What is Physics and its Scope??
Answer:
Physics is the branch of science that deals with the study of matter and energy, and their mutual relationship.
Or
Physics is the branch of science that involves the study of the physical world in the specific and the physical universe in general: energy, matter, and how they are related.
Or
The branch of science that deals with the study of modeling the natural world with theoretical & mathematical descriptions.
Or
The word physics is derived from the Greek word "physica" which means "nature" so the study of nature is called physics
Scope of Physics:
Physics is based on experimental observations, and quantitative measurement and is concerned with the fundamental laws of the universe. Therefore, physics is the most basic branch of the physical sciences.
Like electrons around the nucleus, all the other subjects of physical science are revolving around physics. We depend on Physics for nearly everything. From walking to driving a car, from cooking to using a gadget, from cutting a tree to building a new house everything involves physics. Physicists investigate the motions of electrons and rockets, the energy in sound waves and electric circuits, the structure of the proton, and the universe.
Physics a fundamental Science:
Physics is the fundamental science because the other branches of natural science like chemistry, astronomy, geology, and biology are constrained by the laws of physics. We can say 'All other natural sciences stem from physics'.
Use of Physics in the development of Technologies:
Physics is essential in the development of technology. It generates fundamental knowledge needed for future technological advances to drive further the economic engines of the world. So many key findings and discoveries of the 2016 century that include the laser, television, radio, computer technology plus internet, DNA, and nuclear weapons are all credited to advancement in physics. Physics provides the technical infrastructure and provides the necessary personnel needed to utilize scientific advances and discoveries.
What is System International (SI) and write its significance?
Answer:
The International System (SI) of Units is a scientific method of expressing the magnitude or quantities of important natural phenomena.
This system was established by the international committee of scientists in 1960 in Paris, France. The International Committee agrees on a set of definitions and standards to describe the physical quantities.
The International System is abbreviated as "SI" i.e. Systeme Internationale, the French version of the name)
In earlier times scientists around the world were using a different system of units for their liking. Three such Systems are
1. MKS (Meter, kilogram second)
2. CGS (Centimeter, gram second)
3. FPS (British System) (Foot, Pound second)
System International is built on three types of units, Base units, derived units, and Supplementary units
Significance of SI:
1. It's used throughout the world.
2. It is easy for trading internally & externally.
What are Physical quantities?
Answer:
Science requires quantities that must be defined and measured. So, All those quantities that can be defined and measured e.g length, mass, time, temperature, current, speed, force, electric flux, etc. are called Physical Quantities.
On the other hand love, hate, smile, beauty, etc can't be measured so these are all not science or physical quantities.
What are Base Quantities?
Answer:
A complete set of units for all physical quantities is called a system of units. However, to form a system we do not need to define every quantity, we take only a few quantities (called base quantities) and base units to agree on accessible and invariable standards for measurement such that all other quantities and units are expressed in terms of those quantities.
The minimum number of quantities in terms of which other physical quantities can be defined (ie which is the base for other physical quantities) are called Base Quantities.
In SI, Seven physical quantities are chosen arbitrarily as base quantities. These are Length, mass, times current, thermodynamics temperature, amount of Substance, and luminous intensity.
All The base quantities are Scalar except Electric Current which is a "tenser quantity"
What are Derived Quantities?
Answer:
The physical quantities other than base quantities are called derived quantities.
or
Those physical quantities that can be expressed in terms of base quantities are called derived quantities.
It may be a vector or Scalar.
e.g. Speed, force, electric flux, pressure, work, etc are derived quantities.
Define Base units, Derive Units, and Supplementary Units:
Answer:
The unit associated with the base quantities is called the Base Unit
Or
The units which can't be derived from other units and are based on other Units are called Base units: (m, kg, Second, A, K, cd, and mol )
Derived Units:
SI Units that are derived from the base and supplementary units are called derived units.
Or
The units which are associated other than base and supplementary quantities eg: N, J, W, pa, C, etc.
