Chapter 1, Problem 1P

a)

To determine

Correct SI form of $\text{mm}\cdot \text{MN}$.

Explanation of Solution

Given:

$\text{mm}\cdot \text{MN}$

Calculation:

Convert the quantities.

  $\begin{array}{c}\text{mm}\cdot \text{MN}=\left(1\text{ mm}\times \frac{1\text{ m}}{{10}^3\text{mm}}\right)\cdot \left(1\text{MN}\times \frac{\left({10}^3\right)\text{kN}}{1\text{ MN}}\right)\\ \text{mm}\cdot \text{MN}=\frac{1}{\left({10}^3\right)}\text{m}\cdot \left({10}^3\right)\text{kN}\\ =\text{kN}\cdot \text{m}\end{array}$

Thus, the correct SI form for $\text{mm}\cdot \text{MN}$ is $\underset{\_}{\text{kN}\cdot \text{m}}$.

b)

To determine

Correct SI form of $\text{Mg}/\text{mm}$.

Explanation of Solution

Given:

$\text{Mg}/\text{mm}$

Calculation:

Convert the quantities.

  $\begin{array}{c}\text{Mg}/\text{mm}=\left(\text{Mg}\times \frac{1\text{ Gg}}{{10}^3\text{ Mg}}\right)/\left(\left(1\text{ mm}\times \frac{1\text{ m}}{{10}^3\text{mm}}\right)\right)\\ =\frac{{10}^3\text{Gg}}{{\text{10}}^3\text{m}}\\ \text{=}\text{Gg}/\text{m}\end{array}$

Thus, the correct SI form for $\text{Mg}/\text{mm}$ is $\underset{\_}{\text{Gg}/\text{m}}$.

c)

To determine

Correct SI form of $\text{km}/\text{ms}$.

Explanation of Solution

Given:

$\text{km}/\text{ms}$

Calculation:

Convert the quantities.

  $\begin{array}{c}\text{km}/\text{ms}=\left(\text{1 km}\times \frac{1\text{ Mm}}{{10}^3\text{ km}}\right)/\left(\left(1\text{ ms}\times \frac{1\text{ s}}{{10}^3\text{ms}}\right)\right)\\ =\frac{{10}^3\text{Mm}}{{\text{10}}^3\text{s}}\\ \text{=}\text{Mm}/\text{s}\end{array}$

Thus, the correct SI form for $\text{km}/\text{ms}$ is $\underset{\_}{\text{Mm}/\text{s}}$.

d)

To determine

Correct SI form of $\text{kN}/{\text{mm}}^2$.

Explanation of Solution

Given:

$\text{kN}/{\text{mm}}^2$

Calculation:

Convert the quantities.

  $\begin{array}{c}\text{kN}/{\text{mm}}^2=\left(\text{1 kN}\times \frac{1\text{ GN}}{{10}^6\text{ kN}}\right)/\left(\left({\left(1\text{ mm}\right)}^2\times \frac{1{\text{ m}}^2}{{10}^6{\text{mm}}^2}\right)\right)\\ =\frac{{10}^6\text{GN}}{{\text{10}}^6{\text{m}}^2}\\ \text{=}\text{GN}/{\text{m}}^2\end{array}$

Thus, the correct SI form for $\text{kN}/{\text{mm}}^2$ is $\underset{\_}{\text{GN}/{\text{m}}^2}$.