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