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Physics
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Phys - 1
Units And Measurements
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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.
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Session Objectives
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Session Objective
Standard and Units
Dimensions
Errors
Significant Figures
Accuracy and Precision
Dimensional Analysis
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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.
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Standards and Units
Physical quantity (q) given by a number and a unit.
q = n . u
n : pure number.
u : unit of the standard.
1n
u
Because q is the same whatever be the standard
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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
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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
3V L
Area is 2 dimensional in length
2A L
a
b
c
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Dimension
• Quantities with same dimensions only can be added
• Power of dimension on both sides of an equation must match
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Questions
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Class Exercise - 7
Dimensionally, specific heat is proportional to dimension of mass as
(a) [M0] (b) [M1]
(c) [M–1] (d) [M2]
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Solution - 7
Specific heat is (dimensionally)
Heat (energy) per unit mass
per unit temperature (q)
Then,
[Energy][C]
[M ]
–20 2 –2 –1[MLT ]
[M L T ][M ]
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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
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Questions
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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 ()
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Solution - 8
Time period = T
Then [T] m g
Relation with cannot be found dimensionally.
–2 –2M L LT M L T 0 0 1M L T m g
0, –2 1, – 1 1
or – , 2 2
So T Constantg
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Class Exercise - 9
What is the value of a force of 10 N in a system with fundamental units of centimetre, gram and hour?
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Solution - 9q = n1u1 = n2u2
10 N = n2 new unit
2Newton
n 10 New unit
–2
2 –2kg m s
n 10 g cm hr
23 210 g 10 cm hr10
1 g 1 cm s
= 106 × 60 × 60 = 3.6 × 109
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Class Exercise - 10
Check dimensionally if the relation
is correct. 21s ut at
2
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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 21 1
at Acceleration Time M L T T2 2
1 has no dimension
2= [M0L1T0] [Same as LHS] Equation is dimensionally correct.
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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
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Errors
Random errors are expected when several observations (qi) are made
n
2i
i 1x
RMS error :n(n 1)
n
ii 1
i i i
1Meanq q
n
Error in q x q q
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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 BC A B
o
oC
percentage error 100C
AC
BC A B
C A B
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Questions
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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 y z
Percentage errors are added in a product.
Solution :- b
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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
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(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.
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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.
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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.
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Questions
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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 :-
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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.
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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
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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.
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Solution - 1
In powers of 10 placed as:
212.2 = 2.122 × 102,,102
is not significant.
Ans. c
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Thank you