CBSE CLASS XI PHYSICS UNIT -1 PHYSICAL WORLD AND MEASUREMENT CHAPTER-2 UNITS AND MEASUREMENT

CBSE 

CLASS XI

PHYSICS 

UNIT -1 

PHYSICAL WORLD AND MEASUREMENT

CHAPTER-2 

UNITS AND MEASUREMENT

Physical Quantities: The quantities which can be measured directly or indirectly is known as physical quantities. e g : Mass , Length , Time etc.

Unit: Unit is the standard by which we can compare the physical quantities. e g : Kilogram, meter, second etc.

Magnitude of a quantity Q = numerical value x size of its unit.

Q=nu

Now Q= n₁u₁= n₂u_2.If u₁>u₂, then n₁<n₂ i.e. a bigger unit has smaller numerical value and  vice-versa.

e g    Length of a road is =  3 m = 300 cm

Fundamental quantities: The quantities which are basic and cannot derived from other quantities are called fundamental or basic physical quantities. e g mass , length ,time .

Fundamental Units: The units of measurement of all fundamental quantities are called fundamental units. e g mass- kilogram .

S N	Basic Physical Quantities	Fundamental units	Symbol used
1	Mass	Kilogram	Kg
2	Length	metre	m
3	Time	second	s
4	Temperature	kelvin	K
5	Electric Current	ampere	A
6	Luminous Intensity	candela	cd
7	Quantity of matter	mole	mol
S N	Supplementary quantities	Supplementary units	Symbol used
1	Plane angle	radian	rad
2	Solid angle	steradian	Sr

Derived units :The units of measurement of all other physical quantities , which can be obtained from fundamental units are called derived units.

e g Speed= distance/time ,units of distance/units time =m/s

International System of Units (S I) :

Complete the following table:

S N	PHYSICAL QUANTITY	Method	S I UNIT	Symbol
1	Mass	Mass	Kilogram	Kg
2	Length	Length	Meter	m
3	Time	Second	Second	s
4	Distance	Length
5	Displacement	Length
6	Area	Lxb=lxl=l2	Meter square	m2
7	Volume	Length3	Meter3
8	Density	Mass/Volume	Kilogram/meter3	Kg/m3
9	Speed	Distance/time	Meter/second	m/s
10	Velocity	Displacement/time
11	Acceleration	Velocity/time
12	Force	Mass x acceleration	Kgm/s2
13	Work	Force x displacement
14	Energy	Work
15	Heat Energy	Energy
16	Potential Energy	Energy
17	Kinetic Energy	Energy
18	Momentum	Mass x velocity
19	Power	Work/time
20	Temperature	Kelvin
21	Thrust	Force
22	Pressure	Thrust/Area
23	Gravity	Acceleration

Note:

·       Derive S I unit using the formula given in the method e g Force = mass x acceleration S I unit will be the product of S I unit of mass and acceleration i. e. Kgm/s².

·       m/s can be written as ms^-1.

·       Some of the physical quantities S I units has special name like Force-Kgms^-2 and Newton(N), Work has Joule .

·       Work , Energy and all types of energy in class 9^th measured in joule.

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DIMENSIONAL FORMULAE

Now we will relate the above topic to another important topic dimensional formulae.

We will write Mass [M] , Length [L] , Time [T], Temperature[K] , Current [A] .

Dimensions: The dimensions of a physical quantity are the powers or exponents to which the units of base quantities are raised to represent a derived unit of that quantity.

Complete the table:

S N	PHYSICAL QUANTITY	Method	Dimensional formula	S I UNIT
1	Mass	Mass	[M]	Kg
2	Length	Length	[L]	M
3	Time	Second	[T]	S
4	Distance	Length	[L]
5	Displacement	Length
6	Area	Lxb=lxl=l2	L x L=[L2]	m2
7	Volume	Length3
8	Density	Mass/Volume	M/L3=[ML-3] ,Denominator written -3	Kg/m3
9	Speed	Distance/time		m/s
10	Velocity	Displacement/time	L/T=[LT-1]
11	Acceleration	Velocity/time
12	Force	Mass x acceleration
13	Work	Force x displacement	MLT-2 x L=[ML2T-2]
14	Energy	Work	[ML2T-2],all energy has same d f
15	Heat Energy	Energy
16	Potential Energy	Energy
17	Kinetic Energy	Energy	[ML2T-2]
18	Momentum	Mass x velocity
19	Power	Work/time
20	Temperature	Kelvin	[K]
21	Thrust	Force
22	Pressure	Thrust/Area
23	Gravity	Acceleration

Note:  i) There are some physical quantities which has no D F

          e g Plane angle= Arc / radius=L/L= No dimensions i e  [L⁰].

ii) Power are added and subtracted as we have done in lower classes.

Q Find some physical quantities which has no dimensional formula and no units?

Q Write physical quantities other than work and energy which have same dimensional formula?

Solve the following questions:
Q 1 Energy density and pressure have the same dimensions. Comments.
Q 2 Justify L+L = L and L-L = L.
Q 3 Convert 1 dyne into Newton.
Q 4 If the unit of force, energy and velocity are 20 N , 200 J and 5 m/s , find the unit of length , mass and time.
Q 5 Convert 15 J into erg by dimensional analysis.
Q 6 Check the correctness of the equations:
 i) V= Π p r²/8ηl , V is rate of flow liquid through a tube, η viscosity , r is radius , l is length of tube , p is pressure of tube.
ii) v = (2 G M /R)^1/2
iii) h = 2 S cos θ/ r⍴g , S is surface tension, r radius , h height, g acceleration due to gravity , ⍴ density.
Q 7 In Vander Waal equation [P + a /V²] [V-b]= RT . What is the unit and dimensions of a and b.
Q 8 v = A/t + Bt²+ Ct³ , v is velocity and t is time. A,B and C are constant find the unit and dimension AB/C.