**Complete Notes Chapter 2 Measurement**

**Topics covered in chapter 2 Measurement are: **

**Physical quantities.****Derived units.****Measuring instruments.****Significant figures and accuracy.**

**Q1. What is meant by measurement?**

**MEASUREMENT: **

**Definition:**

**Measurement** is defined as:

To find out the magnitude or size of something, by comparing that unknown quantity with some standard quantity, known as **measurement**.

**Measurement** can also be defined as:

“The Comparison of an unknown quantity with some known or standard quantity” is known as measurement.

**Q.2 What are physical quantities? And also describe its types?**

**Physical Quantities: **

The quantities which can be measured by using any method are known as physical quantities.

**Or **

Quantities that can be measured are called physical quantities.

**Or **

The characteristic of any object which can be measured like length, height, mass or width, known as physical quantities.

**Kinds or types of physical quantities:**

There are two kinds of physical quantities which are as follows.

- Fundamental or base quantities
- Derived quantities

**1. Fundamental or Base quantities **

In physics length, mass and time are supposed to be the main fundamental quantities.

**OR **

The main physical quantities length, mass and time are known as fundamental quantities.

They can be said as the pillars for other quantities (derived quantities).

S.No. | Physical quantities | symbol | Name of unit | Symbol of unit |

1 | length | l | meter | m |

2 | mass | m | kilogram | kg |

3 | time | t | second | s |

**2. Derived quantities**

The quantities which are derived from fundamental quantities are called as derived quantities. For example force, speed, volume etc.

These quantities can be obtained by the multiplication and division of fundamental quantities.

Some derived quantities listed below.

Quantity | Symbol | Unit | Unit Symbol |

Speed | v | meter/second | m/s |

Acceleration | a | meter/second^{2} | m/s^{2} |

Volume | V | cubic meter | m^{3} |

Force | F | newton | N(=kg m/s^{2}) |

Pressure | P | pascal | Pa(=N/m^{2}) |

Work | W | joule | J=(N.m) |

Charge | q | coulomb | C=(A.s) |

**Q.3. Define unit and also the types of physical units?**

**Unit: **

An internationally accepted standard for measurement of a physical quantity is known as a unit.

or

A standard for measurements of physical quantities is called a unit.

Or

A standard of physical quantities which has to be measured is called a unit.

**Types of physical units: **

There are 2 main groups of units.

- Fundamental units
- Derived units

**Fundamental Units**:

The units of physical quantities which express the fundamental quantities are known as fundamental units. For instance length(meter), time(second) and mass(kilogram).

**Or **

Units for Fundamental or base quantities (like length, time etc.) are called **Fundamental units**.

**Derived Units**:

The units of physical quantities which are derived from fundamental units are known as derived units. For instance: unit of force is newton (m.kg/s^{2}) and unit of speed is meter/second (m/s) etc.

**Or **

Units which are a combination of fundamental units are called **Derived units**.

**Q4. What is the system of units? also describe the different systems of units which are used in the world?**

**System of Units:**

A set of fundamental and derived units is known as a system of units.

The following three systems of units are being used in the world for scientific work.

- CGS system
- British Engineering System:
- International system of units (S.I system)

**CGS system: **The system in which centimetre, gram and second are the fundamental units for length, mass and time respectively, is the CGS system of units.

**British Engineering System:** It is an old system. In this system, fundamental quantities are length, force and time and their units are foot, pound and second respectively. In this system, mass is a derived quantity and its unit is derived from the unit of force i.e., pound(lb), and is called a slug. (1 slug = 32.17 lb mass = 14.59 kg).

**International system of units (S.I system):** A system consisting of seven fundamental quantities (Time, Length, Mass, Amount of substance, temperature, Electric current and Luminous intensity) is known as an international system.

These quantities with their units are listed below:

No. | Quantity | Name | Symbol |

1 | Time | second | s |

2 | Length | metre | m |

3 | Mass | kilogram | kg |

4 | Amount of substance | mole | mol |

5 | Thermodynamic temperature | kelvin | K |

6 | Electric current | ampere | A |

7 | Luminous intensity | candela | cd |

This system is very convenient and provides simple methods of calculations for the scientific world so nowadays, S.I units are used throughout the world.

**Q5. Define standards of length, mass and time?**

**Standard of Length (Meter)**

By the current definition, meter is defined as:

“The metre is the length of the path travelled by light in vacuum during a time interval of 1 ÷ 299,792,458 of a second”.

It is also defined as:

A distance between two marks engraved on an iridium-platinum alloy bar kept at international bureau of weights and measures near Paris.

1 km (kilometer) = 1000 m = 10^{3}m

1 cm (centimeter) = 1 ÷ 100 m = 10^{-2}m

1 mm (millimeter) = 1 ÷ 1000m = 10^{-3}m

1 μm (micrometer) = 1 ÷ 1,000,000 m = 10^{-6}m

1 nm (nanometer) = 1 ÷ 1,000,000,000 = m = 10^{-9}m

** Standard of Time (Second) **

A second is defined in terms of the time period of cesium atom(CS-133) that one second is equal to 9,192,631,770 periods of vibrations of CS-133 atoms.

