Question

The density of a material in CGS system is $2g/{cm}^3$. In a system of units in which unit of length is $2cm$ and unit of mass is $4g$, what is the numerical value of the density of the material?

Answer 1

The density of the material in the other system can be found as:

$n_1{u}_1=n_2{u}_2$

$n_2=\frac{u_1}{u_2}{n}_1$

The dimensions of the density is $\left[M{L}^{-3}\right]$.

$n_2=\left[\left[\frac{M_1}{M_2}\right]{\left[\frac{L_1}{L_2}\right]}^{-3}\right]\times 2$

$n_2=\left[\left[\frac{1g}{4g}\right]{\left[\frac{1cm}{2cm}\right]}^{-3}\right]\times 2$

$n_2=4$

So, the density in new system will be $4$.