# Length, mass and time measurements:

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## Measurement of Length

When we talk about the magnitude of a quantity, most of the time it is sufficient to know about the order of magnitude of that quantity instead of knowing its absolute value. For example, velocity of light is 3 × 108 ms-1. But in rough figures, most of the time we consider only the order of magnitude, i.e. 108 ms-1.

The order of distances varies from 10-14 m (radius of nucleus) to 1025 m ( radius of the Universe ). To measure these distance, there are two main methods :

• Direct methods

• Indirect methods

### Direct methods

In direct methods, we compare the distance or length to be measured with the chosen standard of length.

In direct method a length of about 10-5 m to 102 m can be measured. For this  metre scale or metre rod, screw gauge and slide callipers can be used. A metre rod can measure distances as small as 1 mm, a vernier calliper can measure upto 0.1 mm and a screw gauge  upto 0.01 mm.

### Indirect methods

To find very small lengths or very large distances, we often use indirect methods. Following are indirect method to measure these distances :

### 1.Parallax method :

Measurement of distances of stars or planets cannot be possible directly with a metre scale. So we use the parallax method in such cases.

suppose you hold a pencil in front of you against some specific point on the background (a wall ) and look at the pencil, first through your left eye, say A ( closing the right eye) and then look at the pencil through your right eye, say B (closing the left eye). you will  notice here that the position of the pencil seems to change with respect to the point on the wall, this is called parallax. The distance between the two points of observation ( here between two eyes I e.  AB ) is called basis

To measure the distance D of a planet or a star, say S, by the parallax method we observe it from two different positions (observatories) A and B on the earth, separated by a distance AB ( here, AB = b ) at the same time as shown in the figure Use of Parallax method to find distance

In the figure, ∠ASB represented by the symbol θ, is called parallax angle or parallactic angle.

As the planet is so far, so the angle θ is very small. Hence we can consider the length AB between two points on earth as an arc of length b of a circle with centre at S and radius D. For this can we can get easily from equation

θ = b / D

or      D =  b / θ,

By knowing the value of b and θ on earth we can easily find the distance of planets or stars from earth.

### 2. Measurement of very small length : size of a molecule :

An Electron microscope can be used to measure the distances of atomic orders i.e. upto 10-10 m. You can also use two different methods to find that distances of this order :

According to this hypothesis, the actual volume occupied by the atoms in 1 gram of a substance is two-third of the volume occupied by 1 gram of the substance.

By using this hypothesis, we can easily get the radius of an atom of the substance (you will learn about the explanation of this formula in further classes) and is given by

r  =  ( M / 2 πNρ )

here ρ is the density of the substance,

M is molecular weight and N is avagadro's number.

Size of a molecule of a liquid :

A simple method to estimating molecular size of oleic acid is mentioned here. It has a large molecular size of the order of 10-9 m.

Suppose a solution of known concentration of oleic acid in alcohol is prepared. To prepare a solution of 1 /500 concentration (suppose), co 1 cm3 of oleic acid is dissolved in 500 cm3 of alcohol. Then  some lycopodium powder is sprinkled in the surface of the water and Nn drops of this solution are poured in the surface of water. Oleic acid drop will spread into a thin and roughly circular film. The area A of the film is measured carefully by using tracing paper.

If v is the volume of each drop of oleic acid, then

Now, if v is the volume of a drop of oleic acid solution, then volume of oleic acid in n drop of solution is

= nv × ( 1 / 500 )

If t is the thickness of the film of oleic acid of surface area A, then

If we consider here that the film of oleic acid was stretched in such a way that it has the thickness of one molecule only, then above expression for t gives the diameter of one molecule of oleic acid.

Important units of lengths to be remembered :

• 1 fermi        =  1 f  = 10-15 m

• 1 angstrom = 1 Å = 10-10m

• 1 astronomical unit = 1 AU

= 1.496 × 1011 m

• 1 light year = 1 ly = 9.46 × 1015 m

• 1 parsec     =  3.08 × 1016 m

### Measurement of Mass :

Mass is the basic property of matter. It does not depend upon temperature, pressure and position of the given object in space. A wide range of mass is to be measured in this physical world. As we studied earlier in the chapter - physical world. It ranges from 10-31 kg ( i.e.  mass of electron ) to 1055 kg (i.e.  mass of universe ).

The SI unit of mass is kg. And we can use common balance as available in the shops to measure the  mass of any object. But use of kg is not preferable while measuring mass of atoms and molecules. In that case we use another standard unit called unified atomic mass unit (u) as

1 unified atomic mass unit = 1 u

= (1/12) of the mass of an atom of Carbon-12 isotope.

• Mass of such atomic or subatomic particles are done by using mass spectrograph, in which radius of trajectory is proportional to the mass of a charged particle moving in uniform electric and magnetic field

• Measurements of heavy masses like mass of planets or stars are done by using Newton's law of Gravitation.

### Measurement of time :

For the measurement of any time interval, a clock is used. These clocks can be of different types. Actually any phenomenon that repeats itself periodically can be regarded as a clock.

Mostly the atomic clock is used in national standard. It is also called the Cesium clock. It is based on the periodic vibrations produced in Cesium atom. These clocks are very accurate. A cesium atomic clock is also used at the National Physical Laboratory ( NPL), New Delhi to maintain the Indian standard of time( IST).