Question

by dimension analysis prove
$1j = {10}^{7} erg$
find the dimensions of work and
density

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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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