics Temperature Scales and Thermal Expansion Calorimetry Thermal Conduction Kinetic Theory of Gases Thermodynamics Oscillations Simple Harmonic Motion Free, Damped and Forced Oscillations & Resonance Wave Motion and Doppler’s Effect Electrostatics Capacitance and Capacitor Current electricity and Heating Effects of Current Magnetic Effect of current and Magnetism Electromagnetic Induction Alternating Current and EM Waves Ray Optics and Optical Instruments Wave Nature of Light and Wave Optics Modern Physics Semiconductor and Digital electronics Important Tables (a) Some Fundamental Constants (b) Conversions (c) Notations for units of measurements (d) Decimcal prefixes for units of measurements Dictionary of Physics

Page No. 1-4 5-8 9-14 15-21 22-25 26-30 31-33 34-38 39-47 48-50 51-58 51-52 53-54 55 56 57-58 59-69 59-60 61 62-64 65-66 67-69 70-74 70-72 73-74 75-80 81-85 86-89 90-95 96-100 101-104 105-108 109-118 119-122 123-130 131-137 138-140 138 138 139 139 141-166

© All rights including trademark and copyrights and rights of translation etc. reserved and vested exclusively with Allen Career Institute®. No part of this publication may be copied, reproduced, adapted, abridged or translated, stored in any retrieval system, computer system, photographic or other system or transmitted in any form or by any means whether electronic, mechanical, digital, optical, photocopying, recording or otherwise, or stood in any retrieval system of any nature. Any breach will entail legal action and prosecution without further notice. This study material is sold/distributed by Allen Career Institute® subject to the condition and undertaking given by the student that all proprietary rights (as defined under the Trademark Act, 1999 and Copyright Act, 1957) of the Study Materials and/or Test Series and/or the contents shall belong to Allen Career Institute's Tests and neither the Study Materials and/or Test Series and/or the contents nor any part thereof shall be reproduced, modify, re-publish, sub-license, upload on website, broadcast, post, transmit, disseminate, distribute, sell in market, stored in a retrieval system or transmitted in any form or by any means for reproducing or making multiple copies of it. Any violation or infringement of the propriety rights of Allen shall be specifically punishable under Section- 29 & 52 of the Trademark Act, 1999 and under Section- 51, 58 & 63 of the Copyright Act, 1957 and any other Act applicable in India. All disputes are subjected to the exclusive jurisdiction of courts, tribunals and forums at Kota, Rajasthan only. Note:- Due care and diligence has been taken while editing and printing this book/study materials. Allen Career Institute shall not hold any responsibility for any mistake that may have inadvertently crept in. Allen Career Institute shall not be liable for any direct, consequential or incidental damages arising out of the use of this book.

CHAPTER

CHAPTER

0°

30° /6)

45° /4)

60° /3)

90° /2)

120° /3)

135° /4)

150° /6)

180°

270° /2)

360° )

CHAPTER

Physics HandBook

CHAPTER

$//(1 IMPORTANT NOTES

4

E

CH APTER

Physics HandBook

$//(1

VECTORS Vector Quantities A physical quantity which requires magnitude and a particular direction, when it is expressed.

Triangle law of Vector addition G G G R AB

Addition of More than Two Vectors (Law of Polygon) If some vectors are represented by sides of a polygon in same order, then their resultant vector is represented by the closing side of polygon in the opposite order. C D

R

A 2  B2  2AB cos 

tan  

R

B sin  A  B cos 





C

B Bsin

B A

Bcos

A

  If A = B then R  2A cos &   2 2 Rmax = A+B for =0° ;Rmin = A–B for =180°

Parallelogram Law of Addition of Two Vectors

D

G G G G G R  ABCD

ˆ

R

 A



Ax

 B

ˆ

A 2  B 2  2AB cos 

Ay

B sin  A sin  and tan   A  B cos  B  A cos 

m

A  A 2y  A 2z 2 x

Az

A  A 2y  A 2z A, m, n are called direction cosines

A +m +n =cos +cos +cos = 2

A

A  A2y  A 2z 2 x

Angle made with z-axis A cos   z  A

A

tan  

Angle made with y-axis Ay cos    A

+B =A

JJJG JJJG JJJG JG G G G AB  AD  AC  R or A  B  R  R 

G A  A xˆi  A y ˆj  A z kˆ

Angle made with x-axis A cos   x  A

C

B

B

A

Rectangular component of a 3–D vector

If two vectors are represented by two adjacent sides of a parallelogram which are directed away from their common point then their sum (i.e. resultant vector) is given by the diagonal of the parallelogram passing away through that common point. D

R

2

2

2

2

2



2 x

A 2x  A 2y  A 2z A A A 2 x

2 y



2 z

n

2

1

or sin2 + sin2 + sin2 =2

General Vector in x-y plane Vector subtraction Bcos



Bsin 

R

E

y











G r  xiˆ  yjˆ  r cos ˆi  sin ˆj

r

B

x

EXAMPLES : 1. Construct a vector of magnitude 6 units making an angle of 60° with x-axis.

