Arihant AIEEE Physics

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PHYSICS

D. B. SINGH

Director

Vigyan Gurkui, KOTA

ARIHANT PRAKASHAN K A L I N D I , T.R NAGAR, M E E R U T - 2 5 0 0 0 2

URGETIIT 2 0 0 6 - 0 7

Other Useful Books "7ext S»4 The unit of force

2 = kilogram metre per second

4. Abbreviations for multiples and submultiples: Symbol Prefix Factor 10 24

yotta

Y

10 21

zetta

Z

10 18

exa

E

(b) 1 X-ray unit = l x u = 10 m -to, (c) 1 angstrom = 1 A - 10""" m

10 15

peta

P

10 12

tera

T

(d) 1 micron = 1 (.im = 10~6 m

109

g'g a

G

(e) 1 astronomical unit = 1 Au = 1.49 x 1011 m [Average distance between sun and earth, i.e., radius of earth's orbit]

106

(a) 1 fermi = 1 fm = 10~15 m -13

mega

M

103

kilo

k

102

hecto

h

(f) 1 light year = 1 l y = 9.46 x l 0 1 5 m [Distance that light travels in 1 year in vacuum]

101

deka

da

10- 1

deci

d

(g) 1 parsec = 1 pc = 3.08 x 10 16 m = 3.26 light year [The distance at which a star subtends an angle of parallex of 1 s at an arc of 1 Au].

ur2

centi

cm

10" 3

milli

m

10" 6

micro

10" 9

nano

M n

10" 12

pico

(h) (i) (j) (k)

One One One One

shake = 10 _s second. slug = 14.59 kg pound =453.6 gram weight metric ton =1000 kg

io-

15

femto

P f

8 Units and Measurements Factor 10 -18

atto

a

10- 21

zepto

z

10- 24

yocto

y

10 6

million

109

billion

Prefix

Symbol

8. Dimensions and Dimensional Formulae: The dimensions of a physical quantity are powers raised • to fundamental units to get the derived unit of that physical quantity. The corresponding expression is known as dimensional formula. In the representation of dimensional formulae, fundamental quantities are represented by one letter symbols.

10 12

trillion 5. Some approximate lengths:

Fundamental Quantity

Measurement

Length in metres

Distance to the first galaxies formed

2 x 10 26

Distance to the Andromeda galaxy Distance to the nearest star. (Proxima Centauri)

2 x 10 4 X 10 16

Distance of Pluto

6 X 10 12

Radius of Earth

6 x 106

Height of Mount Everest

9 x 103

Thickness of this page

1 x 10 _ 4

Length of a typical virus

1 x 10" 8

Radius of a hydrogen atom

5 x 107 11

Radius of a proton 6. Some approximate time intervals: Measurement

1 X 10~

on

15

Time interval in second ,39

Life time of a proton (predicted)

1 xlO'

Age of the universe Age of the pyramid of cheops

5 x 10 17 1 x 1 0 11

Human life expectancy

2xl09

Length of a day Time between human heart beats

9 x 10 4 8 x 1 0 -1

Life time of the Muon

2 x 10" 6

Shortest lab light pulse

6x10

Life time of the most unstable particle

1x10

The Plank time

1 x 1 0, - 4 3

R

15

I-23

Object

Mass in kilogram

Known universe

1 x 10 M

Our galaxy

2 x 10 41

Sun

2 x 10 30

Moon

7x

Asteroid Eros

5 x 10 15 10 12

Small mountain

1x

Ocean liner

7 x 107

Elephant

5xl03

Grape

3 x 10~3

Speck of dust

7x10

Penicillin molecule

5 x 10 - 1 7

Uranium atom

4x10

-25

Proton

2x10

-27

Electron

9x10

-31

-10

M L T I K mol cd

Mass Length or Distance Time Electric current Temperature Amount of substance Luminous intensity

Method for finding dimensional formulae : Step I : Write the formula of physical quantity. Step I I : Convert the formula in fundamental physical quantity. Step I I I : Write the corresponding symbol for fundamental quantities. Step I V : Make proper algebraic combination and get the result. Example : Find the dimensions of momentum. Solution : Step I

Momentum = Mass x Velocity Displacement Step II —> Momentum = Mass x Time Step III —> Momentum _=M A

IT]

7. Some approximate masses:

10 22

Symbol

Dimensional formula of momentum = [Momentum] = [MLT - 1 ] The dimensions of momentum are 1 in mass, 1 in length and - 1 in time. Example: The unit of gravitational constant is Nm /kg . Find dimensions of gravitational constant. Solution : Step I —> Write physical quantities of corresponding units. Here,

Nm 2 Force (Length)2 =- = 5 kg 2 (Mass)2

Step II —> Convert derived fundamental quantities. Gravitational constant =

physical

quantities in

Force x (Length) (Mass)2

(Mass x Acceleration) x (Length) (Mass) Mass

Change in velocity

(Mass)2

Time

(Length)'

/ Distance

Mass x Time

Time

^

(Length)2

9 Step III —> Use proper symbols of fundamental quantities. [L2] Gravitational constant = [MT]

Units and Measurements

= [Gravitational constant] =

[L] [T]

MT T

= [M~ 1 L 3 T~ 2 ]

.•. The dimensional formula of gravitational constant 9. Unit and Dimensions of some Physical Quantities s. No.

