*♦ Learn about : Physical quantity , Fundamental quantities , derived unit , Meter , Kilogram , Second ♦
*

**Physical Quantity**

A physical quantity is a quantity that can be measured i.e. a physical quantity is properly defined, has proper units, and its value can be measured by an instrument.

Physical quantities are classified as fundamental and derived quantities.

**Fundamental Quantities **

Fundamental quantities are those that are defined directly by the process of measurement only. They are not defined in terms of other quantities; their units are not defined in terms of other units. In mechanics we treat length, mass and time as basic or fundamental quantities.

**Derived Units**

The units of all other physical quantities, which can be obtained from fundamental units, are called derived unit.

**Name of System **

F.P.S (Foot -Pound – Second)

C.G.S (Centimeter-Gram- Second)

M.K.S. (SI System)( Meter-Kilogram- Second)

**Illustration :** Find the unit of speed.

**Solution :** Speed = distance/time = ms^{-1}

__Definitions of Base Units:__

1.** Meter:**

Since 1983, the standard metre is defined as the length of the path travelled by light in vacuum in (1/299,792,458) th part of a second.

2. **Kilogram:**

Nowadays the standard kilogram is the mass of a cylinder made of platinum-iridium alloy and stored in a special vaule in the International Bureau of Weights and Measures at Sevres in France.

3. **Second:**

At present second is defined on the basis of an atomic clock, which uses the energy difference between the two lowest energy states of the cesium atom. When bombarded by microwaves of precisely the proper frequency, cesium atoms undergo a transition from one of these states to other. One second is defined as the time required for 9,192,631,770 cycles of this radiation

**In physics SI system is based on seven fundamental and two derived units**.

**Basic Physical Quantities** & their** Fundamental Unit**

Mass → kilogram

Length → meter

Time →second

Temperature→ kelvin or Celsius

Electric current→ ampere

Luminous intensity→candela

Quantity of matter → mole

**Illustration : **Fill in the blank by suitable conversion of units

1 kg m^{2}s^{-2} =….. g cm^{2}s^{-2}

**Solution :** 1kg m^{2}s^{-2} = 1×10^{3} g (10^{2}cm)^{2}s^{-2} = 10^{7}g cm^{2}s^{-2}

**Exercise 1:** (i) What is the value of one micron in centimeter ?

(ii) What is the value of a pressure of 10^{6} dynes/cm^{2} in S.I unit ?

**Exercise 2:**Fill in the blanks :

(a) The volume of a cube of side 1 cm is equal to …..m^{3}

(b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to …….(mm)^{2}

(c) A vehicle moving with a speed of 18 km/h covers………m in 1 s

(d) The relative density of lead is 11.3. Its density is …….g cm^{3} or ……..kg m^{3}.

**Exercise 3:** Fill in the blanks by suitable conversion of units :

(a) 1 kg m^{2} s^{2} = ….g cm^{2} s^{2}

(b) 1 m = ….. ly

(c) 3.0 m s^{-2} = …. km h^{-2}

(d) G = 6.67 × 10^{-11} N m^{2} (kg)^{-2} = …. (cm)^{ 3} s^{-2} g^{-1}

**Exercise 4:** A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m^{2} s^{-2}.

Suppose we employ a system of units in which the unit of mass equals α kg , the unit of length equals β m , the unit of time is γ s. Show that a calorie has a magnitude 4.2 α^{-1} β^{-2} γ^{2} in terms of the new units.