Question

Using dimension show that 1 joule = 10raised to the power 7 erg

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.

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