Supplementary Unit:
Pure geometrical units (Radian and Steradian) were classified by the system international (SI) as supplementary units. But this designation was abrogated (nullified) in 20th CGPM ( French: Conférence Générale des Poids et Mesures) abbreviated from General Conference on weight and measurement in 1995 and units were grouped as derived units.
Define Radian and Steradian,
Answer:
Radian:
The most natural way to measure the angle θ is not a degree but a radian. It is a two-dimensional plane angle and it is defined as, " the angle (θ) subtended at the center of the circle by an arc with a length equal to the radius of that circle", as shown in the figure and it is equal to the ratio between the lengths of the arc and radius. It is denoted by 'rad'.
 |
Let the angle "θ", which is subtended by an arc of length "S" along a circle of radius "r" then;
θ = `\ frac {S}{r}`(rad) -------(1)
For one revolution.
Length of the boundary of the circle (S) = circumference of the circle = 2Ï€r
by putting values { S = 2Ï€r } in equation (1)
θ = `\frac {2πr}{r}` = 2π rad
This shows that
Numbers of radians in One revolution = 2Ï€ rad
= 2ｘ 3.1416 rad
= 6.2832 rad
There are a little more than 6 radians in one full rotation.
⇒ From equation (1)
S = r θ ---------------(2)
Again using equation (1) when the length of the arc is equal to the length of the radius of that circle i.e. S = r
θ = `\frac {r}{r}` = 1 rad (shown the figure above)
Steradian:
Steradian is a three-dimensional solid angle and is defined as " the angle subtended at the center of the sphere, by which the surface area of the sphere is equal to the square of the radius of that sphere", as shown in the figure below and it is equal to the ratio between the subtended spherical area to the square of the radius. It is denoted by 'sr'.
Angle θ = `\frac {(Spherical'area)}{r^2}`(sr)
But the spherical area = 4Ï€r²
θ = `\frac {4πr^2}{r^2}` (sr)
θ = 4π (sr) ------------ (1)
θ = 4ｘ 3.1416 (sr)
θ = 12.5664 (sr) -------------(2)
Equations (1) and (2) show that there are 4Ï€, or approximately 12.5664, steradians in a complete sphere.
Derive a Relation between degrees and radians
Answer:
 |
For one complete rotation, there are 360°
Degrees in one revolution = 360° ---------(1)
and
Numbers of radians in 1 revolution = Circumference of the circle ➗ Radius of that circle
Numbers of radians in 1 revolution = `\frac {2Ï€r}{r}`
Numbers of radians in 1 revolution = 2Ï€ rad --------(2)
we know that number of degrees in one revolution is equal to the number of radians in one revolution, so
2Ï€ rad = 360°
1 rad = `\frac {360°}{2Ï€}`
1 rad = `\frac {360°}{2ｘ 3.1416}`
1 rad = 57.3° the required relation between radians and degrees
How many radians are there in one degree?
Answer:
The number of radians in one degree:
We know that
57.3° = 1 rad
1° = `\frac {1}{57.3°}` rad
or
1° = 0.01745 rad ---------Ans
Related Example:
Show 35° in radians
Solution:
As we know that
1° = 0.01745 rad
so
35° = 0.01745 x 35 rad
35° = 0.595 rad --------------Ans
How many radians are there in a circle or the Number of radians in One Revolution?
Answer:
We know that
Numbers of radians in 1 revolution = Circumference ➗ Radius
Numbers of radians in 1 revolution = `\frac {2Ï€r}{r}`
Numbers of radians in 1 revolution = 2Ï€ rad
Numbers of radians in 1 revolution = 2ｘ 3.1416 rad
Numbers of radians in 1 revolution = 6.2832 rad
There are a little more than 6 radians in one full rotation.
Numbers of radians in 1 revolution = Circumference ➗ Radius
Numbers of radians in 1 revolution = `\frac {2Ï€r}{r}`
Numbers of radians in 1 revolution = 2Ï€ rad
Numbers of radians in 1 revolution = 2ｘ 3.1416 rad
Numbers of radians in 1 revolution = 6.2832 rad
There are a little more than 6 radians in one full rotation.
