Answer:
(a) km/s
(b) mm
(c) Gs/kg
(d) mmN
Explanation:
(a) Given:
m / ms => the proper SI unit should be m/s
So let's convert to m/s
m / ms = [tex]\frac{m}{ms}[/tex]
The denominator is ms which means milliseconds.
But milli = 10⁻³
∴ [tex]\frac{m}{ms}[/tex] = [tex]\frac{m}{10^{-3}s}[/tex] = [tex]\frac{10^3m}{s}[/tex]
Also 10³ = kilo (k)
[tex]\frac{10^3m}{s}[/tex] = [tex]\frac{km}{s}[/tex]
∴ m / ms = [tex]\frac{km}{s}[/tex] = km/s
(b) Given:
μkm => the proper SI unit should be m
So let's convert to m
μkm = 10⁻⁶ km [since μ = 10⁻⁶]
=> μkm = 10⁻⁶ x 10³ m [since k = 10³]
=> μkm = 10⁻³ m
But 10⁻³ = milli (m)
=> μkm = 10⁻³ m = mm
∴ μkm = mm
(c) Given:
ks/mg => the proper SI unit should be s/kg
So let's convert to s/kg
ks/mg = 10³s / mg [since k = 10³]
=> ks/mg = 10³s / 10⁻³g [since m = 10⁻³]
=> ks/mg = 10³ x 10³ s / g
=> ks/mg = 10⁶ s / g
=> ks/mg = [tex]\frac{10^6 s}{g}[/tex]
Multiply the numerator and denominator by 10³
=> ks/mg = [tex]\frac{10^6 X 10^3s}{10^3 X g}[/tex]
=> ks/mg = [tex]\frac{10^9s}{10^3 X g}[/tex]
=> ks/mg = [tex]\frac{Gs}{10^3 X g}[/tex] [since 10⁹ = Giga (G) ]
=> ks/mg = [tex]\frac{Gs}{kg}[/tex] [since 10³ = Kilo (k) ]
∴ ks/mg = [tex]\frac{Gs}{kg}[/tex] = Gs/kg
(d) Given:
km.μN => the proper SI unit should be mN or Nm
So let's convert to km.μN
km.μN = 10³m.μN [since k = 10³]
=> km.μN = 10³m.10⁻⁶N [since μ = 10⁻⁶]
=> km.μN = 10⁻³ mN
=> km.μN = mmN [since m = milli = 10⁻³]
∴ km.μN = mmN
