1. Physics aims to quantify natural phenomena precisely using standardized units and measurements. The International System of Units (SI) defines seven base units including the meter, kilogram, and second. 2. All physical quantities can be expressed as a combination of fundamental quantities like length, mass, and time through dimensional analysis. Dimensions must be balanced on both sides of any equation. 3. Measurements have associated errors or uncertainties. Random errors are quantified through calculations of mean and standard deviation. Systematic errors are reduced by improving measurement techniques and instrument precision.

1. Physics

2. Phys - 1
Units And Measurements

3. Session Opener
We know an elephant is heavier
than a feather
Physics wants to know by how
many time, by what standards
and with what accuracy.

4. Session Objectives

5. Session Objective
Standard and Units
Dimensions
Errors
Significant Figures
Accuracy and Precision
Dimensional Analysis

6. Standards and Units
Laws of physics : expressed in terms
of physical quantities
Physical quantities : expressed in
terms of fundamental quantities.
Fundamental quantities : defined by measurements
and expressed by standards.
Measurements : comparison with a
standard.
Standards are defined and universally
accepted by competent authority.

7. Standards and Units
Physical quantity (q) given
by a number and a unit.
q = n . u
n : pure number.
u : unit of the standard.
1
n
u

Because q is the same whatever be the standard

8. Basic physical
quantity
Name of SI
unit
Symbol of SI
unit
1. Length Meter m
2. Mass Kilogram kg
3. Time Second s
4. Electric current Ampere A
5. Temperature Kelvin K
6. Luminous intensity Candela cd
7. Amount of substance Mole mol
SI (International system) units

9. Dimensions of physical quantities
Number of times a fundamental quantity
is repeated in physical quantity q
q M L T ..............
  

       
       
Volume is 3 dimensional in length
3
V L

   
   
Area is 2 dimensional in length
2
A L

   
   
a
b
c

10. Dimension
• Quantities with same dimensions
only can be added
• Power of dimension on both sides
of an equation must match

11. Questions

12. Class Exercise - 7
Dimensionally, specific heat is
proportional to dimension of
mass as
(a)[M0] (b) [M1]
(c) [M–1] (d) [M2]

13. Solution - 7
Specific heat is (dimensionally)
Heat (energy) per unit mass
per unit temperature (q)
Then,

 
[Energy]
[C]
[M ]
  

–2
0 2 –2 –1
[MLT ]
[M L T ]
[M ]

14. Dimensional Analysis
To test whether a relation is wrong.
For interconversion of units
To justify /derive interrelation of quantities.
Dimensional analysis is a powerful
method

15. Questions

16. Class Exercise - 8
Show dimensionally which of the following
physical quantities have an influence on the
time period of a simple pendulum?
(i) Mass of the bob
(ii) Length of the string (l)
(iii) Acceleration due to gravity (g) and
(iv) Angular displacement ()

17. Solution - 8
Time period = T
Then
  
 

 
[T] m g
Relation with  cannot be found
dimensionally.
 

    
   
  
   
 
–2 –2
M L LT M L T
  
 
 
 
0 0 1
M L T m g
      
0, –2 1
, –    
1 1
or – ,
2 2

So T Constant
g

18. Class Exercise - 9
What is the value of a force of
10 N in a system with
fundamental units of centimetre,
gram and hour?

19. Solution - 9
q = n1u1 = n2u2
10 N = n2 new unit
 
2
Newton
n 10
New unit
 
 
 
–2
2 –2
kg m s
n 10
g cm hr
   
    
   
  
2
3 2
10 g 10 cm hr
10
1 g 1 cm s
= 106 × 60 × 60 = 3.6 × 109

20. Class Exercise - 10
Check dimensionally if the relation
is correct.
  2
1
s ut at
2

21. Solution - 10
Dimension of left-hand side (s)
= [M0L1T0]
On right-hand side: ut =
Velocity × Time
= [M0L1T–1][T]
= [M0L1T0] same as LHS
   
   
   
2 2 0 1 –2 2
1 1
at Acceleration Time M L T T
2 2
 
 
 
1
has no dimension
2
= [M0L1T0] [Same as LHS]
Equation is dimensionally
correct.

22. Errors
An observation is limited by the
least count of instrument
Measured value qm = qreal  q
Exact value of qreal is not known
Only mean value of q can be found

23. Errors
Random errors are expected when
several observations (qi) are made

 


n
2
i
i 1
x
RMS error :
n(n 1)


  

n
i
i 1
i i i
1
Meanq q
n
Error in q x q q

24. Errors
In sums and differences,
ABSOLUTE ERRORS are added
A  B = C
C  C = A  B  ( A + B)
In products or quotients,RELATIVE ERRORS
are added
A B C
C A B
C A B
 
  
 
   
 
 

  o
o
C
percentage error 100
C

  
 
   
 
 
A
C
B
C A B
C A B

25. Questions

26. Class Exercise - 3
The percentage errors of X, Y, X are x,
y and z respectively. The total
percentage error in the product XYZ is
(a) xyz (b) x + y + z
 
1 1 1
(c)
x y z
 
 
xy yz xz
(d)
x yz
Percentage errors are added in a product.
Solution :- b

27. Class Exercise - 6
The least count of a stop watch is
0.2 s. The time of 20 oscillations of
a pendulum is measured to be 25 s.
The percentage error in the
measurement of time is
(a)8% (b) 1.8%
(c) 0.8% (d) 0.1%
Solution
Total time measured is important and not
time period.
So percentage error   
0.2
100% 0.8%
25

28. (i) Accuracy
Sign has to be retained while expressing accuracy.
Accuracy : degree of agreement
of a measurement with the true
(accepted) value.
Accuracy and Precision
(ii) Precision
Precision is expressed without any sign.
Precision : degree of agreement
between two or more measurements
done in an identical manner.

29. Significant figures
Significant figures in 1.007,
12.012 and 10.070 are 4, 5
and 5 respectively.
Significant figures are the meaningful
digits in a measured or calculated
quantity.

30. i. All non-zero digits are significant.
Rules to determine significant
figures
iv Zeroes to the right of the decimal point are
significant.
iii. Zeroes between non-zero digits are significant.
ii. Zeroes to the left of the first non-zero
digit are not significant.

31. Questions

32. Class Exercise - 2
Which of the following, in the
measurement of length,
is most accurate?
(a) 2 × 102 m (b) 200.0 m
(c) 20 × 102 m (d) 200 m
200.0 has four significant figures,
which is maximum in the group.
Solution :-

33. Class Exercise - 5
Which of the following measurements
is most precise?
(a) 2345 m (b) 234.5 m
(c) 23.45 m (d) 2.345 m
Solution - d
2.345 m measures till the smallest
fraction of a meter.

34. Class Exercise - 4
With regard to the significant figures,
(12.5)2 is equal to
(a) 156.250 (b) 156.25
(c) 156.2 (d) 156
(12.5)2 = 156.25. But as only three
significant figures are to be considered,
156 is the right answer.
Solution

35. Class Exercise - 1
Which of the following statements
is false among the statements
given below?
(a) All non-zero digits are significant.
(b) Zeroes in the middle of a numerical expression are
significant, while those immediately following a decimal
point are not.
(c) While counting the number of significant figures,
the powers of 10 are to be considered.
(d) Greater the number of significant figures in a
measurement, smaller is the percentage error.

36. Solution - 1
In powers of 10 placed as:
212.2 = 2.122 × 102,,102
is not significant.
Ans. c

37. Thank you