Definition of 7 SI Base Units (Meter, Kilogram, Second, Ampere, Kelvin, Mole, and Candela)
1. Metre (m):
It is the base unit of length in the International System of Units (SI), having the unit symbol 'm'.
Definition:
One Metre is the distance between the two points of alloy rod/bar of Platinum (90%) and Indium (10%) placed under controlled conditions in Paris (France)
or
or
The length of the path traveled by light in a vacuum during a time interval of 1/299,792, 458 of a second.
2. Kilogram (kg):
It is the base unit of mass in the International System of Units (SI), having the unit symbol 'kg'.
Definition:
The mass of 1 liter of water at 4°C.
or
The mass is equal to the mass of slandered Platinum-Indium Cylinders ( 90% platinum % 10% Iridium). This cylinder is about 3.9 cm high and 3.9 cm in diameter.
3. Second (s):
It is the base unit of time in the International System of Units (SI), having the unit symbol 's'.
Definition:
The 1/86400 part of the average day of the year.
or
The duration that the light takes to travel is 299,792,458 meters of distance in a vacuum.
or
4. Ampere (A):
It is the base unit of electric current in the International System of Units (SI), having the unit symbol 'A'.
One Ampere is the electric current that would need to pass through two parallel conductors placed one meter apart producing a force of 2x10⁻⁷ N/m.
or
One ampere is an electrical current equivalent to 10¹⁹ elementary charges passing every 1.602176634 seconds.
One ampere of current represents one coulomb of electrical charge (6.24 x 10¹⁸ charge carriers) moving past a specific point in one second.
5. Kelvin (K):
It is the base unit of temperate in the International System of Units (SI), having the unit symbol 'K'.
One Kelvin is equal to the `\frac {1}{100}` part of the difference between the melting point of ice and the boiling point of water.
Or
One Kelvin is equal to `\(frac {1}{273.16})^{th}` part of the thermodynamic temperature of the triple point of water ( 273.16K)
Triple point temperature: The temperature at which all the three states of matter co-exist at equilibrium or thermodynamically same.
6. Mole (mol):
It is the base unit of the 'amount of substance' in the International System of Units (SI), having the unit symbol 'mol'.
The mole is the amount of substance of a system that contains as many elementary particles as there are in 0.012 kg of C-12.
7. Candela (cd):
It is the base unit of 'luminous intensity' in the International System of Units (SI), having the unit symbol 'cd'.
The candela is the luminous intensity, in the perpendicular direction, of a surface of 1 / 600 000 square meters of a black body at the temperature of freezing platinum under a pressure of 101,325 Newton per square meter.
or
The candela is the luminous intensity in a given direction of a source that emits monochromatic radiation of frequency 540 x 10¹² Hz.
What is Scientific Notation?
Answer:
A Standard form to represent very big or very small numbers using the power of ten is called Scientific notation.
It is done by converting the number in terms of some power of ten (10) multiplied by a number that lies between 1 and 10 (called Mantissa) (i.e. one non-zero digit should be written at the left side of the decimal point.)
Example: The number of molecules in one mole is 602,300,000,000,000,000,000,000 (larger value) and can be represented in scientific notation as 6.023 x 10²³. Similarly, for smaller values let the radius of the hydrogen atom (0.000,000,000,053 m) = 5.3 x 10⁻¹¹ m
Assignment:
Convert the following numbers into scientific notation.
i. 3000 g ii. 0.00002345 m iii. 0.0001 s
What are Prefixes? Explain
Answer:
The magnitude of physical quantities varies over a wide range. When the value of the physical quantities is very large or very small then it is difficult to express them in terms of the fundamental units. For this, some specific letters are used before the fundamental units. So "The letters used with a fixed value in the form of power of Ten (10) before the fundamental units are called prefixes.
or
The mechanism at which the scientific notation is expressed in the proper name of the power of 10 is called prefixes.
The Prefixes Table is given below.
What are Significant Figures? State the Rules for determining the number of Significant figures:
Answer:
Significant Figure (SF):
In the measurement, the accurate known digits and the first doubtful digit are called Significant figures.