**Or**

The time period in which a cesium atom(CS-133) completes 9,192,631,770 vibrations.

1 min (minute) = 60 s

1 h (hour) = 60×60 s = 3600 s

1 ms (millisecond) = 1 ÷ 1000 s =10^{-3}s

1 μs (microsecond) = 1 ÷ 1,000,000 s = 10^{-6}s

1 ns (nanosecond) = 1 ÷ 1,000,000,000 s = 10^{-9}s

**Standard of Mass (Kilogram)**

One kilogram is the mass of a platinum-iridium alloy cylinder which is kept at the International Bureau of Weights and Measures, near Paris.

1 g (gram) = 1 ÷ 1,000 kg = 10^{-3}kg

1 mg (milligram) = 1000000 kg = 10^{-6}kg

1 μg (microgram) = 1 ÷ 1,000,000,000 kg = 10^{-9}kg

**Q6. What are measuring instruments? Also describe some measuring instruments?**

**Measuring Instruments: **

The instruments by which we measure the physical quantities, called measuring instruments.

**1. Vernier Caliper**

A device or instrument that can measure a distance up to 0.1mm or 0.01cm, known as Vernier caliper.

Vernier caliper is an instrument that can be used to measure a distance accurately up to 1/100 cm or 0.1mm.

A device by which we can accurately make measurement up to one tenth of a millimetre or one hundredth of a centimeter, known as Vernier calipers.

**Construction: **

- A vernier callipers consist of a rectangular steel bar.
- It is consists of two scales one is called the main scale. (MS) and other is called Vernier scale (VS).
- The main scale is fixed and graduated in millimetres.
- Vernier scale is 9mm long and consists of 10 divisions. It is not fixed and moves on the main scale.
- The instrument has two jaws called callipers, which enables it to measure the internal as well as the external diameter of a cylindrical object.
- A thin flat rod is attached to the sliding scale on its back which enables it to measure the inner depth of the hollow cylinder.

**Vernier Constant (VC) or Least Count (LC)**

Vernier Constant (VC) or Least Count (LC) is the minimum distance that can be measured with the help of vernier calipers.

Here,

10 vernier divisions = 9 main scale divisions

= 9 mm

1 vernier devision = 9 mm ÷ 10 = 0.9 mm

1 main scale division= 1mm

Least count = difference between 1 MS division and

1 VS division

So,

= 1mm – 0.9mm

= 0.1mm or

=0.01cm

The least count can also be calculated as follows:

LC = Value of the smallest division on MS ÷ Total number of divisions on the VS

= 1 mm ÷ 10

= 0.1mm 0r

= 0.01cm.

**Zero Error **

An error which arises when we closing the jaws, the zero of main scale do not coincides with zero of Vernier scale,is called zero error.

**Types of Zero Error **

- Positive zero error
- Negative zero error

**Positive Zero Error:**

If zero of Vernier scale is on the right side of the zero of main scale ,is called positive zero error.

**Negative Zero Error:**

If zero of Vernier scale is on the left side of the zero of main scale ,is called positive zero error.

** Working:**

- To measure the length of an object, it is placed between the two jaws of, the vernier callipers.
- The distance between the zero of the main scale and the zero of the vernier scale is equal to the length of the object.
- Note the main scale reading just before the zero of the vernier scale.
- Note the number of vernier scale division which coincides with one of the main scale divisions.
- Multiply this number by the least count. This will give vernier scale reading, it is known as the fractional part.
- Add main scale reading and fractional part. This is the length of the object.
- If there is zero error, adjust it to get the correct length of the object.

**2. Screw Gauge:**

Screw gauge is a device or instrument that can measure a distance accurately up to 1/100 or 1/1000 mm (0.01 cm or 0.001 cm)

**Construction:**

- It is consist of a U shaped metal frame.
- At one end of the frame, there is a small stud called anvil which is fixed.
- At other ends of the frame, there is a screw called a spindle, having threads on it which are graduated in millimetres.
- At one end of the spindle, there is a hollow cylinder which is known as sleave. On it there is a scale graduated in millimetres is called main scale or linear scale.
- A drum known as thimble has a circular scale at one end with 50 or hundred divisions on it.
- The circular scale moves on the main scale by rotating thimble clockwise or anticlockwise.
- Ratchet is a device which avoids undue pressure on the object.

**Working:**

- Place object between anvil and spindle.
- Rotate the thimble clockwise till spindle touches the object
- Turn the ratchet so that the object pressed gently between anvil and spindle.
- Note the main scale reading and circular scale reading.
- If there is a zero error adjust it to get the correct measurement.

**The pitch of Screw Gauge:**

The distance between two consecutive threads of the linear screw known as pitch of screw.

