Question

Convert One joule to ergs.

Answer 1

Hint: Joule is the SI unit of work done and erg is the CGS unit of work done. The conversion can be done by writing the units in the SI system and then converting the mass length and time of the unit into the CGS system.

Step by step solution:
Let us now see the unit of work done in the SI system. We can even derive the units on our own for work done using the formula as below
Work done is given as force times displacement and force is mass times acceleration so work done can be expressed as :

Workdone =
Force $\times$ displacement = mass $\times$ acceleration $\times$ displacement

Units for length, mass, and time are :

Using the above units in SI system we can write the units for Work are $kg\times{\dfrac{m}{s}}^2\times m$ which is equal to one joule and now let us write each component or quantity in the CGS system in the above unit. We get as below

Work done = $kg\times{\dfrac{m}{s}}^2\times m$ = $1000 \times{\dfrac{100cm}{s}}^2\times 100cm$.

so we got after substituting the equivalent values with their CGS values as:

1 Joule = ${10}^7\ \times g\times\dfrac{cm^3}{s} = 10^7 ergs$
Where the unit for the ergs becomes $g\times\dfrac{cm^3}{s}$

Note: The key tip in solving the above type of questions is to write the units in the known system and then substitute the units of length, mass and time in the required system. This tip can be used to solve this kind of problem easily.