**Physical Quantities:** All quantities that can be measured are called physical quantities.

Eg: Time, Length.

**Measurement:** It is the comparison of a quantity with a standard of the same physical quantity.

Units: All physical quantities are measured as compared to the standard magnitude of same physical quantities and these standards are called units.

**Types of Physical Quantities:**

**Fundamental Quantities: There are seven fundamental quantities:**

**Characteristics of Fundamental Units:**

- Fundamental Units are well defined and are of suitable
- They are easily reproducible.
- They do not vary with temperature , pressure and time.

**Fundamental Units**

- Meter: The distance traveled by light in Vaccum in 1/299,792,458 second is called 1m.
- Kilogram: 1 kg is the mass of the cylinder made of the platinum-iridium alloy at the international bureau of weights .
- Second: Electromagnetic radiation by Cesium -133 are emitted at several wavelengths. Radiation is selected which corresponds to the transition between the two levels of ground state of Cs -133.

**Principal System of Units:**

**CGS System:** Centimetre , gram and second .

**FPS System:** Foot , Pound and Second

**MKS System: ** Meter, Kilogram and Second

**Dimensions:**

They are the powers to which the fundamental quantities are being raised to represent given physical quantities.

**For Example:**

**Force = Mass x Acceleration**

= mass x velocity /time

= mass x length / (time ) ^{2 }

= MLT^{-2}

**2. Derived Units:** Physical Quantities which depend on fundamental quantities or which can be derived from fundamental quantities are known as derived quantities.

The principle of Homogeneity: The dimension of the quantities on the left side is equal to the right side. This is the principle of homogeneity.

E = ½ mv^{2} (Kinetic Energy)

**E= mass x (velocity ) ^{2}**

**½ is a number and has no dimensions. **

**E = M x [ L/T ] ^{2}**

E = ML^{2}T ^{-2}

**Significant Figures:**

Measurements made by an instrument are not correct . The degree of precision is given by the significant figures to which measurement has been recorded. The number of figures requires specifying a certain measurement perfectly are called significant figure .

Rules for the Significant Figures:

- Zeros occurring between now- zero digits are significant.
- All zeros to the right of a decimal point and to the left of the no – zero digits are not significant figures.

If a measurement contains no decimal point , the number of final zeros are ambiguous and are not counted are significant. **Eg:** In 5x 10 ^{3} Significant figure is 1 .

**Vernier Callipers and Screw Gauge:**

It is used for measuring length.

**Vernier Calipers:**

It is used to measure accurately up to 1/10 of a millimeter. It consists of Main scale and Vernier Scale. The main scale is fixed and Vernier scale is movable.

Vernier Constant:

The size of one main scale division is S and that of Vernier scale is V units.

(n-1 ) S = nV

nS – S = nV

S-V = S/n

n = Length of one division of main scale / Number of divisions on Vernier Scale

**Screw Guage: **

It is used to measure small lengths like the diameter of a wire or thickness of the sheet. It consists of a U shape metal frame. The main scale is also called pitch scale.

**Pitch:** It is the defined as the linear distance moved by the screw forward or backward when one complete rotation is given to the circular cap.

L.C. = Pitch/ Total number of divisions on the circular scale.

If there are 50 divisions on the circular scale, then least count :

Distance traveled on the pitch scale is 2 mm

So Pitch is 2 mm/4 = 0.5 mm

LC = 0.05/50 = 0.01 mm

**Error:**

The lack of accuracy in the measurement due to the limit of the accuracy of the instrument.

Types of Error :

- Absolute Error : The difference between the true value and measured value is called absolute error.

a_{m} = a_{1} +a_{2} + a_{3} +—-/n

- Relative Error : The ratio of the mean absolute error to the true value is called relative error.

- Percentage Error: The relative error expressed in percentage is called percentage error.

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