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Physics Measurements Notes for JEE Main 2015 by ednexa.com
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9011041155 / 9011031155
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Measurements
Physics
Physics is a branch of science which deals with study
of natural phenomenon of non-living things.
Origin “fuses”
Physical quantities
The quantities which can be measured with physical
apparatus or physical means are called physical
quantities.
e.g.mass Length
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Time Temperature
etc.
Physical quantities are expressed in terms of
magnitude and unit.
Non – physical quantities
The quantities which cannot be measured with physical
apparatus or no physical apparatus is available for their
measurement are called non-physical quantities.
e.g. Intelligence of a person, happiness etc.
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Measurement
Measurement of a physical quantity is its careful and
accurate comparison with the standard of that quantity.
Unit
The standard used for comparison of a physical
quantity is called unit of that quantity.
e.g. 1kg
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Magnitude
Magnitude of a physical quantity is the number which
indicates how many times the unit is contained in it.
e.g. 10 litres
The physical quantities are classified in to two
types
1. Fundamental quantities :- The physical quantities
which can be independently measured and
expressed are called fundamental quantities. Thus,
these quantities can be measured and expressed
without taking help of other quantities.
e.g. length, mass, time, temperature etc.
Fundamental units :- The units of the fundamental
quantities are called fundamental units.
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e.g. metre, kilogram, second etc.
Fundamental quantities
i. length Metre (m)
ii. mass Kilogram (kg)
iii. time Seconds (s)
iv. temperature Kelvin (K)
v. Electric current Ampere (A)
vi. Luminous
Intensity
Candela (cd)
viii. Amount of
substance
Mole (mol)
Supplementary Quantities
i. Plane angle → Radian → rad
ii. Solid Angle → Steradian → sr
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iii. Frequency → 1/t = 1/s = Hertz (Hz)
2. Derived quantities :- The physical quantities which
require two or more fundamental quantities for their
measurement and expression are called derived
quantities.
e.g. speed, acceleration, force etc.
Derived units :- The units of derived quantities are
called derived units.
e.g. m/s, m/s2, newton etc.
Requirements of good units
1. The unit should be easy to use and read.
2. Its magnitude should not change with respect to
time, temperature, place and observer.
3. It should be easily reproducible. It means, it should
be easy to copy and can be produced anywhere
any quantity.
4. It should be acceptable worldwide.
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(universally acceptable )
System of units
The fundamental units together with all derived units
form a system of units. Formerly there were different
unit systems used in different countries. Some of the
most common unit systems were as follows :-
1. C.G.S.
2. M.K.S.
3. F.P.S.
4. S.I.( System International ) :- To avoid difficulties
in inter conversions of units and to have uniformity
in the units used all over the world, General
Conference of weights and Measures suggested an
improved metric system called System International
in 1960. It was accepted by I.S.O.( International
Standards Organization ) in 1962. This includes all
the fundamental units from M.K.S. and over 450
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derived units. As far as possible the units are
named after renowned scientists to honour them.
Before the introduction of S.I. exchange of
information between the scientists of different
countries was difficult because of the difference
between the unit systems used by them. With the
worldwide use of S.I. this difficulty is removed.
Now in this common language of units, scientists
engineers and technicians all over the world can
exchange their ideas, criticism easily. So, this
system has bridged-up the gap between them.
Rules of writing S.I. units
1. metre, joule, newton
Metre, Joule,Newton
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2. cm, m/s, J, N
Cm, M/s, j, n etc.
3. singular form only. plural form of units:- not allowed,
e.g. While speaking, we may say that the mass is
100 kilograms,
but while writing, we should write 10kg only and
not 10kgs.
4. No punctuation marks
e.g. the unit newton metre should be written as Nm
and not like N-m or N,m etc. m/s is a valid unit
because the slash (/) is not a punctuation mark. It is
a mathematical operator.
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Dimensions
Increasing the power of fundamental units to find out
units of derived quantities is known as dimensions.
1.
0 1 1
displacementVelocity
Time
VT
[ M L T ] m / s
l
2. Area = ℓ2
= [ M0 L
2 T
0] = m
2
3. Volume = ℓ3
= [ M
0L
3T
0] = m
3
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4.
2
0 1 2 2
V / TAcceleration
T T
T
M LT m / s
l
l
5. Force = ma
= m × ℓ / T2
= [ M1L
1T
-2] = kg m / s
2 = N
6. Work = F . ℓ
= ma . ℓ
= m . ℓ / T2 . ℓ
= m . ℓ2 / T2
= [ M1 L
2 T
-2] = kg . m / s
2 = J
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7.
