Question

Derive a relationship between S.I and C.G.S unit of work.

Answer 1

Hint – In this question use the concept that Joule is a unit in the SI system whereas erg is a unit in the C.G.S system of measurement. C.G.S refers to the unit of centimeter, gram and second. So $1 \text{erg} = 1 \text{gm}\times \dfrac{\text{cm}^2}{s^2}$. This will help get the right relationship for the given problem statement.

Complete step-by-step solution -
As we all know that the unit of work is joule
Now, as we know that both Joule and erg are the unit of work.
Where, Joule is a S.I unit and erg is a C.G.S unit.
S.I = system of international unit, where as
C.G.S = centimeter gram second.
Now as we know that $1\text{joule} = 1 \text{kg}\times \dfrac{\text{m}^2}{s^2}$.
And $1 \text{erg} = 1 \text{gm}\times \dfrac{\text{cm}^2}{s^2}$.
Now first convert kilogram into gram we have,
As we know that 1Kilograms = 1000grams....................... (1)
Now convert meter into centimeter we have,
As we know that 1m = 100cm
Now square on both sides we have,
1 square meter = 10000 square centimeter.......................... (2)
Now multiply equation (1) and (2) we have,
$1 \text{kg}\; {\text{m}^2} = 1000(10000) \text{gm}\; {\text{cm}^2}$.
Now divide by second square on both sides we have,
$1\text{kg}\times\dfrac{\text{m}^2}{s^2}$=$1000(10000)\text{gm}\times \dfrac{\text{cm}^2}{s^2}$.
Therefore,
$1\text{kg}\times\dfrac{\text{m}^2}{s^2}$ = ${10^7} \text{gm} \dfrac{\text{cm}^2}{s^2}$.
Therefore, 1 joule = ${10^7}$ erg.
So S.I unit of work = ${10^7}$ times the C.G.S unit of the work.
So this is the required relation between the S.I and the C.G.S unit of the work.
So this is the required answer.

Note – SI units is known as international systems of units, it is a system of physical units based upon the meter, kilogram, second, ampere, kelvin, candela and mole together with a set of prefixes to indicate the multiplication or division by a power of 10.