The density of a substance is $4 \mathrm{~g} / \mathrm{cc}$ in a system in which unit of length is $5…
The density of a substance is $4 \mathrm{~g} / \mathrm{cc}$ in a system in which unit of length is $5 \mathrm{~cm}$ and unit of mass is $20 \mathrm{~g}$. The density of the substance in CGS system is
16 units
40 units
25 units
50 units
Solution
Density of substance, $\rho=4 \mathrm{~g} / \mathrm{cc}$
Unit of length, $\mathrm{L}=5 \mathrm{~cm}$
Unit of mass, $M=20 \mathrm{~g}$ density of substance in $\mathrm{CGS}_7$
$\begin{aligned}
& \text { density }=\frac{\text { Mass }}{\text { volume }}=\frac{M}{L^3} \\
& \rho^{\prime}=\frac{4 \mathrm{gm}}{1 \mathrm{~cm}^3}=\frac{4 \times \frac{20}{20}(\mathrm{gm})}{\left(1 \times \frac{5}{5}\right)^3 \mathrm{~cm}^3} \\
& =\frac{\left(\frac{4}{20}\right)(20 \mathrm{gm})}{\left(\frac{1}{5}\right)^3(5 \mathrm{~cm})^3} \\
& \Rightarrow \frac{4}{20} \times \frac{(5)^3}{1}\left[\frac{20 \mathrm{gm}}{5 \mathrm{~cm}^3}\right] \\
& \Rightarrow \frac{1}{5} \times 5^3 \text { unit } \\
& \Rightarrow 5^2=25 \text { unit } \\
& \rho^{\prime}=25 \text { unit }
\end{aligned}$