Question

The correct relation between joule and erg is:
$\left(A\right)1J={10}^{-5}erg$
$\left(B\right)1J={10}^{5}erg$
$\left(C\right)1J={10}^{-7}erg$
$\left(D\right)1J={10}^{7}erg$

Answer 1

Hint: Erg and Joule both are the units for work done. Joule is the amount of work done by applying a force of one newton for a distance of $1m$ while $erg$ is the amount of work done by applying force of one dyne for distance of $1cm$.

Formula used: The work done of on any object can be calculated by: $W=F\ast d$
Where $F$- force applied on the object
$d$- distance

Complete step by step answer:
erg is the unit for work done in the CGS base units, i.e. gram centimetre-squared.
So,
$1$joule = $1N\times 1m$
$1J={\displaystyle \frac{1kg\times 1m}{1s^2}}\times 1m$
$\begin{array}{rl}& 1J={\displaystyle \frac{1000g\times 100cm}{1s^2}}\times 100cm\\ & 1J={10}^{7}erg\end{array}$

So, the correct answer is “Option D”.

Additional Information: Joule is defined as the SI unit of work or energy, adequate to the work done by a force of one newton when its point of application moves one metre within the direction of action of the force, like one ${3600}^{th}$ of a watt-hour. Work done by a force on a body are often positive, negative and zero i.e.,
(a) Work done is positive: - Force is within the same direction as displacement for instance work done by force for pushing a block of mass m.
(b) Work done is negative: - Force is opposite to the displacement for instance when a body slides on level work done by frictional forces on the body is negative as frictional force always acts opposite to displacement of the body.

Note: Unit of work done in any system of units is adequate to the unit of force multiplied by the unit of distance. In SI system International unit of work is $1Nm$ and is said Joule(J). Thus,
$1J=1Nm$
In CGS system unit is erg
$1erg=1dyne-cm$