Explanation:
The measurement of physical quantities made by related instruments often involves some errors or uncertainties. These uncertainties are due to the following factors:
(ii) Quality and condition of the apparatus
(iii) Skill of the observer
(iv) Different recorded observations by the same apparatus.
In the presence of these complications, the reported result contains both certain and uncertain digits and the total number of all these certain and uncertain digits are known as significant figures.
Example:
Let the mass of a sphere measured is 1.53 kg. In this case, 1 and 5 are certain digits while 3 is uncertain and the measured value has three significant figures.
Similarly, the length of a simple pendulum measured is 102.5 cm, this value has four significant figures, the digits 1, 0, and 2 are certain while 5 is uncertain.
Rules for determining the number of significant figures:
I. All the non-zero digits (1,2,3,4,5,6,7,8,9) are significant. e.g. 1735 has 4 significant figures.
II. Zero may or may not be significant and it is explained as;
a) All the zeros between two non-zero digits are significant, whether the decimal point exists or does not exist. e.g. 20035, 2.0035, 20.035, in all these cases significant figures are five.
e.g. 6000 Kg can be written as.
6 x 10³ Kg (1 Significant figure)
6.0 x 10³ Kg (2 Significant figures)
6.00 x 10³ Kg (3 Significant figures)
3.040 x 10³ Kg (4 Significant figures)
c) Zero to the right of a non-zero digit in a number without a decimal point is NOT significant. e.g. 2000 has 1 significant figure.
d) When the value is assigned to the measurement (i.e value with fundamental units), it's then counted as SF. e.g. 2000 m has 3 SF.
e) The terminate zero in a number with a decimal point is significant.
e.g. 0.2300, 0.1540, 3.600 All these three numbers have four significant figures each.
d) If the number is less than one, the zero on the right of the decimal point and to the left of the "non zero digits" is not significant, e.g. 0.00123 in this case zeros are not significant and the number of significant figures is three, i.e. 0.00123 = 1.23 x 10⁻³.
III. No change occurs in the number of significant figures by changing the units of the measured value. c.g. 23.15 mm = 2.315 cm = 0.02315 m
All these numbers have four significant figures each.
IV. When two or more measurements are added or subtracted, the result is as precise as the least precise of the quantities. After adding or subtracting, the result should be rounded to the least number of decimal places (DP) as given in the input given number. Some example
+ 23.24 (2DP) - 172.49 (2DP) + 172.49 - 1.3 (1DP)
2378.47 (2DP) 15 427.51 (2DP) 1 5772 (0DP) 12.4 (1DP)
6.9 (2SF) 29.21 (4SF) 10.0 (3SF)
123.1 (4SF) ➗ 23 (2SF) = 5.4 (2SF)
Keep the same number of significant figures as the factor with the least.
(Remember the least S.F in Multiplication or Division)
What is the difference between Precision, and Accuracy?
Answer:
Precision: In the measurement, the precise value is one whose values are close to each other (observer Values). For example:
Observers A, B, and C measured the length of a table which is 10.35 m, 10.50 m, and 11.00 m respectively. But the actual length of the table is 14 m.
So the observer's values are close to each other, so it's called précised values.
⇒ The precise measurement is one that has the least absolute uncertainty.
⇒ The precise measurement depends upon the instrument used in the measurement.
⇒ The instrument with the smaller least count has greater precision and accuracy in the merriment.
Accuracy: In a measurement, accuracy means how much the observable value is close to the actual value.
Example: The actual value of the length of the table is 14 cm. Observers A, B, and C measured the length of the table which is 12.08 cm, 13.05 cm, and 14.50 cm respectively, which is close to the actual value.
⇒ An accurate value is one that has less fractional or percentage uncertainty.
⇒ Accuracy of measurement depends upon the number of significant figures. Greater SF will give us a more accurate value.
What is an Error in measurement? Explain Types of Error:
Answer:
Error:
The difference between the actual value and the observed value is called an error. Or Error is the doubt that exists in the result of any measurements.
