Question

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

Answer 1

Answer: 5

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,
$0.5\frac{gm}{c{m}^3}=x\frac{kg}{m^3}$
$\frac{0.5\times 10^{-3}}{10^{-6}}kg/m^3=xkg/m^3$
$x=\frac{0.5\times 10^{-3}}{10^{-6}}=500$
In terms of $N$ , we have $x=5\times 10^2$ , so $N=5$ .