B

G G G G G G R  A  B  R  A   B 

G ˆ  6  1 ˆi  3 ˆj   3iˆ  3 3ˆj Sol. r  r(cos 60iˆ  sin 60j)   2 2 

B sin  R  A2  B2  2AB cos  , tan   A  B cos 

2. Construct an unit vector making an angle of 135° with x axis.

If A = B then R  2A sin

 2

Sol. ˆr  1(cos135ˆi  sin135ˆj) 

1 2

( ˆi  ˆj)

5

C HAP TE R

Physics HandBook

$//(1 Differentiation

Scalar product (Dot Product) G G G G Angle between   1 A  B ˆ A.B  AB cos     cos   AB  two vectors ˆ

G G If A  A xˆi  A y ˆj  A z kˆ & B  B xˆi  B yˆj  B zkˆ then G G A.B  A x Bx  A y B y  A z Bz and angle between G G A & B is given by

G G A.B cos    AB ˆ ˆ

ˆ

When a particle moved from (x1, y1, z1) to (x2, y2, z2) then its displacement vector

A x Bx  A y B y  A z Bz A  A 2y  A 2z B2x  B2y  B2z 2 x

(x1,y1,z1)

ˆ ˆ  1 , ˆi.jˆ  0 , ˆi.kˆ  0 , ˆj.kˆ  0 ˆi.iˆ  1 , ˆj.jˆ  1 , k.k G G Component of vector b along vector a , G G b|| b . aˆ aˆ



ˆ

G G d G G dA G G dB (A.B)  .B  A. dt dt dt G G d G G dA G G dB (A  B)  BA dt dt dt



r

(x2,y2,z2)

r1 r2

G G G ˆ  (x ˆi  y ˆj  z k) ˆ r  r2  r1  (x 2ˆi  y 2ˆj  z 2 k) 1 1 1

= (x2  x1 )iˆ  (y 2  y1 )ˆj  (z 2  z1 )kˆ

b

G Magnitude: r  r  (x2  x1 )2  (y2  y1 )2  (z2  z1 )2

Lami's theorem a

b

ˆ

A

G G Component of b perpendicular to a ,

G G G G G b   b  b||  b   b  aˆ  aˆ

c

Cross Product (Vector product) ˆ

G G ˆ where nˆ is a vect or A  B  AB sin  n G G perpendicular to A & B or their plane and its direction given by right hand thumb rule.

3

b

B

2 C

a

F3

F1 F2 F3   sin 1 sin 2 sin  3

sin A sin B sin C   a b c

Area of triangle G G AB 1 Area   AB sin  2 2

A B

1

C

B

A ×B

A

F2

F1

A

B Bsin  A

B

Area of parallelogram ˆ

ˆi G G A  B  Ax

ˆj Ay

kˆ Az

Bx

By

Bz

B 

Bsin

G G Area = A  B = ABsin

A

ˆ

 ˆi  A y B z  A z B y   ˆj (AxBz–BxAz) + kˆ (AxBy–BxAy) G G G G A  B  B  A G G G G G G j (A  B).A  (A  B).B  0 G G G ˆi  ˆi  0 , ˆj  ˆj  0 , kˆ  kˆ  0 positive

ˆ

ˆi  ˆj  kˆ ; ˆj  kˆ  ˆi ,

ˆ ˆ

i negative

kˆ  ˆi  ˆj ; ˆj  ˆi  kˆ kˆ  ˆj  ˆi , ˆi  kˆ  ˆj

6

k

F r parallel vectors G G G AB 0

For perpendicular vectors G G A.B  0

For coplanar vectors G G G A.(B  C)  0

If A,B,C points are collinear JJJG JJJG AB   BC

E

CH APTER

Physics HandBook

C HAP TE R

$//(1 IMPORTANT NOTES

8

E

C HAP TE R

Physics HandBook

$//(1

Units, Dimension, Measurements and Practical Physics Systems of Units

Fundamental or base quantities The quantities which do not depend upon other quantities for their complete definition are known as fundamental or base quantities. e.g. : length, mass, time, etc.

(i) (ii) (iii)

Derived quantities

(iv)

The quantities which can be expressed in terms of the fundamental quantities are known as derived quantities. e.g. Speed (=distance/time), volume, acceleration, force, pressure, etc.

