Question

Show that :
1 joule = 10^7 ergs

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Answer 1

Answer:

We know

1 joule = 1 N force x 1 m

comparing with cgs system

1 erg = 1 dyne force x 1 cm

therefore,

1 joule = 10 ^ 5 dyne x 10^2 cm

thus

1 joule = 10 ^7 ergs

Answer 2

To show that : $1 \ joule = 10^{7} \ ergs$

Proof :  

• As we know that erg is a unit of energy in CGS and joule is unit of energy in MKS.
• We know that dimensional formula for energy is $\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$
• Therefore, by dimensional formula we prove the above expression.
• Let,

       $1 \text { joule }=\mathrm{X} \text { erg }$

      $\mathrm{I}\left[\mathrm{M}_{1} \mathrm{~L}_{1}^{-} \mathrm{T}_{1}^{-}\right]=\mathrm{X}\left[\mathrm{M}_{2} \mathrm{~L}_{2}^{2} \mathrm{~T}_{2}^{-2}\right]$

                         $\mathrm{X}=\frac{\left[\mathrm{M}_{1} \mathrm{~L}_{1}^{2} \mathrm{~T}_{1}^{-2}\right]}{\left[\mathrm{M}_{2} \mathrm{~L}_{2}^{2} \mathrm{~T}_{2}^{-2}\right]}$

                         $\mathrm{X}=\left[\frac{\mathrm{M}_{1}}{\mathrm{M}_{2}}\right]\left[\frac{\mathrm{L}_{1}}{\mathrm{~L}_{2}}\right]^{2}\left[\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right]^{2}$

                        $\mathrm{X}=\left[\frac{\mathrm{Kg}}{\mathrm{gm}}\right]\left[\frac{\mathrm{m}}{\mathrm{cm}}\right]^{2}\left[\begin{array}{l}\mathrm{s} \\- \\\mathrm{s}\end{array}\right]^{-2}$

                        $\mathrm{X}=\left[\frac{1000 \mathrm{gm}}{\mathrm{gm}}\right]\left[\frac{100 \mathrm{~cm}}{\mathrm{~cm}}\right]^{2}(1)^{-2}$

                           $\begin{array}{l}=(10)^{3}\left(10^{4}\right) \\=(10)^{7}\end{array}$

Therefore , $1 \ joule = 10^{7} \ ergs$  .

Hence proved .