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Example : Distance, mass, time, speed, density etc.
These quantities can be added according to
Physics is a branch of science in which we
ordinary algebraic rules.
study the laws of nature. In this branch the
nature and its laws are described

Vector quantities :
quantitatively and qualitatively. The
The physical quantities which can be
quantitative study of nature involves the
described completely only by both their
estimation and measurement of various
magnitude and direction are called vectors.
physical quantities like distance, weight
temperature etc.
Example : Force, velocity, acceleration etc.

Addition of these quantities can be done by
Physical quantity :
special methods of addition.
The quantities which can be defined and
Ex. parallelogram etc.
measured are called physical quantities.

Example : Force, distance, time, current etc.
Fundamental law of vector and addition
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Derived quantities and their units :
The laws of physics can be described in
terms of these physical quantities.

The physical quantities are classified into two
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categories - fundamental quantities and
Measurement of physical quantities and
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their units :
Measurement is a method of comparison of 
an unknown quantity with a standard
quantity. This fixed or definite quantity which
we take as a standard and by the help of
which we can measure other quantities of
the same kind is defined as the unit.
Fundamental quantities :
The measure of a physical quantity is
expressed in two parts, namely the magnitude
and the unit. e.g., when we say force is 12
newton, force is the physical quantity, 12 is
the magnitude and newton is the unit of force. 
temperature, luminous intensity and
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derived quantities.
The physical quantities that do not depend
on any other physical quantity for their
measurement are called fundamental
quantities.
Mass, length, time, electric current,
amount of substance are the fundamental
quantities.
Derived quantities :
The physical quantities that are derived from
Scalar quantities :
the fundamental quantities are called the
The physical quantities which can be
described completely by their magnitude only
are called scalar quantities.
derived quantities.
Area, volume, density, force, velocity etc.
are some examples of derived quantities.

Rules followed in writing units :
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
The symbol for a unit, which is named after (i)
a scientist, should start with an upper case
letter.
Example : Newton-N, Joule-J, Pascal-Pa,
Kelvin-K etc.

F.P.S. system : In this system, the units of
mass, length and time are pound, foot and
second respectively.
(ii)
C.G.S. system : In this system, the units of
mass, length and time are gram, centimetre
and second respectively.
The symbol for a unit, which is not named
after a person, is written in lower case.
(iii)
Example : Metre-m, mole-mol, second-s.
M.K.S. system : In this system, the units

of mass, length and time are kilogram, metre
and second respectively.
In their full form the units should start with
(iv)
a lower case letter.
S.I. (System International units) : This
system is an improved and extended version
Example : Newton, metre, joule, second, hertz etc.
of M.K.S. system. This system defines

Symbol of a unit should not be in plural
form.
seven fundamental quantities and two
supplementary quantities.
Example : 500 metres should be written as 500 m
and not 500 ms.
S.No.
Wrong notation
Ns
Ks
Mols

Correct notation
N
K
mol
Symbol
metre
m
kilogram
kg
Time
second
s
Electric current
ampere
A
5
Temperature
kelvin
K
6
Luminous intensity
candela
cd
7
Amount of substance
mole
mol
8
Angle
radian
rad
9
Solid angle
steradian
sr
Some derived quantities
S.I. units
Symbol
Force
newton
N
Work
joule
J
Frequency
hertz
Hz
Charge
coulomb
C
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Example : Unit of torque-N m (or) N.m
Length
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A compound unit (obtained from units of
two or more physical quantities) is written
either by putting a dot or leaving a space
between symbols of two units.
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S.I. Units
1
Quantity
Mass
Unit of impulse-N s (or) N.s
Pole strength of magnet-A m (or) A.m

The denominators in a compound unit should
be written with negative powers.
Example :
–3
Unit of density is kg m , not kg/m

3
Unit of acceleration is m s–2, not m/s3

Definitions of units :
Systems of Units :
(i)
Metre : One metre is 1,650,763.73 times
the wavelength of orange light emitted by a
The following systems of units are in common
use
krypton atom at normal pressure.
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(ii)
One kilogram is the mass of a
certain cylinder made from an alloy of
platinum-iridium, maintained at 0°C, in the
International Bureau of Weights and

Measures.
K
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a
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The quantity of the three fundamental
quantities mass, length and time are denoted
by M, L and T respectively.
:
Definition : The powers to which the units
of fundamental quantities mass, length and
time are raised to obtain the unit of a physical
quantity is known as dimensions of the given
quantity.
(iii)
Second : One second is the time taken by
a cesium atom (Cs133) to complete 9, 192,
631, 770 vibrations.
(iv)
Ampere : The ampere is that current which, Example : Unit of density of a body
if maintained in two straight parallel
unit of mass

 kg m 3
conductors of infinite length, of negligible
unit of volume
Here, mass appears once is the numerator
circular cross-section, and placed 1 metre
and length appears thrice in the denominator.
apart in vacuum, would produce between
Thus the dimensional formula of density is
these conductors a force equal to 2 × 10–7
[M1 L–3 T0]. Since the physical quantity time
newton per metre of length.
is not involved in th density, its exponent is
Kelvin : Kelvin is the fraction 1/273.16 of
shown as zero.
the thermodynamic temperature of the triple
Thus in density the dimension of mass = 1,
point of water.
the dimension of length = – 3 and the
dimension of time = 0.
Mole : Mole is the amount of substance of
(v)
(vi)
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a system, which contains as many elementary
entities as there are atoms in 0.012 kilogram
1.
of carbon-12.
Sol.
Candela : Candela is the luminous intensity,
in a given direction, of a source that emits
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monochromatic radiation of frequency
540 × 1012 hertz and that has a radiant
intensity in that direction of 1/683 watt per
steradian.

