Step-by-Step Solution
Step 1
We are given the units ${\rm{kN/\mu s}}$, ${\rm{Mg/mN}}$ and ${\rm{MN/}}\left( {{\rm{kg}} \cdot {\rm{ms}}} \right)$.
We are asked to estimate the correct SI form of the units.
Step 2
(a)
To find the SI form of unit ${\rm{kN/\mu s}}$ we need to reduce the combinations of units.
Since $1\;{\rm{kN}} = {\rm{1}}{{\rm{0}}^3}\,{\rm{N}}$ and $1\;{\rm{\mu s}} = {\rm{1}}{{\rm{0}}^{ – 6}}\;{\rm{s}}$, then\[\begin{array}{c} {\rm{kN/\mu s}} = \left( {\frac{{{\rm{kN}} \times \frac{{{{10}^3}\,{\rm{N}}}}{{1\;{\rm{kN}}}}}}{{{\rm{\mu s}} \times \frac{{{{10}^{ – 6}}\,{\rm{s}}}}{{1\;{\rm{\mu s}}}}}}} \right)\\ {\rm{kN/\mu s}} = \left( {{{10}^9}\;{\rm{N/s}} \times \frac{{1\;{\rm{GN/s}}}}{{{{10}^9}\;{\rm{N/s}}}}} \right)\\ {\rm{kN/\mu s}} = 1\;{\rm{GN/s}} \end{array}\]
Step 3
(b)
To find the SI form of unit ${\rm{Mg/mN}}$ we need to reduce the combinations of units.
Since $1\;{\rm{Mg}} = {\rm{1}}{{\rm{0}}^3}\,{\rm{kg}}$ and $1\;{\rm{mN}} = {\rm{1}}{{\rm{0}}^{ – 3}}\;{\rm{N}}$, then\[\begin{array}{c} {\rm{Mg/mN}} = \left( {\frac{{{\rm{Mg}} \times \frac{{{{10}^3}\,{\rm{kg}}}}{{1\;{\rm{Mg}}}}}}{{{\rm{mN}} \times \frac{{{{10}^{ – 3}}\,{\rm{N}}}}{{1\;{\rm{mN}}}}}}} \right)\\ {\rm{Mg/mN}} = \left( {{{10}^6}\;{\rm{kg/N}} \times \frac{{1\;{\rm{Mkg/N}}}}{{{{10}^6}\;{\rm{kg/N}}}}} \right)\\ {\rm{Mg/mN}} = 1\;{\rm{Mkg/N}} \end{array}\]
Step 4
(c)
To find the SI form of unit ${\rm{MN/}}\left( {{\rm{kg}} \cdot {\rm{ms}}} \right)$ we need to reduce the combinations of units.
Since $1\;{\rm{MN}} = {\rm{1}}{{\rm{0}}^6}\,{\rm{N}}$ and $1\;{\rm{ms}} = {\rm{1}}{{\rm{0}}^{ – 3}}\;{\rm{s}}$, then\[\begin{array}{c} {\rm{MN/}}\left( {{\rm{kg}} \cdot {\rm{ms}}} \right) = \left( {\frac{{{\rm{MN}} \times \frac{{{{10}^6}\,{\rm{N}}}}{{1\;{\rm{MN}}}}}}{{{\rm{kg}} \cdot \left( {{\rm{ms}} \times \frac{{{{10}^{ – 3}}\,{\rm{s}}}}{{1\;{\rm{ms}}}}} \right)}}} \right)\\ {\rm{MN/}}\left( {{\rm{kg}} \cdot {\rm{ms}}} \right) = \left[ {{{10}^9}\;{\rm{N/}}\left( {{\rm{kg}} \cdot {\rm{s}}} \right) \times \frac{{1\;{\rm{GN/}}\left( {{\rm{kg}} \cdot {\rm{s}}} \right)}}{{{{10}^9}\;{\rm{N/}}\left( {{\rm{kg}} \cdot {\rm{s}}} \right)}}} \right]\\ {\rm{MN/}}\left( {{\rm{kg}} \cdot {\rm{ms}}} \right) = 1\;{\rm{GN/}}\left( {{\rm{kg}} \cdot {\rm{s}}} \right) \end{array}\]