Question

If The density of wood in $C.G.S$ system is $0.5\,g\,cm^{- 3}$ .If the corresponding value in $S.I.$ the system is $N\times 10^{2}$ , Find the value of $N$ ?

Answer 1

The unit of density in SI system is $kg\,m^{- 3}$ . From the dimensional analysis method, both densities should have the same amounts. Let the value of the density in standard units is $x$ , then we can write,
$0.5\frac{gm}{cm^{3}}=x\frac{kg}{m^{3}}$
$\frac{0 . 5 \times 10^{- 3}}{10^{- 6}}kg/m^{3}=xkg/m^{3}$
$x=\frac{0 . 5 \times 10^{- 3}}{10^{- 6}}=500$
In terms of $N$ , we have $x=5\times 10^{2}$ , so $N=5$ .