Units of physical quantities The chosen reference standard of measurement in multiples of which, a physical quantity is expressed is called the unit of that quantity. e.g. Physical Quantity = Numerical Value × Unit

MKS Length (m) Mass (kg) Time (s) –

CGS Length (cm) Mass (g) Time (s) –

FPS Length (ft) Mass (pound) Time (s) –

MKSQ Length (m) Mass (kg) Time (s) Charge (Q)

MKSA Length (m) Mass (kg) Time (s) Current (A)

Fundamental Quantities in S.I. System and their units S.N. 1 2 3 4 5 6 7

Physical Qty. Name of Unit Mass kilogram Length meter Time second Temperature kelvin Luminous intensity candela Electric current ampere Amount of substance mole

Symbol kg m s K Cd A mol

SI Base Quantities and Units Base Quantity

E

S Units Name

Symbol

Definition

Length

meter

m

The meter is the length of the path traveled by light in vacuum during a time interval of 1/(299, 792, 458) of a second (1983)

Mass

kilogram

kg

The kilogram is equal to the mass of the international prototype of the kilogram (a platinum-iridium alloy cylinder) kept at International Bureau of Weights and Measures, at Sevres, near Paris, France. (1889)

Time

second

s

The second is the duration of 9, 192, 631, 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom (1967)

Electric Current

ampere

A

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 Newton per metre of length. (1948)

Thermodynamic Temperature

kelvin

K

The kelvin, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. (1967)

Amount of Substance

mole

mol

The mole is the amount of substance of a system, which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. (1971)

Luminous Intensity

candela

Cd

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian (1979).

Note :- On November 16, 2018 at the General Conference on Weights and Measure (GCWM) the 130 years old definition of kilogram was changed forever. It will now defined in terms of plank's constant. It will adopted on 20 May, 2019 (World Metrology Day - 20 May). The new definition of kg involves accurate weighing machine called "Kibble balance".

9

CH APTER

C HAP TE R

Physics HandBook

$//(1

DIMENSIONS OF IMPORTANT PHYSICAL QUANTITIES Physical quantity

Dimensions

Momentum

M L T–

Calorie

M1 L2 T – 2 M0 L2 T – 2

1

Latent heat capacity Self inductance Coefficient of thermal conductivity Power Impulse Hole mobility in a semi conductor Bulk modulus of elasticity

1

1

M1 L2 T– 2A –2 M1 L1 T– 3K –1

Physical quantity

Dimensions

Capacitance

M–1 L– 2 T 4 A 2

Modulus of rigidity

M1 L– 1 T – 2 M1 L1 T –2A– 2

Magnetic permeability

M1 L– 1 T – 2 M1 L2 T– 1

Pressure Planck's constant

M1 L2 T – 3 M1 L1 T – 1

Solar constant

M – 1 L0 T 2 A1 M1L– 1 T– 2

Current density

Magnetic flux

M1 L0 T– 3 M1 L2 T– 2 A–1

Young modulus

M0L– 2 T0 A1 M1 L– 1 T – 2

Potential energy

M1 L2 T – 2

Magnetic field intensity

M0L– 1 T0A 1

Gravitational constant

M–1 L3 T –2

Magnetic Induction

M1T–2A– 1 M– 1 L–3 T4A 2

Light year Thermal resistance Coefficient of viscosity

M 0 L1 T 0

Permittivity

M– 1 L–2 T 3  M1 L–1 T –1

Electric Field Resistance

M1L1 T– 3A - 1 ML2T– 3 A– 2

SETS OF QUANTITIES HAVING SAME DIMENSIONS S.N.

Quantities

1.

Strain, refractive index, relative density, angle, solid angle, phase, distance gradient, relative permeability, relative permittivity, angle of contact, Reynolds number, coefficient of friction, mechanical equivalent of heat, electric susceptibility, etc.

[M0 L0 T0]

2. 3.

Mass or inertial mass Momentum and impulse.

[M1 L0 T0 ] [M1 L1 T–1 ]

4.

Thrust, force, weight, tension, energy gradient.

5. 6.

Pressure, stress, Young's modulus, bulk modulus, shear modulus, modulus of rigidity, energy density. Angular momentum and Planck's constant (h).

[M1 L1 T–2 ] [M1 L–1 T–2 ]

7.

Acceleration, g and gravitational field intensity.

8. 9.

Surface tension, free surface energy (energy per unit area), force gradient, spring constant. Latent heat capacity and gravitational potential.

10.

Thermal capacity, Boltzmann constant, entropy.

[ M0 L2 T–2] [ ML2T–2K–1]

11.

Work, torque, internal energy, potential energy, kinetic energy, moment of force,

[M1 L2 T–2 ]

2 (q2/C), (LI 2), (qV), (V2C), (I 2Rt), V t , (VIt), (PV), (RT), (mL), (mc T) R

12.