The error occurs due to:
i) Negligence or inexperience
ii) The faulty apparatus
ii) inappropriate method.
Types of Errors:
Errors are classified as:
1. Systematic Error
2. Random Error:
1. Systematic Error:
The error is made in one direction either positive or negative. These are of two types.
a) Instrumental Error: The error occurs due to zero error of the instrument or incorrect marking.
b) Personal Error: The error occurs due to inexperience, lack of knowledge, or carelessness in the experiment setup or apparatus.
Random Error:
If the repeated measurement of a quantity gives a different value under the same condition, the error is called Random Error.
The random error occurs due to some unknown cause.
What is Uncertainty in measurement? Explain its Types and Rules with examples:
Answer:
Uncertainty:
The estimate of the possible range of an error in any measurement is called Uncertainty.
OR
The magnitude of error in the measurement 0r doubt in the measurement is called uncertainty.
⇒ Uncertainty estimates small or large the error is given by .
Measurement = Best Estimate ± Uncertainty
Types of uncertainty:
Absolute uncertainty:
The least count of the measuring instrument is called Absolute Uncertainty. It's denoted by "Δ" and has the same unit as the quantity.
Fractional Or Relative Uncertainty:
Relative uncertainty = Absolute error / Measured Value
It is denoted by " ε " and has no unit
Percentage uncertainty:
% uncertainty = fractional uncertainty x 100%
% uncertainty = (Absolute uncertainty / Measured value) x 100%
Rules for Uncertainty:
(1) Addition and Subtraction:
For the Assessment of total uncertainty in the final result of addition and subtraction, absolute Uncertainty is added.
Example: Find displacement between points X₁ = 10.5 ± 0.1 cm & X₂ = 26.8 ± 0.1 cm
Given :
X₁ = 10.5 ± 0.1 cm
X₂ = 26.8 ± 0.1 cm
Required:
displacement = X = ?
Solution:
X = X₂ - X₁ = (10.5 ± 0.1 cm) - (26.8 ± 0.1 cm)
x = 16.3 ± 0.2 cm
(2) Multiplication and Division:
In the multiplication and division, the percentage uncertainty is added in the final result for the assessment of total uncertainty
Example:
if the potential difference of V= 5.2 ± 0.1V is applied across the ends of the conductor, and as the result the current I = 0.84 ± 0.05 passes through the conductor. Determine the resistance.
Given:
Potential difference V = 5.2 ± 0.1 V
Current I = 0.84 ± 0.05
Required:
Resistance R =?
Solution:
By Using Ohm's law
V = I R
or
R = `\frac {V}{I}`
by putting a best estimate
R = `\frac {5.2}{0.84}`
R = 6.2 Ω
Now
% uncertainty in V = `\frac {0.1}{5.2}` X `\frac {100}{100}`
% uncertainty in V = 2 %
% uncertainty in I = `\frac {0.05}{0.84}` X `\frac {100}{100}`
% uncertainty in I = 6 %
So therefore % uncertainty in R = 2% +6% = 8 %
So Resistance R = 6.2 Ω with 8% uncertainty
R = 6.2 ± 8% Ω
R = 6.2 ± `\frac {8}{100}` Ω
R = 6.2 ± 0.08 Ω
(3) Power factor:
In order to find out the total uncertainty in the measurement having an exponent, we multiply the percentage uncertainty by the power.
Example: Find out the volume of a sphere whose radius 2.25 ± 0.01 cm?
Given:
Potential difference r = 2.25 ± 0.01 cm
Required:
Volume V = ?
Solution:
The volume of the sphere
V = `\frac {4}{3}`ã„«r³
V = `\frac {4}{3}`x (3.1416) (2.25)³
V = 47.7 cm³
Now % uncertainty in r = `\frac {0.01}{2.25}` X `\frac {100}{100}`
% uncertainty in r = 0.4 %
and
% uncertainty in V = 3 x 0.4 % = 1.2 %
V = 47.7 cm³ with 1.2% uncertainty
V = 47.7 ± 1.2% cm³
V = 47.7 ± `\frac {1.2}{100}` cm³
V = 47.7 ± 0.6 cm³
(4) Uncertainty in the Average value of many measurements:
The uncertainty on the average value of many measurements as equal to the mean deviation.
