Question

Work done is defined as force times displacement i.e $F.s$. The unit of work done is $\text{Newton-meter}$ and SI unit is called as $\text{Joule}$. The CGS unit of work done is called $\text{erg}$. Then, $1\text{joule}$ is equal to ${10}^n\text{erg}$. The value of $n$ is

Answer 1

SI unit of work done = $\text{Joule}$
$1\text{Joule}=1\text{N-m}$
Converting $1\text{N-m}$ to CGS units.
$1\text{N-m}=1{\text{kg m}}^2{\text{s}}^{-2}$
$1{\text{kg m}}^2{\text{s}}^{-2}=1\times {10}^3\times {10}^4{\text{gram-cm}}^2{\text{s}}^{-2}$
$1\times {10}^3\times {10}^4{\text{gram-cm}}^2/{\text{s}}^2={10}^7\text{erg}$

Hence, $1\text{Joule}={10}^7\text{erg}$