Measurement | Physics, Type, Facts, Quantities, Definition |

Physics describes the laws of nature. This description is quantitative and involves measurement and comparision of physical quantities. To measure a physical quantity, we need some standard amount of that quantity.

Physical Quantity

The quantities by means of which we describe the laws of physics are known as physical quantity.

We specify the physical quantity completely if it has

(i) Numerical values i.e., ratios, e.g., dielectric constant, refractive index etc.

(ii) Magnitude only i.e., scalar, e.g., current, mass etc.

(iii) Magnitude and direction both i.e., vector e.g., displacement, torque etc.

Units

For the measurement of physical quantity, a standard value (as unit) of the same physical quantity is required. That eudicants how many it is used during the measurment times the quantity contains that unit.

Fundamental Unit

It is an independent unit. Fundamental units in any system of measurements are independent of each other. In other words, one fundamental unit cannot be expressed in the form of other fundamental unit.

Fundamental units in different system of measurement are :

MKS system
CGS SYSTEM
FPS system
SI system

A. MKS system (Meter, Kilogram, Second System)

S.No.	Quantity	Unit	Abbreviation
1	Mass	Kilogram	kg
2	Length or Distance	meter	m
3	Time	second	s

B. CGS System or Gaussian System (Centimeter, Gram, Second System)

S.No.	Quantity	Unit	Abbreviation
1	Mass	gram	g
2	Length or Distance	centimeter	cm
3	Time	second	s

C. FPS System (Foot, Pound, Second System)

S.No.	Quantity	Unit	Abbreviation
1	Mass	pound	lb
2	Length or Distance	foot	ft
3	Time	second	s

D. SI System (International System of Units)

This system is result of CGPM meeting in 1971. Due to the variability of system of units a common system of unit was required to be opted. Now-a-days this system is popular throughout the world.

S.No.	Quantity	Unit	Abbreviation
1	Mass	kilogram	kg
2	Length	meter	m
3	Time	second	s
4	Electric current	Ampere	A
5	Temperature	Kelvin	K
6	Amount of substance	mole	mol
7	Luminous intensity	candela	cd

Supplementary Unit

The unit having no dimensions is supplementary unit. e.g.,

Plane angle = Radian

Solid angle = Steradian

Practical Unit

A larger number of units are used in general life for measurement of different quantities in comfortable manner. But they are neither fundamental units nor derived units.

e.g., per sec, tonne, day etc.

Derived Unit

The units of all other physical quantities except fundamental physical quantities which are obtained with the help of fundamental units are called derived units.

Derived units of some physical quantities are as follows:

S. No.	Physical Quantity	Derived Units
1	Area	m²
2	Volume	m³
3	Density	kg/m³
4	Speed	m/s
5	Acceleration	m/s²
6	Force	kg - m/s² or Newton
7	Work	kg - m/s² or Joule
8	Power	kg - m²/s³ or Watt
9	Charge	Ampere - sec or Coulomb
10	Potential	Joule/Coulomb or volt
11	Resistance	volt/Ampere or ohm

Some Other Units of Length Mass and Time

For Length

1 Angstrom (Å) = 10-¹⁰ m

1 Nanometer (nm) = 10-⁹ m

1 Micrometer (μ) = 10-⁶ m

1 Milimeter (mm) = 10-³ m

1 Centimeter (cm) = 10-² m

1 Kilometer (km) = 10³ m

1 Megameter (Mm) = 10⁶ m

1 Gigameter (Gm) = 10⁹ m

1 Tarometer = 10¹² m

1 Light year = 9.46 × 10¹⁵m or 10¹⁶ m

For Mass

1 Microgram (μg) = 10-⁹ kg

1 Milligram (mg) = 10-⁶ kg

1 Gram (g) = 10-³ kg

1 Quantal = 10² kg

1 Metric tonne = 10-³ kg

For Time

1 Picosecond = 10¹² s

1 Nanosecond = 10-⁹ s

1 Microsecond = 10-⁶ s

1 Millisecond = 10-³ s

Error in Measurement

There are many causes of error in measurement. Error may be due to instrumental defects, ignoring certain facts, carelessness of experimenter, random change in temperature, pressure, humidity etc. Therefore, difference between measured value and true value of a quantity represents error of measurement.

The Significant Figures

The significant figures express the accuracy with which a physical quantity may be expressed.

"The digits, whose values are accurately known in a particular measurement, are called its significant figures,"

The following rules have been set up for determining the number of significant figures.

1. All non-zero digits are significant. 65324 has five significant figures.

2. All zeros between two non-zero numbers are significant. The measure or data 309.009 has six significant figures.

3. All zeros to the right of a decimal point and to the left of a non-zero digit are never significant. The measure 0.00956 has three significant figures. In this type of expression, traditionally even a single zero placed to the left of the decimal point is never significant.

