The density of a material in CGS system is 10 g cm^-3 . If unit of length becomes 10 cm and unit of mass becomes 100 g, the new value of density will be

$$\begin{gathered} \because \mathrm{Density}=\frac{\mathrm{Mass}}{\mathrm{Volume}} \\ \therefore \mathrm{Dimensions} \mathrm{of} \mathrm{density}=\frac{\left[\mathrm{M}\right]}{{\left[\mathrm{L}\right]}^3}=\left[{\mathrm{ML}}^{-3}\right] \end{gathered}$$
Given, n₁ =10, M₁ =1 g, L₁=1 cm,
In new system, n₂ = ?, M₂ =100 g, L₂ =10 cm
So, conversion of 10g cm^-3 into new system
$$\begin{gathered} {\mathrm{n}}_2={\mathrm{n}}_1 \mathrm{x} \left[\frac{{\mathrm{M}}_1}{{\mathrm{M}}_2}\right]{\left[\frac{{\mathrm{L}}_1}{{\mathrm{L}}_2}\right]}^{-3} \\ =10 \mathrm{x} \left(\frac{1}{100}\right){\left(\frac{1}{10}\right)}^{-3} \\ =10 \mathrm{x} \frac{1}{100} \mathrm{x} 10 \mathrm{x} 10 \mathrm{x}10 \\ =100 \mathrm{units} \end{gathered}$$