Question

convert 1 joule to erg in dimensional analysis​

Answer 1

Joule is the SI unit of energy, while erg is the CGS unit of energy.

1 Joule of Energy = 1 Newton x 1 metre

1 erg = 1 dyne x 1 cm

1 joule= 1 newton x 1 metre=

1 joule = 105 dynes x 102 cm

1 joule =107 erg

Dimension Formula for Joule is [M¹L²T⁻²]

Let N1(joule) = N2(erg)

N1[M₁¹L₁²T₁⁻²] = N2[M₂¹L₂²T₂⁻²]

N2 = N1[M₁¹L₁²T₁⁻²] /[M₂¹L₂²T₂⁻²]

N1 x [M1/M2]¹ x [L1/L2]² x [T1/T2]⁻²

1 x [1kg/gm]¹ x [1m/1cm]² x [1s/1s]⁻²

1 x (1000g/gm) x (100cm/1cm)² x (1s/1s)⁻²

⇒ 10⁷

N1(joule) = N2(erg)

∴ 1 Joule = 10⁷erg