Physical Quantites

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FOUNDATION

IN

SCIENCE

PHYSICS-A

1

NIRWANA COLLEGE



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



PhysicalQuantities

Base

Quantities

Derived

Quantities

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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.

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Physical Quantites