## Chapter 2 Units and Measurement

**Chapter 2 Units and Measurement** available here. These notes are based on latest **CBSE Class 11 Physics syllabus 2017-18** and NCERT textbook for Class 11 Physics. With these chapter wise key notes, you can easily understand the concepts. These Class 11 Physics Notes on Units and Measurements are also important for 11^{th} Physics exams and various medical and engineering entrance examinations. These notes are continuation of **Class 11th Physics Notes: Units and Measurement (Part – I)**. In part I, we have studied the following topics: Physical quantities, Units (Meaning), Fundamental (or Base) units & Derived units, System of Units, The international system of units, SI System of Units, SI units of 7 Fundamental & 2 Supplementary Physical Quantities.

Now, in this part of Class 11 Physics Chapter wise revision notes on Units and Measurement (Part II) are:

Order of Magnitude |

Measurement of length |

Direct Method |

Indirect Method
• Parallax method • Echo method |

Range of variations of length |

Measurement of Mass |

Range of Masses |

Measurement of Time |

The notes are given below:

**Order of Magnitude:**

Order of magnitude gives us the value nearest to the actual value, in terms of suitable powers of 10. (It does not tell us the absolute value of the quantity).

To express a number in nearest power of 10, a number less than 5 is treated as 1 and a number between 5 and 10 is treated as 10

Example: Radius of earth is 6.4 ×10^{6} m. Taking 6.4 as 10, size of the earth is of the order of 10^{7}m.

**Measurement of length:**

There are two ways to measure length or distances

(*i*) Direct method (*ii*) Indirect method

*Direct Method:*

• A metre scale for distances from from 10^{‒3} m to 10^{2} m

• A verner calipers for distance upto 10^{‒4} m

• A screw gauge and a spherometer for distances upto 10^{‒5} m

*Indirect method for measuring large distances:*

Some indirect methods to measure large distances are:

**Parallax method**

This method is used to measure distances of planets which are very far away from earth.

When a man holds a pen in front of him against some specific point on the background (a wall) and look at the pen first through his left eye A (closing the right eye) and then look at the pen through his right eye B (closing the left eye), he would observe that the position of the pen seems to change with respect to the point on the wall. This is called **parallax.**

The distance between the two points of observation is called the **basis.** In this example, the basis is the distance between the eyes.

*The situation mentioned above is shown in the figure given below*

As the planet is very far away, (*b*/*D*) << 1, and therefore, θ is very small.

Then we approximately take AB as an arc of length *b* of a circle with centre at S and the distance *D*as

The radius *AS* = *BS* so that AB = *b *= D θ where θ is in radians or we can write D = *b*/ θ

*Some other indirect methods used to measure long distances are:*

**Echo method:**

An echo is the phenomenon of repetition of sound on reflection from an obstacle.

Here, a sound wave is sent to the obstacle and we observe the time it takes to return.

Suppose, distance between source producing the sound and the object is *x*, then, the total distance sound wave covered is going and coming back will be 2 *x.*

As we know, speed = (distance covered) / (Time taken) or speed of sound = (2*x*) / Time taken.

Other methods for measurement of distances, based on the same principle are:** Laser method**, **RADAR method**, **SONAR method**.

*Indirect method for measuring very small distances or length:*

A simple method for estimating the molecular size of oleic acid is given below. Oleic acid is a soapy liquid with large molecular size of the order of 10^{–9} m.

The idea is to first form mono-molecular layer of oleic acid on water surface.

• We dissolve 1 cm^{3} of oleic acid in alcohol to make a solution of 20 cm^{3}.

• Then, we take 1 cm^{3} of this solution and dilute it to 20 cm^{3}, using alcohol.

• So, the concentration of the solution is equal to [1/(20×20)] cm^{3} of oleic acid/cm^{3} of solution.

• Next we lightly sprinkle some lycopodium powder on the surface of water in a large trough and we put one drop of this solution in the water.

• The oleic acid drop spreads into a thin, large and roughly circular film of molecular thickness on water surface.

• Then, we quickly measure the diameter of the thin film to get its area *A*.

• Suppose we have dropped *n* drops in the water.

• Initially, we determine the approximate volume of each drop (*V* cm^{3}).

• Volume of *n* drops of solution = *nV* cm^{3}

• Amount of oleic acid in this solution = [*nV*] [1/(20×20)] cm^{3}

• This solution of oleic acid spreads very fast on the surface of water and forms a very thin layer of thickness *t*. If this spreads to form a film of area *A* cm^{2}, then the thickness of the film

*t* = (volume of the film) / (area of the film) or t = [*nV*/(20×20*A*)] cm

If we assume that the film has mono-molecular thickness, then this becomes the size or diameter of a molecule of oleic acid. The value of this thickness comes out to be of the order of 10^{–9} m.

**Range of variations of length:**

The sizes of the objects in the universe vary over a very wide range. Some examples are given in table given below:

**Measurement of Mass**

Mass is a basic property of matter. It does not depend on the temperature, pressure or location of the object in space. The SI unit of mass is kilogram (kg).

While dealing with atoms and molecules, we use another important standard unit of mass, called the unified atomic mass unit (u), which has been established for expressing the mass of atoms as

1 unified atomic mass unit = 1u = (1/12) of the mass of an atom of carbon-12 isotope (^{12}C_{6}) including the mass of electrons = 1.66 × 10^{–27} kg

Small masses of commonly available objects can be determined by a common balance (the one used in shops).

Large masses in the universe like planets, stars, etc., based on Newton’s law of gravitation can be measured by using gravitational method (will be discussed in further chapters).

Measurement of small masses of atomic/subatomic particles etc., is done by mass spectrograph technique in which radius of the trajectory is proportional to the mass of a charged particle moving in uniform electric and magnetic field.

**Range of Masses**

The masses of the objects, we come across in the universe, vary over a very wide range. Some examples are given below in the table

**Measurement of Time**

For measurement of any time interval, we need a clock. Any phenomenon which repeats itself after a fixed interval can serve the purpose of a clock.

Atomic clock: We now use an atomic standard of time, which is based on the periodic vibrations produced in a cesium atom. This is the basis of the cesium clock, sometimes called atomic clock, used in the national standards. It is highly accurate.

Other clocks, for example, wrist watch, pendulum clock etc., loose and gain time due to the effect of temperature, pressure and variation of acceleration due to gravity, so they are not considered as accurate.

In view of the tremendous accuracy in time measurement, the SI unit of length has been expressed in terms the path length light travels in certain interval of time (1/299, 792, 458 of a second).