## Physics and Measurement Notes PDF in English for Class 11, NEET and JEE Exams

Physics and Measurement Notes PDF: Find below the important notes for the chapter, Physics and Measurement as per the NEET and JEE Physics syllabus. This is helpful for aspirants of NEET and JEE and other exams during last-minute revision. Important notes for Physics and Measurement Notes PDF cover all the important topics and concepts useful for the exam. ## Physics and Measurement Notes PDF

The comparison of any physical quantity with its standard unit is called measurement. To measure a physical quantity like length, mass and time we require a standard of measurement. This standard of measurement is called the unit of that physical quantity.

Physical Quantities
Those quantities which can describe the laws of physics are called the physical quantity. A physical quantity is one that can be measured. Thus, length, mass, time, pressure, temperature, current and resistance are the physical quantities. The physical quantities that are independent of each other are called fundamental quantities. All the other quantities which can be expressed in terms of the fundamental quantities are called the derived quantities.

Unit
The unit of a physical quantity is an arbitrarily chosen standard which is widely accepted by the society and in terms of which other quantities of similar nature may be measured.

Properties of Unit

• The unit should be of some suitable size
• The unit must be well-defined
• The unit should be easily reproducible at all places
• The unit must not change with time
• The unit should not change with physical conditions like temperature, pressure etc.
• The unit must be easily comparable experimentally with similar physical quantities.

Types of Units

• Fundamental Units: The units defined for the fundamental quantities are called fundamental units.
• Derived Units: The units of all other physical quantities which are derived from the fundamental units are called the derived units.

Systems of Units: Earlier three different units systems were used in different countries. These were CGS, FPS and MKS systems. Now-a-days internationally SI system of units is followed. In SI unit system, seven quantities are taken as the base quantities.

• FPS System: In this system, the unit of length is foot, unit of mass is pound and the unit of time is second.
• CGS System: In this system, the units of length, mass and time are centimetre, gram and second, respectively.
• MKS System: In this system, the unit of length, mass and time are meters, kilogram and second, respectively.
• SI System: This system is widely used in all measurements throughout the world. The system is based on seven basic units and two supplementary units.
 Quantity Unit Symbol of the unit Length metre m Mass kilogram kg Time second s Temperature kelvin K Electric current ampere A Number of particles mole mol Luminous intensity candela cd

Supplementary Units
There are two supplementary base units.

• Radian (rad): The radian is the angle subtended at the centre of the circle by the arc whose length is equal to the radius of the circle.
• Steradian (Sr): The steradian is the solid angle subtended at the centre of a sphere by a spherical surface of an area equal to the square of its radius.
 Quantity Unit Symbol of the unit Plane angle radian rad Solid angle Steradian sr

Measurement of Mass
Mass can be defined usually in terms of kg but a unified atomic mass unit (u) will be used for atoms and molecules. Mass of planets is measured by the use of gravitational methods and mass of atomic particles are measured by the usage of the mass spectrograph (radius of trajectory will be proportional to the mass of charged particle which is in motion in uniform electric and magnetic field), apart from using balances for normal weights.

Measurement of Time
Time has been calculated by the use of a clock. Atomic standard of time being now used, measured by the Cesium or Atomic clock, as a standard.

• A second will be equivalent to 9,192,631,770 vibrations of radiation from the transition between two hyperfine levels of an atom of cesium-133 in a Cesium clock.

• The caesium clock will be working on the vibration of the Cesium atom which is identical to vibrations of quartz crystal in a quartz wristwatch and balance wheel in a normal wristwatch.

• National standard time and frequency will be maintained by 4 atomic clocks. Indian standard time will be maintained by a Cesium clock at National Physical Laboratory (NPL), New Delhi.

Error
The measured value of the physical quantity is usually different from its true value. The result of every measurement by any measuring instrument is an approximate number, which contains some uncertainty. This uncertainty is called error. Every calculated quantity, which is based on measured values, also has an error.

Causes of Errors in Measurement

• Least Count Error. The least count error is the error associated with the resolution of the instrument. Least count may not be sufficiently small. The maximum possible error is equal to the least count.
• Instrumental Error. This is due to faulty calibration or change in conditions (e.g., thermal expansion of a measuring scale). An instrument may also have a zero error. A correction has to be applied.
• Random Error. This is also called chance error. It makes to give different results for same measurements taken repeatedly. These errors are assumed to follow the Gaussian law of normal distribution.
• Accidental Error. This error gives too high or too low results. Measurements involving this error are not included in calculations.
• Systematic Error. The systematic errors are those errors that tend to be in one direction, either positive or negative. Errors due to air buoyancy in weighing and radiation loss in calorimetry are systematic errors.

Dimensions
The dimensions of a physical quantity are the powers to which the fundamental units of mass, length and time must be raised to represent the given physical quantity.

Characteristics of Dimensions

• Dimensions do not depend on the system of units.
• Quantities with similar dimensions can be added or subtracted from each other.
• Dimensions can be obtained from the units of the physical quantities and vice versa.
• Two different quantities can have the same dimension.
• When two dimensions are multiplied or divided it will form the dimension of the third quantity.

Dimensional Formula

• The dimensional formula of a physical quantity is an expression telling us how and which of the fundamental quantities enter into the unit of that quantity.
• It is customary to express the fundamental quantities by a capital letter, e.g., length (L), mass (AT), time (T), electric current (I), temperature (K) and luminous intensity (C). We write appropriate powers of these capital letters within square brackets to get the dimensional formula of any given physical quantity.

Units and dimensions of a few derived quantities

 Physical Quantity Unit Dimensional Formula Displacement m M0L1T0 Area m2 M0L2T0 Volume m3 M0L3T0 Velocity ms-1 M0L1T-1 Acceleration ms-2 M0L1T-2 Density Kg m-3 M1L-3T0 Momentum Kg ms-1 M1L1T-1 Work/Energy/Heat Joule (or) Kg m2/sec2 M1L2T-2 Power Watt (W) (or) Joule/sec M1L2T-3 Angular velocity rad s-1 M0L0T-1 Angular acceleration rad s-2 M0L0T-2 Moment of Inertia Kg m2 M1L2T0 Force Newton (or) Kg m/sec2 M1L1T-2 Pressure Newton/m (or) Kg m-1/sec2 M1L-1T-2 Impulse Newton sec (or) Kg m/sec M1L1T-1 Inertia Kg m2 M1L2T0 Electric Current Ampere (or) C/sec QT-1 Resistance/Impedance Ohm (or) Kg m2/sec C2 ML2T-1Q-2 EMF/Voltage/Potential Volt (or) Kg m2/sec2 C ML2T-2Q-1 Permeability henry/m (or) Kg m/C2 MLQ-2 Permittivity Farad/m (or) sec2C2/Kgm3 T2Q2M-1L-3 Frequency Hertz (or) sec-1 T-1 Wavelength m L1

Defects of Dimensional Analysis

• While deriving the formula the proportionality constant cannot be found.
• The equation of a physical quantity that depends on more than three independent physical quantities cannot be deduced.
• This method cannot be used if the physical quantity depends on more parameters than the number of fundamental quantities.
• The equations containing trigonometric functions and exponential functions cannot be derived

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