What is the relationship between diameter and mass per length in a steel wire?

[nesan]

Homework Statement

http://puu.sh/frpk5/eae7bce2e3.png

Homework Equations

v = sqrt(T / (m / L));

The Attempt at a Solution

7.86 g / cm^3 = 7860 kg / m^3

T = v^2 * m/L

T = 160 ^ 2 * 7860 which is a huge number

I have no idea where the diametre plays a part.

 

[Nathanael]

m/L ≠ 7860 (check the dimensions)

 

[nesan]

m/L ≠ 7860 (check the dimensions)

I'm sorry I really don't understand what you're aiming at. Does it have to do with the m^3?

I know it's mass per unit length but how would I go from 7860 kg / m^3 to what I need? Thank you.

 

[Nathanael]

I'm sorry I really don't understand what you're aiming at. Does it have to do with the m^3?

You were given the mass per volume, but you want to know the mass per length. You used the mass per volume where you should have used the mass per length.

I know it's mass per unit length but how would I go from 7860 kg / m^3 to what I need? Thank you.

Consider a steel wire with a larger diameter. (They are both steel, so the density is the same.) Which one will have the larger mass per length? Or will it be the same? And why?