Distances

Question 1 What precautions should be taken while using a meter scale to measure the length of an object?

Question 2 What is meant by standard unit of measurement? Why is it necessary to have standard units of measurement?

Question 3 Name the S.I. unit of length. Write its symbol?

Question 4 How many centimeters are there in a meter?

Question 5 How many milimeters are there in a centimeters?

Question 6 How many meters make one km?

Question 7 Why a foot step cannot be used as a standard unit of length?

Question 8 Why hand-span method cannot be used as as standard unit of length?

Question 9 Name the various length measuring devices?

Question 10 How will you measure the length of a curved line using thread and scale?

Question 11 What is measuring tape? Explain its use?

Also Read NCERT Solutions for Chapter 10 Motion and Measurement of Distances

Distance

The length of the space between two points (or two places) is called distance.

For example: The distance between Delhi and Agra is 200 kms. If the two points (or two places) are close by, the distance between them will be small otherwise if the two points (or two places) are far off, then the distance between them will be large.

 

Measurement

Measurement is a process of comprising an object with a standard ‘unit of measurement’. Standard unit of measuring length is called meter.

Need of standard units of measurement – we can use a variety of objects as units of measurement of length.

We can measure the length of an an object by using ‘hand-span’, ‘forearm length’ or ‘ foot step’ as the units of measuring length. But hand span, forearm length and foot step cannot be used as standard units measurements because their length is not the same for all the persons. The length of hand-span, forearm-length and foot step of different persons is different. It varies from person to person. So, hand span, forearm length and foot step are not standard units of measuring length.

A unit of measurement which has a fixed value which does not change from person to person or place to place, is called a standard unit of measurement length. Whether a meter is used by one person or another person, whether the meter is used in one country or another country, it always represents exactly the ‘same  length’. The length of meter does not change from one person to person or place to place. It is necessary to have standard units of measurements for the sake of uniformity in measurements.

Every Measurement consists of a number and a unit – The result of every measurement consists of two parts :-

(1) The first part of the measurement consists of a number (1,2,3,4,5 …… etc.) which tells us the ‘magnitude of measurement’

(2) Second part tells us the ‘name of the unit of measurement’. Every measurement consists of a number and a unit.

Every measurement consists of a number and a unit.

For example: if the length of table is 2 meters , then 2 is the number and meter is the unit. The number ‘2’ tells us the magnitude of the length of the table and ‘meter’ tells us the unit in which the length has been measured. A measurement is not complete unless both, the number an the unit are mentioned.

SI unit of Length

The SI unit of measuring length is meter. The symbol of meter is m. The SI unit of measuring mass is Kilogram “kg” and the SI unit of measuring time is ‘second’ (s).

Prefixes used with SI units

Prefix is a kind of word used before the name of an SI unit to get a bigger value or a smaller value of the unit.

Three common prefixes are : kilo, centi and mili

(1) Kilo is a prefix which denotes one thousand, i.e.  kilo means “one thousand or 1000

1 kilometer = 1000 meters

(2) Centi is prefix which denotes hundredth i.e.  centi means “one hundredth” or 1/100

1 meter = 100 centimeters

(3) Milli is a prefix which denotes “one thousandth” i.e. milli means “one thousandth” or 1/1000

So, if we write ‘milli’ before the unit of length ‘meter’ , it becomes ‘millimeter’ which means one thousandth of a meter or 1/1000 meters. In other words 1 meter = 1000 millimeters.

Kilometer is written as ‘km’, centimeter as ‘cm’ and millimeter as mm.

 

Measurement of Length

The length is the distance between two points. Meter is a used as a standard unit for measuring the length of an object. We measure the length of an object by using a meter scale. A meter scale is graduated  (or marked) in 100 centimeters and every centimeter is further divided into 10 divisions called millimeters.

1 meter = 100 centimeters
1 centimeter = 10 millimeter

The use of proper Units of Length

“Meter” is the standard unit of length but sometimes other units of length like centimeters, millimeters and kilometers are also used for the sake of convenience. The type of unit used depends on the magnitude of the length to be measured.

(1) Meter can be used as unit to measure the length of a table or a room or height of a tree or building.

(2) The length of small objects is measured in centimeters , e.g. pencil or a notebook.

(3) The very small lengths are expressed in still smaller units called ‘millimeters’ e.g the thickness of a coin or a thin wire. One mm (millimeter) is the smallest length which can be measured accurately by using a meter scale.

The distances between two cities are very large. The large distances (or lengths) are measured in a big unit of length called “kilometer”

 1 kilometer = 1000 meters
1 km = 1000 m

Length Measuring Devices

The various types of devices which are commonly used for measuring length are : meter scale and measuring tape. A meter scale is made of metal and can not be bend. The rulers are made of plastic, wood or metal and also can not bend. The measuring tape is however made of flexible material which can bend easily around the object which has to be measured.

(1) If the object is straight, we can use either a meter scale or a measuring tape to measure its length. For example: the length of a table can be measured by using a meter scale or a measuring tape. A cloth seller uses a meter rod for measuring cloth.

(2) If the object is round, then we use a measuring tape to measure for making measurement of length. For example: (a) the girth of a tree can be measured only by using a measuring tape because measuring tape can be bent around the tree. (b) The tailor also measures our chest and waist by using a measuring tape.

We can not use an elastic measuring tape to measure lengths. This is because an elastic measuring tape can stretch easily while taking measurements and hence give a wrong value (greater value) of length of an object than its actual length. So, though a measuring tape is flexible but it is made of non stretchable material. A ruler is a short scale marked in centimeters and millimeters. These rulers are usually made of plastic, Scales made of metal or plastic are also available in the market.

Precautions to be taken while using a scale

The precautions to be taken while using a meter scale to measure lengths are as follows :

(1) The scale should be placed to the side of the object being measured. It should also be in touch with the object being measured.

(2) While reading the scale, eye must be placed vertically above the scale mark being read. If the the eye is not vertically above the scale mark being read, then the reading becomes wrong.

(3) If the scale has a damaged zero mark or broken left end, measure the length of an object starting from 1 cm mark of scale and then subtract 1 cm from the reading taken at the right end to get the actual length of objects.

To measure the Length of a curved line 

A wavy line is known as curved line. We can not measure the length of a curved line by using a scale directly.

The length of a curved line can be measured by using a thread and a scale.

(1) We take a piece of thread and put a knot near its one end. This knot will act as a starting point for measuring the length of the curved line .

(2) Place the knot of the thread at a point A on the left end of the curved line with the help of thumb and forefinger.

(3) Hold the thread a little distance away from the knot and keep it along the curved line with the help of right thumb and forefinger.

In this way, run the thread all along the curved line in little steps at a time, keeping the thread taut, till the other end B of the curved line is reached. Make an ink mark on the thread where it touches the other end B of the curved line. Now, straighten the thread and measure its length between the knot and the ink mark by keeping it along a scale. This will give us the length of  the curved line.

 

Notes for Chapter 10 Motion and Measurement of Distances Types of Motion Distances