Question

$convert \: {10}^{ - 3} erg \: in \: joule$
Fast as you can ​

Answer 1

$1erg \: = {1.0} \times {10}^{ - 7} joule$

$answer \: -$

$1 .0 \times {10}^{ - 10} joule$

Answer 2

Answer: $1\times10^{-10}\:J$

Explanation:

Convert $10^{-3}$erg in joule :-

The CGS and SI units of work or energy are erg and joule respectively.

Work = Force × displacement

So, the dimensional formula for Work;

= [MLT⁻²] [L]

= [ML²T⁻²]

Thus, 1 erg = (1 g) (1 cm) (1 s)⁻²

and 1 joule = (1 kg) ( 1 m) (1 S)⁻²

Now, for conversion of units of a physical quantity, [MᵃLᵇTᶜ]

We use the formula;

$\boxed{n_2=n_1\bigg(\frac{M_1}{M_2}\bigg)^a\:\bigg(\frac{L_1}{L_2}\bigg)^b\:\bigg(\frac{T_1}{T_2}\bigg)^c}$

Putting values in the above formula;

$= 10^{-3} \bigg(\frac{1\:g}{1\:kg}\bigg) \bigg(\frac{1\:cm}{1\:m}\bigg)^2\bigg(\frac{1\:s}{1\:s}\bigg)^{-2}\\\\\\= 10^{-3}\bigg(\frac{1\:g}{1000\:g}\bigg)\bigg(\frac{1\:cm}{100\:cm}\bigg)^2$

$=10^{-3} (10^{-3}) (10^{-4})\\\\= 10^{-10}$

$\implies \bf \underline {\boxed {10^{-3}\:erg=1\times10^{-10}\:J}}$