Exercises – Conversion of the Unit of Speed, Density and Pressure

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1. Complete the following unit conversion of speed.

1. 90 kmh^-1 = __________ ms^-1
2. 110 kmh^-1 = __________ ms^-1
3. 1.3 ms^-1 = __________ kmh^-1
4. 8.12 ms^-1 = __________ kmh^-1

Answer:
a. $$\begin{array}{l}90km{h}^{{}_{-1}}\\ =\frac{90km}{1h}=\frac{90\times {10}^{3}m}{60\times 60s}=25m{s}^{-1}\end{array}$$ b. $$\begin{array}{l}110km{h}^{{}_{-1}}\\ =\frac{110km}{1h}=\frac{110\times {10}^{3}m}{60\times 60s}=30.6m{s}^{-1}\end{array}$$ c. $$\begin{array}{l}1.3m{s}^{{}_{-1}}\\ =\frac{1.3m}{1s}=\frac{\raisebox{1ex}{$1.3km$}\!\left/ \!\raisebox{-1ex}{$1000$}\right.}{\raisebox{1ex}{$1h$}\!\left/ \!\raisebox{-1ex}{$60\times 60$}\right.}=\frac{1.3km}{1000}\times \frac{60\times 60}{1h}=4.68km{h}^{{}_{-1}}\end{array}$$ d. $$\begin{array}{l}8.12m{s}^{{}_{-1}}\\ =\frac{8.12m}{1s}=\frac{\raisebox{1ex}{$8.12km$}\!\left/ \!\raisebox{-1ex}{$1000$}\right.}{\raisebox{1ex}{$1h$}\!\left/ \!\raisebox{-1ex}{$60\times 60$}\right.}=\frac{8.12km}{1000}\times \frac{60\times 60}{1h}=29.2km{h}^{{}_{-1}}\end{array}$$

2. Complete the following unit conversion of density and pressure.

1. 760 kgm^-3 = __________ gcm^-3
2. 12000 kgm^-3 = __________ gcm^-3
3. 5.1 gcm^-3 = __________ kgm^-3
4. 3600 Nm^-2 = __________ Ncm^-2
5. 12x10⁶  Nm^-2 = __________ Ncm^-2
6. 1.5x10³ Nm^-2= __________ Ncm^-2
7. 3.16x10^-5 Ncm^-2= __________ Nm^-2
8. 7.1x10^-3 Ncm^-2 = __________ Nm^-2

Answer:
a. $$\begin{array}{l}760kg{m}^{-3}\\ =\frac{760kg}{1m^3}=\frac{760\times {10}^{3}g}{1000000c{m}^3}=0.76gc{m}^{-3}\end{array}$$ b. $$\begin{array}{l}12000kg{m}^{-3}\\ =\frac{12000kg}{1m^3}=\frac{12000\times {10}^{3}g}{1000000c{m}^3}=12gc{m}^{-3}\end{array}$$ c. $$\begin{array}{l}5.1gc{m}^{-3}\\ =\frac{5.1g}{1c{m}^3}=\frac{\raisebox{1ex}{$5.1$}\!\left/ \!\raisebox{-1ex}{$1000$}\right.kg}{\raisebox{1ex}{$1m^3$}\!\left/ \!\raisebox{-1ex}{$1000000$}\right.}=5100kg{m}^{-3}\end{array}$$ d. $$\begin{array}{l}3600N{m}^{-2}\\ =\frac{3600N}{1m^2}=\frac{3600N}{10000c{m}^2}=0.36Nc{m}^{-2}\end{array}$$ e. $$\begin{array}{l}12\times {10}^{6}N{m}^{-2}\\ =\frac{12\times {10}^{6}N}{1m^2}=\frac{12\times {10}^{6}N}{10000c{m}^2}=12\times {10}^{2}Nc{m}^{-2}\end{array}$$ f. $$\begin{array}{l}1.5\times {10}^{3}N{m}^{-2}\\ =\frac{1.5\times {10}^{3}N}{1m^2}=\frac{1.5\times {10}^{3}N}{10000c{m}^2}=0.15Nc{m}^{-2}\end{array}$$ g. $$\begin{array}{l}3.16\times {10}^{-5}Nc{m}^{-2}\\ =\frac{3.16\times {10}^{-5}N}{1c{m}^2}=\frac{3.16\times {10}^{-5}N}{\raisebox{1ex}{$1m^2$}\!\left/ \!\raisebox{-1ex}{$10000$}\right.}=0.316N{m}^{-2}\end{array}$$ h. $$\begin{array}{l}7.1\times {10}^{-3}Nc{m}^{-2}\\ =\frac{7.1\times {10}^{-3}N}{1c{m}^2}=\frac{7.1\times {10}^{-3}N}{\raisebox{1ex}{$1m^2$}\!\left/ \!\raisebox{-1ex}{$10000$}\right.}=71N{m}^{-2}\end{array}$$

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