Physical Quantity

2.

Displacement or distance or length Mass

3.

Time

4.

Electric current

5.

7. 8.

Thermodynamic temperature Amount of substance Luminous intensit" J Area

9.

Volume

10.

Density

11.

Relative density or specific gravity

1.

6.

12.

Velocity or speed

13.

Acceleration or retardation or g

14.

Force (F)

Formula length

—

ampere

A

kelvin

—

length x breadth length x breadth x height mass volume

time mass x acceleration

Pressure

18.

Work

force area force x distance

mass x velocity

equivalent to work

work time

Gravitational constant (G) mim2 Angle (8)

23.

Angular velocity (co)

cd

cubic metre kilogram per cubic metre

density of substance

distance time change in velocity

arc radius angle (9) time

M°L°T¥

mol

candela square metre

M°L 2 T°

m3

M°L 3 T°

kg/m 3

M1L"3T°

kg/m 3 = no unit

—

metre per second metre per square second newton or kilogram metre square second kilogram metre second newton-sec

per per

pascal or newton per square metre kilogram-square metre per square second or joule kilogram square metre per square second or joule watt (W) or joule per second or kilogram square metre per cubic second newton-square metre per square kilogram radian radian per second

—

m2

kg/m 3

density of water at 4°C

M°L° T 1

K

mole

17.

22.

M W

kg s

force x time interval

21.

M°L 1 T°

second

Impulse

Power (P)

m

—

16.

20.

Dimensional Formula

kilogram

Linear momentum (p)

Energy

metre

SI Units

—

15.

19.

Name of SI Unit

M°L°T 0 or dimensionless

m/s

M°L1T_1

m/s 2

MVT-2

N or kg m/s

M1L1T-2

kg m/s

MVT-1

Ns N/m2 or Pa

MVT

- 1

M 1 L _1 t

-2

kg-m /s or J

MVT-2

kg m 2 /s 2 or J

M1L2T-2

kg m 2 /s 3 or J/s or watt (W)

M1L2T-3

Nm 2 /kg 2

M

- 1

L

3

T

- 2

rad

M°L°T° or dimensionless

rad/s

M0L°T_1

5 Unitsand Measurements Physical Quantity Angular acceleration (a)

Moment of inertia (J) Radius of gyration (K)

Formula change in angular velocity time taken mass x (distance) 2 distance

Angular momentum (L) Torque ( ? )

(Spring) force constant (k) Surface tension Surface energy Stress Strain

Z? force displacement force length energy area force area change in dimenson original dimension or

Young's modulus (Y) Bulk modulus (B)

Compressibility Modulus of rigidity or shear modulus Coefficient of viscosity (r|)

Coefficient of elasticity Reynold's number (R) Wavelength (X) Frequency (v)

Angular frequency (co)

Gas constant (R)

radian second

per

metre kilogram square metre per second newton metre or kilogramsquare metre per square second newton per metre or kilogram per square second newton per metre joule per metre square newton metre No unit

per

Dimensional Formula

square

kilogram square metre

square

rad/s

M°L°T-

kgm2 m

M1L2T° M ^ T

L logitudinal stress logitudinal strain volume s tress or volume strain normal stress volume strain V 7 1_ Bulk modulus shearing s tress shearing strain F 11= /. ^ „ Au A T~ Ax stress strain prVc

kg m 2 /s

MVT-1

N-m or kg m 2 /s 2

M 1 L 2 T~ 2

N/m or kg/s

M 1 L°T~ 2

N/m

M1L°T-2

J/m 2

M ^ T -

N/m 2

M1L-1T-2

newton metre

per

square

newton metre

per

square

square newton newton metre

metre

N/m

per

per square

newton metre no unit

per

square

metre

N/m 1

or poise

N/m

radian per second

joule per mole kelvin

distance

per second

IVTVT2 1

M

L

- 1

t

- 2

M^^T-1 m

il-It-2 M°L°T°

m

MVT0

s" 1 or Hz

MVT-1

per second or hertz

I=ln2n2a2pv or energy watt per square metre transported per unit area per second

velocity change

M'l^T-2

N_1 m2

poise or kilogram per metre per second kg m *s

second

PV

2

N/m

11 distance number of vibrations second co = 2TU>

0

M°L°T°

nT Velocity gradient

SI Units

AL

Time period Intensity of wave (I)

Name of SI Unit

rad/s

mVT-

1

s

MW

W/M

mVT"3

J mol - 1 K" 1

M1L2T_2K_1 M0L0T_1

Units and Measurements

6 S. No.

Physical Quantity

48.

Rate of flow

49.

Thermal conductivity (K)

50. 51.

54.

Stefan's constant (a) Charge

56.

Dielectric constant Electric field

62.

rn

energy frequency PV TNA E AtT" q = It K F AV F E = — or E = —— q a W V:

Potential (electric)

1

Electric dipole moment

p = 2qL

Resistance (R)

r-7

Electric flux (0 or E)