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FOUNDATION
IN
SCIENCE
PHYSICS-A
1
NIRWANA COLLEGE
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CHAPTER-1
2
Physical Quantities
Contents:-
1. Physical Quantities and the types
2. Dimensions
3. Principle of homogeneity
4. Scalars & Vectors
5. Uncertainty
6. Summary
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PhysicalQuantities
Base
Quantities
Derived
Quantities
3
Physical Quantities:-
It is a quantity, which is used to measure something.
Eg:- length, area, volume, speed, weight, temperature, electriccurrent«etc.
Unit System:-
Types:-
Base Quantities:-
Several physical quantities are chosen to become base quantities
particularly for the Unit system. There are 7 base quantities in
general.
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Some examples of derived quantities:-
Derived
quantities
Defining equation Base quantities
used
Derived
units Area length × breadth length m2
Volume length × breadth ×
height
length m3
Speed rate of change of
distance
length , time m s-1
Acceleration rate of change of
velocity
length , time m s-2
Force mass × acceleration mass, length , time kg m s-2 / N
Momentum mass × velocity mass, length , time kg m s-1
Work force × distance mass, length , time kg m2
s-2
/ J
o Two different derived quantities may have the same unit.
Eg: Both Pressure and Yung·s modulus have same unit of Pascal.
o Some derived quantities do not have units at all.
Eg: refractive index and tensile strain do not have units.
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o Some times a constant of proportionality has unit. Its unit can be
deduced from the equation in which that constant appears.
Eg: The universal gravitational constant G has unit.
Dimensions:-
The dimensions of the base quantities together with the way thesebase quantities are combined will determine the dimensions of the
derived quantities.
Symbols:-M (mass)
L (length)
T (time)
(temperature)
N (amount of substance)
A (current)
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Dimensional expression:-
A quantity X in mechanics, for example, speed, momentum, kineticenergy«etc, normally involves with mass, length and time only. Hence,
its dimensions can be expressed in the following way.
[X] = Mx Ly Tz
Where x, y, z are dimensionless quantities.
Dimensionless quantity:-
o A physical quantity may not have dimension. It is said to be
dimensionless.
o A dimensionless quantity does not have unit.
o For example refractive index of a material is dimensionless and has
no unit.
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Quantity Dimensions Quantity Dimensions
Length [L] Force [MLT-2]
Area [L2] Pressure [ML-1 T2]
Volume [L3] Energy/ work [ML2 T-2]
Density [ML-3] Power [ML2 T-3]
Speed [LT-1] Electric charge [IT]
Acceleration [LT-2] Electric potential
difference
[ML2 T-3 I-1]
momentum [MLT-1] Electric resistance [ML2 T-3 I-2]
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Principle of homogeneity:-
All terms appearing on both sides of an equations (i.e. left and right
sides) may have the same dimensions.
o If this is true then the equation is said to be dimensionally
homogenous.
Use:- This principle can be used to determine whether an equation
is correct or not. If the equation is dimensionally nothomogenous , then the equation is in correct.
Scalars and vectors:-
Scalar:- Its is a quantity which has magnitude but no direction.
Eg: length, volume, time, mass, density, speed, pressure, work,
energy, gravitational potential, temperature, electrical
potential«etc.
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Vectors:-
A vector is a physical quantity which has both magnitude anddirection.
Eg:- displacement, velocity, acceleration, force, momentum,
impulse, gravitational field strength«etc.
Uncertainty:-
A measured value of a physical quantity (like length, mass) is not exact
because it has some uncertainty.
Eg: we use a meter ruler to measure the length of a small square
box. The measured value of the length might have been
recorded as 32mm. It does not mean that the length is exactly
32mm long. Using a meter ruler, we can only measure length
to the nearest 1mm because we can read a millimeter scale to
the nearest 1mm. Hence we believe the length to be between
31mm and 33mm and not exactly 32mm.
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Precision:-
The uncertainty in a measured value can be reduced if we use a
more sensitive instrument to measure the quantity.
A measured value having lesser uncertainty than another value
(which is recorded using a less sensitive instrument) is said to be
more precise.
Eg: Referring to the small square box mentioned above, we
might have used a vernier caliper to measure its length. A vernier caliper is more sensitive than a meter ruler in
terms of length measurement.
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Systematic uncertainty:-
Systematic errors are uncertainties which occur when we carry out
measurements which result in the measured values being consistently
higher or lower than the true values.
Some sources of systematic errors:-
oZ
ero errors may be found in instruments such as vernier calipersand micrometer screw gauges.
o Parallax errors might have been consistently committed by
students while reading scales.
o Environmental factors may be the cause, like a light breeze
constantly blowing downward on a sensitive scale balance.
o
The scale of an instrument might have been wrongly calibrated.
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o Suppose we attach a 50 g load to a spring and measure the
extension of the spring. We remove the load and then attach it
back to the spring again in order to repeat the measurement
might be slightly different due to the presence of some random
factors.
o Suppose we place a glass rod on a meter ruler to measure its
length. We remove the rod from the ruler, place it back and
measure again. We might get a slightly different value because
we could never repeat exactly the way we obtained the previous
reading.