Frequency, angular frequency, angular velocity, velocity gradient, radioactivity R 1 1 , , L RC LC

E

Dimensions

[ M1 L2 T–1] [ M0 L1 T–2] [ M1 L0 T–2]

[M0 L0 T–1 ]

13.

 A   m  L   g  ,  k  ,  R  ,(RC), ( LC) , time      

[ M0 L0 T1]

14.

(VI), (I2R), (V2/R), Power

[ M L2 T –3]

12

12

11

CH APTER

Physics HandBook

$//(1

SOME FUNDAMENTAL CONSTANTS

KEY POINTS

Gravitational constant (G)

6.67 × 10–11 N m2 kg–2

Speed of light in vacuum (c)

3 × 10 8 ms–1

Permeability of vacuum (0)

4 × 10–7 H m–1

Permittivity of vacuum (0 )

8.85 × 10–12 F m–1

Planck constant (h)

6.63 × 10–34 Js

Atomic mass unit (amu)

1.66 × 10–27 kg

Energy equivalent of 1 amu

931.5 MeV

Electron rest mass (me)

9.1 × 10–31 kg  0.511 MeV

Avogadro constant (NA)

6.02 × 1023 mol–1

Faraday constant (F)

9.648 × 104 C mol–1

Stefan–Boltzmann constant ()

5.67× 10 –8 W m– 2 K–4

Wien constant (b)

2.89× 10 –3 mK

Rydberg constant (R)

1.097× 107 m–1

Triple point for water

273.16 K (0.01°C)

Molar volume of ideal gas (NTP)

22.4 L = 22.4× 10–3 m3 mol–1

•

Trigonometric functions sin, cos, t an etc and their arrangement s  are dimensionless.

•

Dimensions of differential  dny   y    dx n   x n 

coefficients  •

Dimensions

of

integrals

 ydx    yx    

•

We can't add or subtract two physical quantities of different dimensions.

•

Independent quantities may be taken as fundamental quantities in a new system of units.

PRACTICAL PHYSICS Rules for Counting Significant Figures

Order of magnitude

For a number greater than 1

Power of 10 required to represent a quantity

•

All non-zero digits are significant.

49 = 4.9 × 101  101  order of magnitude =1

•

All zeros between two non-zero digits are significant. Location of decimal does not matter.

•

If the number is without decimal part, then the terminal or trailing zeros are not significant.

•

Trailing zeros in the decimal part are significant.

For a Number Less than 1

51 = 5.1 ×101  102  order of magnitude = 2 0.051 =5.1 × 10-2  10-1order of magnitude = -1

Propagation of combination of errors Error in Summation and Difference : x = a + b then x = ± (a+b)

Error in Product and Division

Any zero to the right of a non-zero digit is significant. All zeros between decimal point and first non-zero digit are not significant.

A physical quantity X depend upon Y & Z as X = Ya Zb then maximum possible fractional error in X. X Y Z = a + b X Y Z

Significant Figures All accurately known digits in measurement plus the first uncertain digit together form significant figure. Ex. 0.108  3SF, 1.23 × 10-19  3SF,

40.000  5SF, 0.0018  2SF

Rounding off

12

6.87 6.9,

6.84  6.8,

6.85  6.8,

6.75  6.8,

6.65  6.6,

6.95  7.0

Error in Power of a Quantity x

  a  x am  b     m    n    n then x    b  a  b

Least count The smallest value of a physical quantity which can be measured accurately with an instrument is called the least count of the measuring instrument.

E

C HAP TE R

Physics HandBook

$//(1

Vernier Callipers

Least count = 1MSD – 1 VSD (MSD  main scale division, VSD  Vernier scale division)

0

1

2

3

4

5

6

14

15

Ex. A vernier scale has 10 parts, which are equal to 9 parts of main scale having each path equal to 1 mm then least count = 1 mm –

9 mm = 0.1 mm [' 9 MSD = 10 VSD] 10

Screw Gauge Circular (Head) scale 0

Ratchet

Spindle

pitch Least count = total no. of divisions on circular scale

5 10

Linear (Pitch) Scale Sleeve

Thimble

Ex. The distance moved by spindle of a screw gauge for each turn of head is 1mm. The edge of the humble is provided with a angular scale carrying 100 equal divisions. The least count =

1mm = 0.01 mm 100

Zero Error in Vernier Callipers :

Main scale

0

0

Main scale

1

5

0

0

10

Vernier scale without zero error

Main scale

1

5

10

Vernier scale with positive zero error

0

0

1

5

10

Vernier scale with negative zero error

(i)

(ii)

Calculation of zero error for vernier callipers :Positive zero error = (No. of Division of VS coincided with MS).LC Negative zero error = (Total division in VS – No. of division of VS coincided with MS).LC Correct reading with zero error Correct reading = (Reading) – (Zero error) The zero error is always subtracted from the reading to get the corrected value.

E

13