#### IIT (NTSE/Olympiad)

# Unit, Dimension & Error

__Units__

__Units__

2.1 That fixed and definite quantity which we take as our

(a) Fundamental Units

(b) Derived Units

There are seven fundamental units.

(i) Unit of mass

(ii) Unit of length

(iii) Unit of time

(iv) Unit of temperature

(v) Unit of electric current

(vi) Unit of luminous intensity

(vii)Unit of amount of substance

The unit of a physical quantity is inversely proportional to its numerical value i.e., u ∝ 1/n where u and n are the units of physical quantity and its numerical value respectively. Relation between unit and its numerical value n

(i) Selected unit must be universal, of proper size and magnitude

(ii) Unit must be not affected by temperature, pressure and time.

(iii) Easily definable and reproducible.

These are of Four types –

(i) C.G.S – (Centimeter – Gram – Second) system.

(ii) M.K.S. – (Metre – Kilogram – Second) system

(iii) F.P.S. – (Foot – Pound – Second) system

(iv) S.I. – (System – international) system

Following table will show the difference between all the systems.

Solid angle Ω = A/R

when A = R

Ω = 1 steradian

**standard of reference**and by which we measure other quantities of same kind, is defined unit. There are of two types.(a) Fundamental Units

(b) Derived Units

**(a) Fundamental Units :**The units which are independent and which are not be derived from other units, are defined as fundamental units. e.g. The unit of mass, length, and time.There are seven fundamental units.

(i) Unit of mass

(ii) Unit of length

(iii) Unit of time

(iv) Unit of temperature

(v) Unit of electric current

(vi) Unit of luminous intensity

(vii)Unit of amount of substance

**(b) Standard Units :**The fixed and definite real value of any physical quantity is defined as standard unit.**2.2 Properties of Units :**The unit of a physical quantity is inversely proportional to its numerical value i.e., u ∝ 1/n where u and n are the units of physical quantity and its numerical value respectively. Relation between unit and its numerical value n

_{1}u_{1}= n_{2}u_{2}**2.3 Selection Criteria Of Units :**(i) Selected unit must be universal, of proper size and magnitude

(ii) Unit must be not affected by temperature, pressure and time.

(iii) Easily definable and reproducible.

**2.4 System Of Units Used :**These are of Four types –

(i) C.G.S – (Centimeter – Gram – Second) system.

(ii) M.K.S. – (Metre – Kilogram – Second) system

(iii) F.P.S. – (Foot – Pound – Second) system

(iv) S.I. – (System – international) system

Following table will show the difference between all the systems.

Quantity | C.G.S. | M.K.S. | F.P.S. | S.I.(Symb.) |
---|---|---|---|---|

Mass | gm | kg | pound | kg |

Length | cm | m | foot | metre |

Time | second | sec | sec | second |

Temperature | kelvin | kelvin | kelvin (K) | |

Electric Current | ampere | ampere(A) | ||

Luminous Intensity | candela (cd) | |||

Amount of substance | mole(mol) |

**2.5 Supplementary Unit :****(a) Radian :**→ 1 radian is the angle subtended by arc of length equal to the radius, at the centre of the circle.**(b) Steradian :**It is defined as the solid angle subtended at the centre of the sphere by an arc of its surface equal to the square of radius of the sphere.Solid angle Ω = A/R

^{2}when A = R

^{2}Ω = 1 steradian

#### IIT (Class X)

- Unit, Dimension & Error

- Vectors

- Motion in One Dimension

- PROJECTILE MOTION

- NEWTON'S LAWS OF MOTION & FRICTION

- WORK, POWER, ENERGY & CONSERVATION LAWS

- CIRCULAR MOTION & ROTATIONAL DYNAMICS

- GRAVITATION