2
2
2 2
1 1 2 2
ForcePr essure
Area
ma
m. / T m
.T
M L T kg m / s
l
l
l l
8.
2
21 2 3 2 3
3
WorkPower
Time
F .
T
ma .
T
m . / T .
T
mM L T kgm / s w
T
l
l
l l
l
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9. P.E = mgh
2
1 2 2 2 2
m. / T .
M L T kgm / s J
l l
10.
2
2 2
1 2 2 2 2
1K.E mv
2
1m. / t
2
[M L T ] kgm / s J
l
11. Impulse = F.T
= ma . T
= m . ℓ / T2 . T
2
1 1 1
m. . T
T
MLT kg m / s Ns
l
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12. Momentum = mv
= m . ℓ / T
= [ M1 L
1T
-1 ]
= kg m / s
13.
3
1 3 0 3
massDensity
Volume
m
M L T kg/m
l
M = [ M1L
0T
0]
ℓ = [ M0L
1T
0]
T = [ M0L
0T
1]
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Uses of dimensional analysis
1. To check correctness of equation.
principle of homogeneity:- It states that dimensions
towards both sides of equation for each term are
same. Then the given equation is dimensionally
correct.
For e.g.
1. 21s ut at
2
s is displacement
u = initial velocity
t = time
a = acceleration
L.H.S = ∴ S = [ M0L
0T
1] ….. (1)
R.H.S
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∴ ut = [ M0L
1T
-1] [ M
0L
0T
1]
= [ M0L
1+0T
-1+1]
= [ M0L
1T
0] …… (2)
21at
2 = [ M
0L
1T
-2] [ M
0L
0T
1]2
= [ M0L
1T
-2] [ M
0L
0T
2]
= [ M0L
1T
0] …….. (3)
From (1), (2) & (3) we can say that the given
equation is dimensionally correct.
2. v2 = u
2 + 2as
3. v = u + at
4. w = w0 + mc2
w = work
w0 = work
m = mass
c = speed of light
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2. To find out conversion factor in between different
units of same quantity .
e.g.1 Let MKS unit of force if Newton (N)
CGS unit of force is Dyne
Let 1 N = x dyne
Substituting dimensions of force in above
equation,
1 1 2 1 1 2
1 1 1
1 1 2
1 1 1
1 1 2
2
M L T x M LT
M L Tx
M LT
kg m s
2g cm s
3 2
3 2
5
5
10 10 cmg
g cm
10 10
x 10
1N 10 dyne
1 J = x erg
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e.g.2
v = u + at
v = final velocity
u = initial velocity
a = acceleration
t = time
L.H.S = v
∴ v = [ M0L
1T
-1] ……… (1)
R.H.S = u
∴ u = [ M0L
1T
-1] ……… (2)
R.H.S at = [ M0L
1T
-2] [ M
0L
0T
1]
= [ M0L
1T
-1] ………… (3)
From (1), (2), (3) we can say that the given
equation is dimensionally correct.
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e.g. 3
v2 = u
2 + 2as
v = final velocity
u = initial velocity
a = acceleration
s = displacement
L.H.S = v2
∴ v2 = [ M
0L
1T
-1]2
= [ M0L
1T
-1] …….. (1)
R.H.S = u2
∴ u2 = [ M0L
1T
-1]
2
= [ M0L
2T
-2] …….. (2)
as = [ M0L
1T
-2] [ M
0L
1T
0]
= [ M0L
1+1 T
-2+0]
= [ M0L
2T
-2] …….. (3)
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From (1), (2), & (3) we can say that the given
equation is dimensionally correct.
e.g.4
w = w0 + mc2
w = work
w0 = work
m = mass
c = speed of light
L.H.S = w
∴ w = [ M1L
2T
-2] ……… (1)
R.H.S = w0 + mc2
w0 = [ M
1L
2T
-2] ……… (2)
mc2 = [ M
1L
0T
0] [ M
0L
1T
-1]2 = [M
1L
0T
0] [M
0L
2T
-2]
= [M1L
0+2 T
0-2] = [M
1L
2T
-2]
From (1), (2), & (3) we can say that the given
equation is dimensionally correct.
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1 J = x erg
Substituting dimensions of energy in above
equation
1 2 2 1 2 2
1 1 1
1 2 2
1 1 1
1 2 2
2 2
M L T x M L T
M L Tx
M L T
kg m secx
2 2g cm sec
2
23 10 cm10g
g
cm
∴ x = 103 × 10
4 ∴ x = 107
∴ 1 J = 107 erg
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