MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
  • Kinematics & Rotational Motion
  • OFFERED PRICE: Rs. 636
  • View Details
Get extra Rs. 127 off
USE CODE: CART20

Measurement of Length

 

Table of Content


Length

Length is defined as the measurement or extent of something from one end to the other end. Length is a scalar quantity and we find it in Lengthalmost every fundamental phenomenon in the physical world.

Every experiment in Physics requires the use of length to get desired results. All the external physical measurements rely on length. As an example take your height. How will you measure your height? What is your height? Height is simply the distance between your feet and head. To measure the height you can use either a scale or measure stick.

We need a unit to define the length of something as without unit we won’t be able to compare measure or correlate two objects on the terms of their length. The standard unit of Length is a meter, but being a small unit we refer to big units to make measurements simple. Some examples of the unit are:

  • Height is measured in “foot” and “inches”, 1 feet contains 12 inches, and 1 inch means 0.0254 meters

  • Distance is measured in kilometers, 1 kilometer or Km equals to 1000 meter

  • While performing experiments in Physics lab we prefer small units like millimeter and centimeter, 1 meter = 100 centimeters, and 1 centimeter = 10 millimeters, to avoid writing meter, again and again, we write centimeter as cm, millimeter as mm and decimeter as dm

Metric Conversion Chart
Into Metric Out of Metric
If you know Multiply by To Get If you know Multiply by  To Get
Length Length
Inches 2.54 Centimeters  Millimeters 0.04 Inches
Foot 30 Centimeters Centimeters 0.4 Inches
Yards 0.91 Meters Meters 3.3 Feet
Area Area
Sq. Inches 6.5 Sq. Centimeters Sq. Centimeters 0.16 Sq. Inches
Sq. Feet 0.09 Sq. Meters Sq. Kilometers 0.4 Sq. Miles
Sq. Miles 2.6 Sq. Kilometers Hectares 2.47 Acres
Mass (Weight) Mass (Weight)
Ounces 28 Grams Grams 0.035 Ounces
Pounds  0.45 Kilograms Kilograms 2.2 Pounds
Short ton 0.9 Metric Ton Metric Tons 1.1 Short Tons
Volume Volume
Teaspoons 5 Milliliters Milliliters 0.03 Fluid Ounces
Tablespoons 15 Milliliters Liters 2.1 Pints
Fluid Ounces 30 Milliliters Liters 1.06 Quarts
Cups 0.24 Liters Liters 0.26 Gallons
Pints 0.47 Liters Cubic Meters 35 Cubic Feet
Quarts 0.96 Liters Cubic Meters 1.3 Cubic Yards
Cubic feet  0.03 Cubic Meters      
Cubic Yards 0.76 Cubic Meters      
Temperature  Temperature
Fahrenheit Subtract 32, then multiply by 5/9 ths to get Celsius Celsius Multiply by 9/5ths, then add 32 to get Fahrenheit

We measure length in certain units, according to our preference which makes our measurement more precise and accurate. Units are always chosen to make measurements simple and to make it error free.
 

Measurement of Length

We know some direct methods of measuring length. There are several kinds of instruments we use to measure the length of objects. For example, when we were kids we used centimeter scale to draw lines and measure the length of small objects. When the nature of measuring objects change, we switch to new instruments. Some examples include

Measurement of Length

  • We use Vernier caliper to measure lengths of order 10-4m

  • We use meter scale to measure lengths from 10-3m to 102m

  • We use a screw gauge to measure lengths of order less than 10-5m

There are some objects which can’t be measured with the help of scales and instruments, like the height of the mountain, the radius of earth or other large bodies. To measure them, we use some special methods.
 

Measurement of Large Distance

To measure large distances like the distance of a planet from earth or sun, we can’t use meter scale. Instead, we use some special methods, which can make complex measurements simple. There are two such methods, which we use to measure infinitely large distances.

  • Parallax Method

  • Echo Method
     

Parallax Method

Parallax Method is used to measure large distances and works on the principle of parallax basis. Parallax is defined as the apparent displacement of an object when observer’s point of view changes.

Parallax Method

Example:

Hold a pencil in your hand. Now close your left eye and see the pencil, now close your right eye and see the pencil. You’ll find that position of the Parallax image of the pencil is different in each case. This is called Parallax and your eyes are used as a basis.

To measure a distance D of point A from a planet S by parallax method, we will observe it from two different views A and B. The distance between A and B is b. The angle ASB or θ is called parallax angle or parallactic angle.

As the distance between planet and observation points is very large, we can assume 

b/D << 1

which means, angle θ to be very small. We proceed further by taking the triangle ASB in form of arc, where the length of the arc is b and radius of the arc are D. 

Arc length = Radius × Angle θ

b = D × θ

Now if we know the distance between two points and parallax angle, we can easily find the distance D, with the help of above relation.

Example 

A planet is observed from two points A and B on earth, the angle θ is 3.32 × 10-2 radian. The diameter of the earth is about 1.276 × 107m. Find out the distance between Earth and Moon.

We have θ = 3.32 × 10-2 radian, taking two points on a diameter of the earth, we have b = 1.276 × 107m. The unknown quantity is D,

Now since D = b/ θ

D = 1.276 × 107m/ 3.32 × 10-2

D = 3.84 × 108 m


Echo Method

Echo Method is used to find the distance of a hill or building from a certain point on the surface of the earth. In this method, we shoot a gun or radio wave and we measure the time interval in which gun or radio wave is fired and instant echo is heard.

Echo Method

If t is the time taken by the sound to travel from observer to the hill and back to the hill, and S be the distance between observer and hill then

We know that

Speed = Distance/ Time

v = 2S/t           

(Since the total distance covered by sound will be double)

If we know the speed of sound, we can easily find the distance between the observation point and hill. This is called Echo Method.
 

Range of Length

The sizes of objects and heavenly bodies vary over a wide range. The length of organisms affects at both macroscopic and microscopic levels. For example, the size of the universe is of the order 1026m whereas the size of a tiny nucleus of an atom is just 10-14m. We use certain units to define length at both levels. They are:

1 fermi or 1f equals to 10-15m

1 Angstrom or 1Å equals to 10-10m

1 Astronomical unit or AU is 1.496 × 1011m (it is also the average distance between the sun and the earth)

1 light year or 1ly equals to 9.46 × 1015m (it is the distance which light travels with velocity of 3 × 108 m/s in 1 year)

The table below depicts range and order of different lengths.

Distance or Size of object Length (m)

Size of proton

10-15

Size of atomic nucleus

10-14

Size of hydrogen atom

10-10

Length of typical virus

10-8

Wavelength of light

10-7

Size of red blood corpuscle

10-5

Thickness of paper

10-4

Height of Mount Everest above sea level

104

Radius of Earth

107

Distance of Moon from Earth

108

Distance from Sun from Earth 

1011

Distance of Pluto from Sun

1013

Size of our galaxy

1021

Distance to Andromeda galaxy 

1022

Distance to boundary of observable universe

1026


Watch this Video for more reference
 


More Readings

Measurement of Length

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details
Get extra Rs. 3,180 off
USE CODE: CART20