Conversion Of Unit From MKS (SI) To (CGS)

1. Velocity:

We know, 

Velocity = distance/(time)
Or, (v = s/t)

Dimensional formula of acceleration,

[v] = L/T = LT^-1

So, 1 m/s = (1 m) (1 s)^-1

      1 cm/s = (1 cm) (1 s)^-1

Thus, (1 m/s)/(1 cm/s) = (1 m/1 cm) (1 s/1 s)^-1

Or, (1 m/s)/(1 cm/s) = (100 cm/1 cm) (1 s/1 s)^-1

Or, (1 m/s)/(1 cm/s) = (10)² (1)^-1

Or, (1 m/s)/(1 cm/s) = 10²

ஃ  1 m/s = 10² cm/s = 100 cm/s.

2. Acceleration:

We know, 

Acceleration = length/ (time) ²     (a = L/t²)

Dimensional formula of acceleration,

[a] = L/T² = LT^-2

So, 1 m/s² = (1 m) (1 s) ^-2

      1 cm/s² = (1 cm) (1 s) ^-2

Thus, (1 m/s²)/ (1 cm/s²) = (1 m/1 cm) (1 s/1 s)^-2

Or, (1 m/s²)/ (1 cm/s²) = (100 cm/1 cm) (1 s/1 s) ^-2

Or, (1 m/s²)/ (1 cm/s²) = (10)² (1)^-2

Or, (1 m/s²)/ (1 cm/s²) = 10²

ஃ   1 m/s² = 10² cm/s² = 100 cm/s².

3. Density:                 

We know, 

Density = mass/volume     (ρ = m/v)

Dimensional formula of density,

[ρ] = M/L³ 

     = ML^-3 ^-

So, 1 kg/m³ = (1 kg) (1 m^-3)

      1 g/cm³ = (1 g) (1cm^-3)

Thus, (1 kg/m³)/ (1 g/cm³) = (1 kg/1 g) (1 m/1 cm)^-3

Or, (1 kg/m³)/ (1 g/cm³) = (1000 g/1 g) (100 cm/1cm) ^-3

Or, (1 kg/m³)/ (1 g/cm³) = (10)³ (10²)^-3

Or, (1 kg/m³)/ (1 g/cm³) = 10^-3           

ஃ 1 kg/m³ = 10^-3 g/cm³ = 0.001 g/cm³.

4. Force:

We know, 

Force = mass * acceleration     (F = m*a)

Dimensional formula of Force,

[F] = [m]*[a] = M LT^-2 = MLT^-2

So, 1 Newton = (1 kg) (1 m) (1 s)^-2

      1 dyne = (1 g) (1 cm) (1 s)^-2

Thus, 1 Newton/1 dyne = (1 kg/1 g) (1 m/1 cm) (1 s/1 s)^-2

Or, 1 Newton/1 dyne = (1000 g/1 g) (100 cm/1 cm) (1 s/1 s)^-2

Or, 1 Newton/1 dyne = (10)³ (10²)  

Or, 1 Newton/1 dyne = 10⁵

ஃ 1 Newton = 10⁵ dyne.

5. Pressure:

We know, 

 Pressure = Force/ (Area)     (P = F/A)

Dimensional formula of Pressure,

[P] = [F]/ [A] = MLT^-2/L² = ML^-1T^-2

So, 1 Pascal = (1 kg) (1 m) ^-1 (1 s)^-2

1 CGS pressure = (1 g) (1 cm)^-1 (1 s)^-2

Thus, 
1 Pascal/1 CGS pressure = (1 kg/1 g) (1 m/1 cm)^-1 (1 s/1 s)^-2

= (1000 g/1 g) (100 cm/1 cm)^-1 (1 s/1 s)^-2

= (10)³ (10²)^-1

= 10

ஃ 1 Pascal = 10 CGS pressure.

6. Work & Energy:

We know, 

Work = Force * distance    (W = F * d)

Dimensional formula of work,

[W] = [F] * [d] = MLT^-2 L = ML²T^-2

So, 1 joule = (1 kg) (1 m)² (1 s)^-2

      1 erg = (1 g) (1 cm)² (1 s)^-2

Thus, 1 joule/1 erg = (1 kg/1 g) (1 m/1 cm)² (1 s/1 s)^-2

= (1000 g/1 g) (100 cm/1 cm)² (1 s/1 s)^-2

= (10)³ (10²)²

= 10⁷

ஃ 1 joule = 10⁷ erg.

Both work and energy are dimensionally identical and same unit.

Dimensionally, Kinetic Energy = mass * (velocity)²  

                = mass* (length/time)²   

Or, Potential Energy = mass * acceleration * distance

                = mass * length/ (time)² * length

Both have same dimensional formula

[E] = ML²T^-2

So, 1 joule = (1 kg) (1 m)² (1 s)^-2

      1 erg = (1 g) (1 cm)² (1 s)^-2

Thus, 1 joule/1 erg = (1 kg/1 g) (1 m/1 cm)² (1 s/1 s)^-2

= (1000 g/1 g) (100 cm/1 cm)² (1 s/1 s)^-2

= (10)³ (10²)²

= 10⁷

ஃ 1 joule = 10⁷ erg.

7. Power:

We know, 

Power = Force * velocity      (P = F * v)

Dimensional formula of Power,

[P] = [F] [v] = MLT^-2 LT^-1 = ML²T^-3

So, 1 watt (J/s) = (1 kg) (1 m)² (1 s)^-3

      1 CGS power (erg/s) = (1 g) (1 cm)² (1 s)^-3

Thus, 

1 watt /1 CGS power = (1 kg/1 g) (1 m/1 cm)² (1 s/1 s)^-3

= (1000 g/1 g) (100 cm/1 cm)² (1 s/1 s)^-3

= (10)³ (10²)²

= 10⁷

ஃ 1 watt (J/s) = 10⁷ erg/s.

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