Measurements

Units and Measurements
If n is the numerical value and u is the unit then ;

Q = nu

n1u1 = n2u2( bigger the unit, smaller is the value )

Systems of Measurement
SI

MKS - meter, kilogram , seconds

CGS - centimeter, gram , seconds

FPS - foot, pound , seconds

Fundamental Units
Mass - kilogram - M

Length - meter - L

Time - seconds - T

Temperature - Kelvin - K

Current - Ampere - I/A

Luminous Intensity - Candela - C

Amount of Substance - mole - mol

Methods of Measurement
For measuring distance of stars, planets , we use the parallax method. For determining mass of planets, we use gravitational methods. For the measurement of masses of atomic species, mass spectrographs are used. For accurate measurement of time, we use atomic clocks based on the vibrations produced in a Cesium - 133 atom.

Dimensional Analysis
Dimensional Analysis deals with the powers to which the unit of a physical quantity is raised to.

Uses of Dimensional Analysis :
 * 1) To check the correctness of an equation
 * 2) To find the conversion factor
 * 3) To find the dimensions by comparison method

Significant Figures
In order to understand significant figures, we must try to understand and accept that no measurement can be accurate. For example, when the Least count of a measuring instrument is 0.01 m , it will give us accurate readings up to 0.01 m only , measurements smaller than 0.01 m cannot be measured by it. This means that no matter how small the least count of the measuring instrument is, there will always be an error of order one less up to 10-∞.

Thus, we need to decide the accuracy , which is enough to give a good idea of the quantity.

For example, a person's height is 1.62 m ; but the measurement is accurate only up to 3 digits or 3 significant figures. The actual height could be 1.61927457634752641 m (even this would have an error beyond least count) .But 3 digits is enough to give a good amount of idea about a person's height. Thus, we measure it with 3 significant figures.

Order of Magnitude
Order of Magnitude is the power to which 10 is raised to ; to indicate the size of the quantity.

Personal Error
Error occurring due to human errors.

Random Error
Error occurring due to random changes in the environment of the experiment.

Systematic Error
Error occurring due to a constant error in the readings of instrument. This is caused due to the faulty calibration of instrument.

Instrumental Error
Error occurring due to faulty construction of instrument.

Error Analysis
Mean Value       :       Average of All readings

Absolute Error    :     Individual Reading - Mean Value

Mean Absolute Error  :   Average of all Absolute values

Relative Error     :        Mean Absolute Error / Mean Value

Percentage Error   :      Relative Error x 100

1) If xn, then Error is multiplied by n

2) The errors in the measurement of two quantities are added when the two quantities are multiplied or divied.

if xy ; then add the errors

3)If the quantities are added or subtracted, then the errors are added.

Tips and Tricks

 * 1) Use dimensional analysis to eliminate options . Try to match dimensions.