Question

Convert the energy of 50 erg into joule by using dimensional analysis

Answer 1

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Joule is the unit for energy

Dimension Formula for Joule is [M¹L²T^-²]

Let n1(joule)=n2(erg)

n1(M₁¹L₁²T₁^-²]=n2[M₂¹L₂²T₂^-²]

n2=n1(M₁¹L₁²T₁^-²] /M₂¹L₂²T₂^-²]

=n1x(M1/M2)¹x(L1/L2)²x(T1/T2)^-²

=1x(1kg/gm)¹x(1m/1cm)²x(1s/1s)^-²

=1x(1000g/gm)x(100cm/1cm)² x(1s/1s)^-²

=10^⁷ 

Therefore n1(joule)=n2(erg)

∴1 Joule=10^⁷erg

or 1erg= 1/10^7 joule

In your question , about converte 50 erg to joule .

1 erg = 1/10^7 joule

than ,

50 erg = 50/ 10^7 joule

= 50× 10^-7 joule

= 5× 10^-6 joule

so your ans is 5×10^-6 joule.

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Answer 2

here your answer, gave me another questions