**Least Count of Screw Gauge:**

Least count= pitch of screw/ number of divisions on the circular scale

Hence,

Pitch of screw = 1mm

Number of divisions on the circular scale = 100

Then,

LC = 1mm/ 100

= 0.01mm or 0.001 cm

**Zero Error**

On closing the gauge, if zero of circular scale coincide with the zero of the main scale then the instrument has no zero error. If zero of both scales does not coincide then there is an error.

**Types of Zero Error**

- Positive zero error

- Negative zero error

**Positive Zero Error**

If the zero of the circular scale is below the reference line then this error is called positive zero error.

**Negative Zero Error**

If the zero of the circular scale is above the reference line then this error is called negative zero error.

**Zero Error of M.S Gauge:**

An error which arises when the gauge is closed and the zero of the main scale does not coincide with zero of circular scale known as zero error of screw gauge.

**OR**

On closing the guage if the zero of the circular scale is above the reference line(zero line) or below the reference line of the main scale is known as zero error of screw gauge.

**3. Physical balance**

A device which is commonly used to find a mass of an object is called physical balance.

**Construction:**

- It consists of a horizontal beam resting at its middle point on a central knife edge.
- Two similar pans are suspended on two more knife edges near each and of The beam.
- A long pointer capable of swinging on a scale is attached to the middle of the beam.
- Leveling screw is used to level the physical balance on a table.
- The beam is set free by rotating the arrestment knob at the front of balance.
- The pointer is brought at the middle of the scale by means of two adjusting screws provided at each end of the beam.

**Working:**

- The object is placed on the left pan and the standard masses on the right pan.
- The beam is set free by turning the arrestment knob.
- The pointer moves toward the side of the smaller masses.
- The standard mass in the pan is adjusted to find the mass of the object.

**4. Stop Watch**

A device which is used to measure time interval for an event, known as stop watch.

**Construction:**

It consists of minute hand and second hand scale and a knob.

**Working:**

- To note the time both hands of the stopwatch are set at zero by pressing and releasing the knob.
- As the knob is pressed and again released the watch starts.
- When the second hand completes one rotation of 60 seconds, the minute’s hands proceeds by one division.
- To stop the watch, the knob is pressed and released again.

**5. Measuring Cylinder:**

A device which is used to find the volume of liquids is called measuring cylinder.

**Construction:**

It consists of a glass cylinder with the scale graduated in cubic centimeter (cm³) or milliliters (ml).

**Working:**

- When a liquid is poured, it rises to a certain height in the cylinder.
- The level of liquid in the cylinder is noted and the volume of liquid is obtained.
- For accurate reading keep the eye in level with the bottom of the meniscus of the liquid surface and cylinder must be on a horizontal table.

**Q7. Define significant figures and also describe rules for finding significant figures?**

**Significant Figures: **

The accurately known digits and first doubtful (uncertain) digit in any measurements is known as significant figures.

**Rules for finding significant figures**:

- All non zero digits are significant. For example, the number 456 has three significant figures 4, 5, 6 and 2456 has four significant figures.
- Zeros lying between non zero digits are significant, for example, the number 50004 has five significant figures.
- All the zeros which locate the decimal point in a number less than one are not significant. For example, the number 0.00632 has only three significant figures that are 6, 3, 2.
- The zeros which are located immediately to the right of the decimal point are significant. For example, the number of 69.000 has five significant figures.
- Zeros locating the decimal point in a number greater than 1 (one) are not necessarily significant. For example, the number 1500m has four significant figures but here it implies that only two significant figures are known so in order to correct this problem we express it in scientific notation 1.50010
^{3 }m(has four significant figures). - When two or more numbers are used in calculations, the number of significant figures with answers is limited by the number of significant figures in the original data (the final answer has a number of significant figures that equals the smallest number of significant figures in any one of the original factors.) For Example

26+7.96+11=44.95 since the least significant figures in original data are only two i.e. 11 has 2 significant figures so,

26+7.96+11=44.95 =44 ans

4.6×15.2=69.92 since the least significant figures in original data are only two i.e.4.6 has 2 significant figures so,

4.6×15.2=69.92=70 Ans

**Q8. Define error and accuracy or What are the types of error?**

**Error:**

The difference between the measured and the actual value is called error.

**Accuracy:**

Accuracy is ascertaining the measurement of the quantities involved a phenomenon is as close to the factual value as possible. OR The closeness of a measured value to a factual or real value (standard value).

**Types of Error:**

There are three types of error.

- Personal Error
- Systematic Error
- Random Error

**1. Personal Error:**

Error that arises due to tendency of a person who takes reading in favour of a particular reading, causes errors in taking observations, called personal error.

**2. Systematic Error:**

The error due to fault in measuring instrument is called systematic error.

**3. Random Error:**

The error found due to the experimental conditions which are at times beyond the control of the person making measurements is called random error for example temperature, humidity, voltage etc. and also known as environmental error.

**Chapter 1 Introduction** or for video Lectures** Click Here**