NEET Revision Notes
Physics
Units and Measurements
Physical quantities: The quantities that describe the physics laws are called
physical quantities. In physics, a physical quantity is defined as a system that can
be quantified and measured using numbers. A physical quantity is completely
specified if it has:
● Numerical value only
Example: Ratio, refractive index, dielectric constant etc.
● Magnitude only
Example: Scalars, length, mass etc.
● Both magnitude and direction
Example: Vectors, displacement, torque etc.
In general, expressing the magnitude of a physical quantity, we choose a unit and
how many times that unit is contained in the physical quantity.
Types:
● Fundamental quantities:
o The quantities not depend on other quantities for complete definition
are called fundamental quantities.
o Length, mass, time, electric current, temperature, amount of
substance and luminous intensity are the seven fundamental
quantities.
● Derived quantities:
o The quantities derived from the base or fundamental quantities are
called derived quantities.
o Speed, velocity, electric field etc. are some examples.
o For example: we define speed to be distance
speed = time i.e. it is
derived from two fundamental quantities distance and time.
Similarly, we can derive a derived quantity from two or more
fundamental quantities.
Unit and its characteristics:
A unit is the quantity of a constant magnitude used to measure the magnitude of
other quantities holding the same behaviour.
The magnitude of a physical quantity is expressed as physical quantity=(numerical) (unit)
● It should be of convenient size.
● It should be well defined.
● It should be easily available so that as many laboratories duplicate it.
● It should not change with time and place.
● It should not change with the change in physical conditions.
● It should be universally agreed upon so that results obtained in different
situations are comparable.
Fundamental and Derived units:
● Fundamental units: The units chosen for measuring fundamental
quantities are known as fundamental units.
Example: kilogram, meter etc.
● Derived units: The units expressed in terms of the base units are called
derived units.
Example: speed, energy etc.
System of units: A complete set of fundamental and derived for all kinds of
physical quantities is called a system of units.
A few common systems are
● CGS (centimetre-gram-second) system:
This system is based on a variant of the metric system based on the
centimetre as the unit of length, the gram as the unit of mass, and the second
as the unit of time.
● FPS (foot-pound-second) system:
This system is based on a variant of the metric system based on the foot as
the unit of length, the pound as the unit of mass, and the second as the unit
of time.
● MKS (metre-kilogram-second) system:
This system is based on a variant of the metric system based on the metre
as the unit of length, the kilogram as the unit of mass, and the second as
the unit of time.
An international system of units (SI):
The system of units that is internationally accepted for measurement is
abbreviated as SI units.
They are:
Physical quantity Name of the unit Symbol
Length metre m
Mass kilogram kg
Time second s
Electric current ampere A
Temperature kelvin K
Amount of substance mole mol
Luminous intensity candela cd
Plane angle radian rad
Solid angle Steradian sr
Radian and steradian:
● Radian is the angle subtended at the centre of a circle by an arc equal in
length to the radius of the circle.
● Steradian is the solid angle subtended at the centre of a sphere by that
sphere's surface, which is equal in area to the square of the sphere's radius.
Practical units:
Practical Units Values
1AU11
1.496 10 m
1 light-year15
9.46 10 m
1 parsec16
3.08 10 m
1 micron6
10 m
1 angstrom10
10 m
1 fermi15
10 m
1 amu27
1.66 10 m
1 lunar month 29.5 days
1 solar day 86400 s
4
Conversion factors:
● To convert a physical quantity from one set of units to the other, the
required multiplication factor is the conversion factor.
● Magnitude of a physical quantity = numerical quantity*unit
● It means that the numerical value of a physical quantity is inversely
proportional to the base unit.
Example: 1m = 100cm = 3.28ft = 39.4inch
Dimensional analysis:
● Dimensions of a physical quantity are the powers to which the base
quantities are raised to represent the quantity.
● Dimensional formula of any physical quantity is that expression which
represents how and which of the basic quantities with appropriate powers
in square brackets.
● The equation obtained by equating a physical quantity with its dimensional
formula is called a dimensional equation.
Examples:Displacement
Velocity Time
1Dimension of length
Dimension of time
v LT
Other examples:
Physical Quantity Dimensional Formula SI Unit
Area2
L2
m
Volume3
L3
m
Density3
ML3
kgm
Frequency1
T Hz or1
s
Speed/Velocity1
LT 1
ms
Force2
MLT N
Acceleration2
LT 2
ms
Strain0 0 0
M L T No units
Surface tension2
MT 1
Nm
Torque2 2
ML T 1
Nm
Critical velocity1
LT 1
ms
Specific heat capacity2 2 1
L T K 1 1
Jkg K
Electric field3 1
MLT A 1
NC
Inductance2 2 2
ML T A H or Henry
Fluid flow rate3 1
L T 3 1
m s
Note: Other units are derived from their respective formulas
Applications:
● To check the dimensional correctness of a given physical relation.
● To convert a physical quantity from one system of units to the other
Example:
Pressure is given by the formulaF
P A
Thus the dimensional formula of pressure is2 1 2
2
F MLT
P ML T
A L
In SI units, 1 Pascal =2
kgms .
In CGS units, 1 Pascal =2
gcms .