4. (a) All zeros to the right of the decimal point are significant, if they are not followed by a non-zero digit. The measure 40.00 has four significant marks.

(b) All zeros to the right of the last non-zero, significant digit after the decimal point. The measure 0.08900 has four significant figures.

5. (a) All zeros to the right of the last (rightmost) non-zero digit are not significant. Measurement 2020 consists of three significant figures.

(b) All zeros to the right of the last non-zero digit are significant, if they come from the measurement.

Main POINTS
If a number is greater than 1 (without involving decimal point), the zeros to the right of the last non-zero digit are not significant.

If a number is greater than 1 and involves decimal point, the zeros to the right of the decimal point are significant.

If a number is less than 1, the zeros on the right of the decimal point but to the left of first non-zero digit are not significant.

Significant Figures in Addition and Subtraction

The accuracy of a sum or a difference is limited to the accuracy of the least accurate observation involved in the addition and subtraction.

Rule – Do not retain a greater number of decimal places in a result computed from addition and / or subtraction than in the observation, envolved which has the fewest decimal places.

Main POINTS
In the final result after addition or subtraction, as many number of decimal places are retained as are there in the data with the least decimal places.

Significant Figures in Multiplication and Division

When the values of different observations are multiplied or divided, the number of digits to be retained in the answer depends upon the number of significant figures in the weakest link.

Rule – Do not retain a greater number of significant figures in a result computed from multiplication and / or division than the least number of significant figures in the data from which the result is computed.

Vernier Callipers

It is an instrument that lets the user measure length, more accurately than could be done by reading a uniformly-divided straight or circular measurement.

Least Count of Vernier Callipers

The least count (LC) of an instrument is the smallest measurement that can be measured accurately with it.

Least count of vernier callipers

LC = Value of one main scale division - Value of one vernier scale division

Or,

LC = Value of the smallest division on main scale / Total number of divisions on vernier scale

= 1/10 = 0.01 cm

Screw Gauge

It is an instrument used to determine the thickness and area of cross-section of different objects. It works on the principle of micrometer screw.

Pitch of Screw Guage

It is defined as the distance between the consecutive threads of a screw, measured along the axis of the screw.

Least count of screw guage

= Pitch / Number of divisions on circular scale

Least count of screw guage is 0.001 cm.

Limitations of Accuracy

Limitations of accuracy of any instrument depends on its least count. So, lesser the least count of an instrument, more will be the accuracy of that instrument.

Some Important Definitions

Standard Meter

It is 1650, 763.73 times of the distance travelled by the wavelength of a particular colour of light emitted by pure Kr⁸⁶.

Light Year

It is the distance travelled by light, in vacuum in a year. It is a unit of length.

Standard Kilogram

1 kg Mass of 5.0188 × 10²⁵ atoms of ₆C¹².

Standard Second

1 s = It is the time taken in the 9, 192, 631.770 vibrations of the atom of CS - 133.

Mean Solar Day

Average of every solar day of a year is called a mean solar day which is equal to 86400 s.

Order of Magnitude

To perform rough calculations or comparisons, a number is rounded off to zero significant figures i.e., a number rounded to the nearest power of 10 is called an order of magnitude.

Determine the Order of Magnitude

To find the order of magnitude, the number is written as the power of 10 such as only one digit is before decimal and rest digits will be after decimal.

Example The data 32400 can be written as 324 × 10 and its order of magnitude is 10⁴.

Related Questions : (Answer in comment box.)

Q1. How much microseconds will be there in a minute?

(a) 7 × 10⁷ μs

(b) 5 × 10⁷ μs

(d) 8 × 10⁷ μs

Q2. Light year is the unit of

(a) mass

(b) time

(d) distance

Q3. What is the least measurement of a vernier calliper?

(a) 0.01 mm

(b) 0.05 mm

(d) None of these

Q4. Screw guage works on the principle of

(a) micrometer screw

(b) screw gauge

(d) none of these

Q5. Which of the following value is most accurate?

(a) 4500 g

(b) 4.5 kg

(b) 450 × 10³ g

(d) 45 × 10³ g

Q6. If light takes 5 yr to reach the Earth from a Star. Find the distance between that Star and the Earth in km.

(a) 3 × 10⁸

(b) 15 × 10⁸

(d) 9.3 × 10¹²

Q7. A particle travels 1260 m in 17s. What will it in appropriate significant figure?

(a) 74.11 m/s

(b) 74 1 m/s

(d) 74.6 m/s

Q8. If mass of one electron is 9.11 x 10-26 g then how many electrons will be there in 1 g of electrons?

(a) 110 × 10²⁵

(b) 1.093 × 10²³

(d) 0.1093 × 10²²

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