Question

using dimension show that 1joule = 10to power 7 erg

Answer 1

Hey there!

Joule is the S. I unit of work done or energy and Erg is the CGS unit of work done or energy

Joule is the energy required to displace a body by 1m using 1 Newton force.

So, Joule = Nm = kgm/s² (m) = 1 kgm²/s²
Erg = DyneCm = gcm²/s²

Now, Proving that 1 Joule = 10^7 erg.

=> 1 Joule

=> 1 kgm/s²

$=> \frac{1 \times ( 10^3g ) \times ( 10^2 \times {10}^{ - 2} m) ^{2} }{ {s}^{2} } \\ \\ => \frac{1 \times ( 10^3g ) \times ( 10^2 \times c m) ^{2} }{ {s}^{2} } \\ \\ = > \frac{1 \times ( 10^3g ) \times ( 10^2 ) ^{2} \times cm ^{2} }{ {s}^{2} } \\ \\ \\ = > \frac{1 \times ( 10^3) \times ( 10^2 ) ^{2} \times gcm ^{2} }{ {s}^{2} } \\ \: \\ = > {10}^{3} \times {10}^{4} erg \\ \\ = > {10}^{7} erg$

Hope helped