Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) Mg/mm, (b) mN/μs, (c) μm∙Mg.
Statics of Rigid Bodies 14th Edition by RC Hibbeler, Problem 1-8
Solution:
Part A
\begin{align*}
\text{Mg/mm} & = \frac{10^6 \ \text{g}}{10^{-3} \ \text{m}} \\
& = 10^9 \ \frac{\text{g}}{\text{m}}\\
& = \text{Gg/m}
\end{align*}Part B
\begin{align*}
\text{mN/} \mu \text{s} & = \frac{10^{-3} \ \text{N}}{10^{-6} \ \text{s}} \\
& = 10^3 \ \frac{\text{N}}{\text{s}} \\
& = \text{kN/s}
\end{align*}Part C
\begin{align*}
\mu \text{m}\cdot \text{Mg} & = \left( 10^{-6} \ \text{m} \right)\left( 10^6 \ \text{g} \right) \\
& = \text{m}\cdot \text{g}\\
\text{This can also be written as:} \\
& = \text{mm} \cdot \text{kg}
\end{align*}
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