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A helium-filled balloon (whose envelope has a mass of mb=0.250kg) is tied to a uniform string of length ℓ=2.00m and mass m = 0.0500 kg. The balloon is spherical with a radius of r = 0.400 m. When released in air of temperature 20∘C and density rhoair=1.20kg/m3, it lifts a length h of string and then remains stationary. We wish to find the length of string lifted by the balloon. (a) When the balloon remains stationary, what is the appropriate analysis model to describe it? (b) Write a force equation for the balloon from this model in terms of the buoyant force B, the weight Fb of the balloon, the weight FHe of the helium, and the weight Fs of the segment of string of length h. (c) Make an appropriate substitution for each of these forces and solve symbolically for the mass ms of the segment of string of length h in terms of mb, r, rhoair , and the density of helium rhoHe, (d) Find the numerical value of the mass ms. (e) Find the length h numerically.