UNIT: 1 UNITS AND MEASUREMENT || chapter 1 of class-11

 UNIT: 1

UNITS AND
MEASUREMENT

Measurement:

The comparison of an unknown quantity
with a known standard quantity is called measurement.

Physical quantity:

Those quantities which can be
measured directly or indirectly are called physical quantities. There are two
types of physical quantities:

•        Fundamental Physical Quantity
•        Derived Physical Quantity

List of fundamental physical quantities with its unit and symbols:

Two supplementary fundamental quantities:

          FUNDAMENTAL
QUANTITIES             UNIT            SYMBOL

1.                                Plane
angle                                         
Radian             rad               

2.                               Solid
angle                                           Steradian           s

System of measurement

1.     FPS System

2.     MKS System

3.     SI system

Dimension

The power in which fundamental quantities are raised to express any physical
quantity is called Dimension.

The fundamental formula is the expression of any physical quantity in terms of its base unit.

Dimension of mass = [M]

Dimension of length = [L]

Dimension of time = [T]

Dimension of temperature = [K]

Dimension of current = [A]

Dimensionless quantity

The Physical quantity which has neither dimension nor variables with the condition is called a Dimensionless
quantity. For example - 1, 2, 3, 4...…, etc.

Note: - exponential, trigonometric, and logarithmic functions are
dimensionless. Dimension of some Physical quantities.

1.     Area = Length
X Breadth

                       =
[L] X [L]

                       = [L²]

2.     Volume = Length
X Breadth X Height

                            = [L]
X [L] x [L]

                            = [L³]

Application of dimensional equation

1.     To check the correctness
of any physical equation

2.     To change the
unit from one system to another system

3.     To derive the
relation between different physical quantities

1.     To check the
correctness of any physical equation =>>

a. V² = u² + 2as

   soln:

   Here,

Dimension of V = [LT^-1]

Dimension of u = [LT^-1]

Dimension of a =[LT^-2]

Dimension of S = [L]

Dimension of LHS = V²

 
                               =
[LT^-1]²

                                = [L²T^-2]

Dimension of RHS = u² + 2as

                                 = [LT^-1]²
+ 2[LT^-2] X [L]

                                 = [L²T^-2]
+ 2[L²T^-2]

                                 = 3[L²T^-2]

3 is dimensionless quantity, so it can be
removed.

∴Dimension of RHS = [L²T^-2]

Here, Dimension of LHS = Dimension of RHS

So, this formula is correct.

Soln:

Here,

Dimension
of V = [LT^-1]

Dimension
of G = [M^-1L³T^-2]

Dimension
of M = [M]

Dimension
of R = [L]

Dimension
of LHS = V

                                 = [LT^-1]

∴ Dimension of RHS = [LT^-1]

Here, Dimension of LHS = Dimension of RHS

So, this formula is correct.

Where, g =
acceleration due to gravity, L = Length, T = Time

Soln:          
Here,                                                                                                                                                                          Dimension of T = [T]                                                                                                                                                    Dimension
of g = [LT^-2]                                                                                                                                              Dimension of L = [L]                                                                                                                                                    Dimension of LHS =
[T]