Question

Derive a relationship between $SI$ and $CGS$ unit of work.

Answer 1

Units of work:

1. $SI$ unit of work is Joule ($J$) or Newton Meter ($Nm$).
2. $CGS$ Unit of work is erg or dyne centimeter ($dyne cm$).

Relation between SI and CGS unit of work

$1N={10}^{5}dyne......\left(i\right)$

$1m=100cm......\left(ii\right)$

Now,

$1J=1Nm........\left(iii\right)$

Substitute$\left(i\right)$and $\left(ii\right)$in$\left(iii\right)$

$={10}^{5}dyne\times 100cm$

$1J={10}^5\times {10}^{2}dyne cm$

$1J={10}^{5+2}erg$

$1J={10}^{7}erg........\left(iv\right)$

From equation$\left(iv\right)$we get, $SI$ unit of work is ${10}^7$times of CGS unit of work.