using dimension show that 1j=10^7er
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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
= 10⁷erg
Hence
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
= 10⁷erg
Hence
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