Question

Show that 1 joule to 10^7 ergs in dimensional analysis

Answer 1

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

Hey there!

(M₁ L₁² T₁⁻²) = (X) (M₂ L₂² T₂⁻²)

  = (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

.: 1 joule =10⁷ ergs

Hope it helps