Question

4. Convert using dimensional analysis
(i) 18/5 kmph into m/s
(ii) 5/18 m/s into kmph
(iii) 13.6 g/cm³ into kg/m³

Answer 1

Dear Student,

$$\begin{gathered} \left(1\right)\frac{18}{5}\mathrm{km}/\mathrm{h}\mathrm{into}\mathrm{m}/\mathrm{s} \\ 1\mathrm{km}=1000\mathrm{m} \\ 1\mathrm{h}=3600\mathrm{s} \\ 1\mathrm{km}/\mathrm{h}=\frac{1000}{3600}\mathrm{m}/\mathrm{s} \\ \frac{18}{5}\mathrm{km}/\mathrm{h}=\frac{18}{5}\times \frac{1000}{3600}=1\mathrm{m}/\mathrm{s} \\ \left(2\right)\frac{5}{18}\mathrm{m}/\mathrm{s}\mathrm{into}\mathrm{km}/\mathrm{h} \\ 1\mathrm{m}=\frac{1}{1000}\mathrm{km} \\ 1\mathrm{s}=\frac{1}{3600}\mathrm{h} \\ 1\mathrm{m}/\mathrm{s}=\frac{3600}{1000}\mathrm{km}/\mathrm{h} \\ \frac{5}{18}\mathrm{m}/\mathrm{s}=\frac{5}{18}\times \frac{3600}{1000}=1\mathrm{km}/\mathrm{h} \\ \left(3\right)13.6\mathrm{g}/{\mathrm{cm}}^3\mathrm{into}\mathrm{kg}/{\mathrm{m}}^3 \\ 1\mathrm{g}=\frac{1}{1000}\mathrm{kg} \\ 1\mathrm{cm}=\frac{1}{100}\mathrm{m} \\ 1{\mathrm{cm}}^3={\left(\frac{1}{100}\right)}^3{\mathrm{m}}^3 \\ 1\mathrm{g}/{\mathrm{cm}}^3=\frac{1000000}{1000}\mathrm{kg}/{\mathrm{m}}^3 \\ 13.6\mathrm{g}/{\mathrm{cm}}^3=1000\times 13.6=13600\mathrm{kg}/{\mathrm{m}}^3 \end{gathered}$$