Class XI Physics www.vedantu.com 6
Thus,1 2
1 pascal 1 1 1
1 CGS pressure 1 1 1
kg m s
g cm s
13 2
10 10 10CGS pressure
Therefore, 1 Pascal = 10 CGS pressure
● Deducing relationships among the physical quantities
● To find the dimensions of constants in a relation
Limitations:
● If dimensions are given, the physical quantity may not be unique as
many physical quantities have same dimensions.
● Numerical constants [K] having no dimensions, cannot be deduced by
the method of dimensions.
● The method of dimensions cannot be used to derive relations other than
the product of power functions.
● The method of dimensions cannot be applied to derive a formula if a
formula depends on more than 3 physical quantities.
Principle of homogeneity:
Principle of homogeneity on dimensions states that the dimensions of equations
of each term on both sides of an equation must be the same i.e. LHS = RHS policy
in dimensions.
Example:
Consider the formula:2
mv
F r
for centripetal acceleration
We have the dimensions:2
mv
F r
21
2 M LT
MLT L
2 2
MLT MLT
Thus, the formula is dimensionally correct according to the principle of
homogeneity.
Errors in measurements:
The difference between the true value and the measured value of a quantity is
known as the error of measurement.
Classification:
● Systematic errors: Systematic errors are errors whose causes are known.
They can be either positive or negative. They are further classified as:
1. Instrumental errors
2. Environmental errors
3. Observational errors
● Random errors: Random errors are errors caused due to unknown
reasons. Therefore they occur irregularly and are variable in magnitude and
sign conventions.
● Gross error: Gross error arise due to human carelessness and mistakes in
reading the instruments or calculating and recording the measurement
values and results.
Representation of errors:
● Absolute error: The difference in the magnitude of the true value and the
measured value of a physical quantity is called absolute error.
Absolute error = True value – Measured value
● Mean absolute error: The arithmetic mean of absolute error is called
mean absolute error.
● Relative error: The ratio of mean absolute error to the true value is called
Relative error.a
r a
Where the numerator is absolute error and denominator is the true
value.
● Least count: The smallest value of a physical quantity measured
accurately with an instrument is called the least count of the measuring
instrument.
Accuracy and precision:
● The accuracy is a measure of how close the measured value is to the true
value.
● Precision tells us to what resolution or limit the quantity is measured by
the measuring instrument, which is done by calculating the least count.
Significant figures:
All accurately known digits in measurement plus the uncertain digit together form
significant figures.
Rules:
● All non-zero digits are significant
● All zeros between two non-zero digits are significant.
● If the number is less than one, the zeros on the right of the decimal are
significant, but to the left are not significant.
● If a number is non-decimal, the terminal zeros are non-significant.
● If a number with a solution decimal point and trailing zeros are significant.
● If the ending number is more than 5, we round off to the next number, and
less would be the same number.
Example:
● 3.200 has 4 significant figures
● 0.008 has 1 significant figure
● 6.87 is rounded off to 6.9.
Points to remember:
● The quantities that describe the laws of physics are called physical
quantities. In physics, a physical quantity is defined as a system that can be
quantified and measured using numbers.
● Types of physical quantities are fundamental and derived quantities.
● Unit is the quantity of a constant magnitude used to measure the magnitude
of other quantities holding the same behaviour.
● Types of units are fundamental and derived units.
● A complete set of fundamental and derived units for all kinds of physical
quantities is called a system of units.
● A complete set of fundamental and derived units for all kinds of physical
quantities is called a system of units.
● Some of them are: FPS, CGS and MKS systems.
● The system of units, which is internationally accepted for measurement, is
abbreviated as SI units.
● Some of the SI units are: m, kg, cm, candela etc. and many other units.
● Magnitude of a physical quantity = numerical quantity*unit
● Dimensions of a physical quantity are the powers to which the base
quantities are raised to represent the quantity.
Class XI Physics www.vedantu.com 9
● Dimensional formula of any physical quantity is that expression
representing how and which of the basic quantities with appropriate powers
in square brackets.
● The equation obtained by equating a physical quantity with its dimensional
formula is called a dimensional equation.
● It is used to check a physical quantity, convert a quantity from one system
to another, Derive relationships between physical quantities etc.
● Principle of homogeneity: The principle of homogeneity on dimensions
states that the dimensions of equations of each term on both sides of an
equation must be the same, i.e. LHS = RHS policy in dimensions.
● The difference between the true value and the measured value of a quantity
is known as the measurement error.
● Types: Absolute error, Mean absolute error, Relative error, Percentage
error.
● The smallest value of a physical quantity measured accurately with an
instrument is called the least count of the measuring instrument.
● The accuracy is a measure of how close the measured value is to the true
value.
● Precision tells us to what resolution or limit the quantity is measured by
the measuring instrument, which is done by calculating the least count.
● All accurately known digits in measurement plus the uncertain digit
together form significant figures.
Formulas used:
● Absolute error: True value – Measured value
●a
r a
where r is relative error
● Mean absolute error:0
i
iM a
● Percentage error:0 100
a
r a
● If X=p q r
A B C or in any form, Then propagation of error is:x A B C
p q r
x A B C
.