How do I identify the unit from the question?

[Tangent100]

EXAMPLE QUESTION:
Calculate the mass per unit length of the wire, μ, given by
μ = g /(2fG)^2
where g = 9.81 N kg–1 and f = 50 Hz.

For example here is it mass per unit length and so would it be kg/m? It kg/m the same as kgm^-1. But then how do I identify the units like kgm^-2 like how would they be written, mass per squared unit length? I'm a bit confused.

Also, if the result was
0.0072 kg/m
Could I say it is 7.2 x10^-3 kg/m or can I convert it to something like g/m?

 

[BvU]

Hello tangent,

Yes, mass per length is kg per m, or kg/m also written as ## {{\rm kg}\over {\rm m}} ## or ## {\rm kg}\, {\rm m}^{-1} ##. Ropes and chains have mass per length as a characteristic.

And ## {\rm kg}\, {\rm m}^{-2} ## is what you get when you divide mass by area. Tiles and floorboards have that. If a tile of 0.3 m x 0.3 m weighs 0.81 kg, the mass per area is 0.81 kg / (0.3 m x 0.3 m) = 0.81 / (0.3 x 0.3 ) kg / (m x m) = 9 kg/m².

Water weighs approximately 1000 kg/m³.


Converting is easy, for example the tiles: 0.81 kg / (0.3 m x 0.3 m) = 0.81 kg x (1000 g/kg)/ (0.3 m x 0.3 m) = 9000 g/m².
Or 0.81 kg / (0.3 m x 0.3 m) = 0.81 kg / (0.3 m x 100 cm/m x 0.3 m x 100 cm/m) = 9 x 10 ^-4 kg/cm².

So, in your example: 0.0072 kg/m is indeed 7.2 x10^-3 kg/m, and multiplying by 1 (namely 1 = 1000 g/kg) gives 0.0072 kg/m x 1000 g/kg = 7.2 kg/m x g/kg = 7.2 g/m.

 

[CWatters]

For example here is it mass per unit length and so would it be kg/m? It kg/m the same as kgm^-1. But then how do I identify the units like kgm^-2 like how would they be written, mass per squared unit length? I'm a bit confused.

As BvU said.. m² is "square meters" which is a unit of area, so m^-2 is "per square meter".

mS^-1 is "meters per second" which is a velocity so
mS^-2 is "meters per second squared" which is an acceleration