Example:
The six measurements were taken of the diameter of the wire using a Screw gauge which is 1.20, 1.22, 1.23, 1.19, 1.22, 1.21. Determine the uncertainty in the final result?
Solution:
Measurement (in mm) = 1.20, 1.22, 1.23, 1.19, 1.22, 1.21
Average diameter of wire = `\frac {1.20+1.22+1.23+1.19+1.22+1.21}{6}`
The average diameter of wire = 1.21 mm
Deviation of each measurement from (Average diameter of wire = 1.21 mm ) is
(0.01, 0.01, 0.02, 0.02, 0.1, 0)
so
Mean deviation = `\frac {0.01+0.01+0.02+0.02+0.1+0}{6}` = 0.01
Thus
Uncertainty in the mean value of deviation is = 0.01 mm
Hence diameter of wire is = 1.21 ± 0.01 mm
(5) Uncertainty in Timing Experiment:
The uncertainty in the time period of a body is found by dividing the least count of the timing devices by the number of Vibrations.
Example:
The Simple Pendulum completes 30 vibrations in 54.6 sec. The least count of Stopwatch is 0.1 sec. Find out uncertainty in the time period of the Simple pendulum.
Given data:
Time for 30 Vibrations = 54.6 sec
To find:
T = ?
Solution:
By unitary method
Time is taken for 30 Vibrations = 54.6 sec
Time taken for 1 vibration T = `\frac {54.6}{30}`
T =1.82 sec
Uncertainty = Least count / Total No of Vibration
Uncertainty = `\frac {0.1}{30}`
Uncertainty = 0.003 sec
Thus
T = 1.82 ± 0.003 sec
What is Dimension ?, Write its Uses, Drawback, and Terms used with Dimension
Answer:
Dimension:
To express any physical quantity in terms of specific symbols of corresponding base quantities written within a square bracket is called Dimension.
Or
The Specific Symbols used to express the base quantities and written within the square bracket is called dimension.
e.g.
Dimension of length = [L]
Dimension of Time = [T]
Advantages of Dimension:
(1) Conversion from one system of units to another.
(2) To test and validate the correctness of a physical formula.
(3) To derive the relationship between different physical quantities.
The drawback of Dimension:
(1) For dimensionless quantities, the nature of quantities cannot be decided whether it's vector or scalar.
(2) The relationship among Physical quantities having exponential, logarithmic and trigonometric functions can't be established.
(3) It can't find the value of the proportionality constant m in the equation.
(4) The dimension of a physical quantity is not unique. i.e. if the dimension is [ML²T⁻²] is the given dimension, it may be a dimension of work or energy.
Dimension of Acceleration:
As acceleration a = `\frac {v}{t}`
Its dimension will be
[a] = `\frac {[v]}{[T]}`
since [v] =[LT⁻¹] as v = `\frac {S}{t}`
[a] = `\frac {[LT⁻¹]}{[T]}`
or
[a] = [LT⁻²]
Dimension of θ :
As
S = r θ
or
θ = `\frac {S}{r}`
[θ] = `\frac {[L]}{[L]}`
[θ] = 1
It means Angle is a dimensionless quantity.
Terms used with Dimension:
(1) Dimensional variable:
The physical quantity that has a dimension but its magnitude is variable (changing).
e.g. Force, Acceleration, etc
(2) Dimensional Constant:
The Physical quantity that has a dimension but a constant magnitude
e.g. plank's constant (h), gravitational constant G, etc.
(3) Dimension-less Variable:
Physical quantities that have no dimension but their magnitude are varying.
e.g. Solid Angle, plane Angle, strain
4) Dimensionless Constant:
The physical quantity that has no dimension but constant magnitude e.g. π, 1002, etc.
 Physics Unit-1, Measurement Complete Notes ( SLO based Physics Notes)){kind=link}
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