Examples
What is the dimensional formula of force?
Force = mass × acceleration
Unit of force = unit of mass × unit of
acceleration
unit of length
(unit of time) 2
Dimensional formula = [M L T–2]
= unit of mass 
2.
Dimensions of physical quantities :
The nature of any physical quantity can be Sol.
described by mentioning the powers to
which the fundamental units are raised to
give the unit of the given quantity.
Write the dimensional formula of speed.
distance length

time
time
In the unit of speed the unit of mass does
not appear, thus its dimension is zero.
Speed 
 [Speed]  [M 0 L1 T 1 ]
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
Dimensional formula and SI units of some physical quantities
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Section - A

1.
2.
3.
4.
Objective Type Question :
Which of following unit is different from
others?
(a) Mass
(b) Length
(c) Time
(d) Density
9.
10.
India adopted metric system of units in -
11.
5.
6.
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The SI unit of luminous intensity (a) ampere
(b) candela
(c) mole
(d) none of these
(b) 6.67 × 10–11
(c) 6.67 × 10–12
(d) 6.67 × 10–13
(a) 1960
(b) 1956
(c) 1947
(d) none of these
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(a) mass
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(b) length
(c) time
(d) temperature
Unit of length in the F.P.S. system is (a) foot
(c) metre
(d) none of these
14.
SI unit of temperature is (a) kelvin
(b) second
(c) mole
(d) candela
SI unit of electric current is (a) ampere
(b) candela
(c) mole
(d) none of these
(a) 6.67 × 10–10
(b) pound
Amount of substance in the SI system of
units is represented by (a) candela
(b) mole
(c) weight
(d) kilogram
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(d) 2000
In the F.P.S. system, Pound is the unit of -
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(c) 1956
SI units were introduced in -
12.
Numerical value associated with a physical
quantity is (a) directly proportional to the unit selected
(b) inversely proportional to the unit selected
(c) independent of the unit selected
13.
(d) directly proportional to the square of the
unit selected
(b) 1950
Value of gravitational constant in C.G.S.
unit is 6.67 × 10–8. What would be its
numerical value in S.I. unit?
Which of the following unit is different from
others?
(a) Speed
(b) Density
(c) Force
(d) Time
Light year is the unit of (a) time
(b) distance
(c) speed of light
(d) intensity of light
(a) 1947
15.
How many fundamental units are present in
the SI system of units?
(a) 5
(b) 6
(c) 7
(d) 3
There are two different quantities A and B
having different dimensions. Then which of
the following operation is dimensionally
correct?
(a) A + B
(b) A – B
(c) A / B
(d) eA / B
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
FIll in the blanks :
16.
S.I. unit of luminous intensity is ________.
17.
Mole is the ________ of a system.

True or False :
18.
Electric current is a derived quantity.
19.
The dimensional formula of work is [ML2T–2].
20.
Section - B

Subjective Type Questions :
1.
Identify the derived physical quantities
Velocity, Mass, Acceleration, Speed, Length,
Temperature, Force, Energy, Work,
Momentum, Charge, Current, Mole, Stress,
Pressure, Luminous Intensity, Time, Area.
Dimension of potential energy and work is
2.
Find the SI unit of (1) volume, (2) force.
3.
Find the dimensions of
same.
(a) linear momentum, (b) frequency and (c)
pressure.

Match the column :
21.
Suppose force (F), area (A) and time (T)
4.
Find the dimensions of Planck’s constant h
from the equation E = hv where E is the
energy and v is the frequency.
5.
Taking force, length and time to be the
fundamental quantities find the dimensions
of
are the fundamental units, then match the
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following :
Column-A
Column-B
(A) Work
(P) [A1/2 T–1]
(B) Moment of Inertia (Q) [FA1/2]
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(R) [F A1/2 T2]
(C) Velocity
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(a) density,
(b) pressure,
(c) momentum and
(d) energy.
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Q. N .
Ans .
Q. N .
Ans .
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a
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b
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a
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b
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c
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b
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c
16. candela (Cd)
17. amount of substance
21. A  Q, B  R, C  P
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18. False
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b
19. True
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b
20. True
Section - B
1.
2.
5.
Velocity, Acceleration, Speed, Force, Energy, Work, Momentum, Charge, Stress, Pressure, Area.
(1) m3, (2) kg m/s2 3.
(a) MLT–1 (b) T–1 (c) ML–1T–2
4.
ML2T–1
(a) FL–4T2 (b) FL–2 (c) FT (d) FL
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