Question

Show that 1 joule = 10'erg.

Answer 1

Answer:

We have to prove that

 1 joule = 10⁷ erg 

Proof:

Lets suppose that 1 joule = Χ erg  ⁻⁻⁻⁻⁻⁻⁻⁻⁻ (1)

Since, 

[E] = M L² T⁻²

Putting this value in equarion (1), we get :

(1) (M₁ L₁² T₁⁻²) = (X) (M₂ L₂² T₂⁻²)

X = (M₁/M₂) (L₁²/L₂²) (T₁⁻²/T₂⁻²)

   = (kg/gm) (m/cm)² (s/s)⁻²

   = (1000gm/1gm) (100cm/1cm)² (1)⁻²

   = (10)³ (10²)² (1)

   = (10)³ (10)⁴

   = (10)³⁺⁴

   = 10⁷

Hence proved.

Answer 2

Answer:

We have to prove that

 1 joule = 10⁷ erg 

Proof:

Lets suppose that 1 joule = Χ erg  ⁻⁻⁻⁻⁻⁻⁻⁻⁻ (1)

Since, 

[E] = M L² T⁻²

Putting this value in equarion (1), we get :

(1) (M₁ L₁² T₁⁻²) = (X) (M₂ L₂² T₂⁻²)

X = (M₁/M₂) (L₁²/L₂²) (T₁⁻²/T₂⁻²)

   = (kg/gm) (m/cm)² (s/s)⁻²

   = (1000gm/1gm) (100cm/1cm)² (1)⁻²

   = (10)³ (10²)² (1)

   = (10)³ (10)⁴

   = (10)³⁺⁴

   = 10⁷

Hence proved.