How High Will the Helium Balloon Lift the String?

[Terrence]

Homework Statement

A helium filled balloon is tied to a 2 m long uniform string of mass 0.05 kg.The balloon is spherical
with a radius of 0.4 m. When released it lifts a length h of the string off of the ground. Find the length h given that
the balloon has a mass of 0.25 kg.

Homework Equations

I think...

P = P₀ + pgH

P is pressure, P₀ is atmospheric pressure, p is density, g is gravity, H is height

The Attempt at a Solution

I'm really lost on this one...

I know desity is mass/volume, so I guess I can use .25 for mass and (4/3)pi*r³ to find the balloon's density. But I don't know the importance of the string's mass or how I am supposed to use all this information to find how high the balloon goes.

 

[ehild]

Homework Equations

I think...

P = P₀ + pgH

P is pressure, P₀ is atmospheric pressure, p is density, g is gravity, H is height

The Attempt at a Solution

Is this the relevant equation? What is the meaning of H? The height of what? And what pressure is p?

ehild