A helium$-$filled balloon, whose envelope has a mass of $0\mathrm{.}29$ kg$,$ is tied to a $1\mathrm{.}6-$m long, $0\mathrm{.}052-$kg string. The balloon is spherical with a radius of $0\mathrm{.}40$ m$.$ When released, it lifts a length h of the string and then remains in equilibrium, as in the figure below. Determine the value of h$.$ Hint: Only that part of the string above the floor contributes to the load being supported by the balloon. $($The density of air is $1\mathrm{.}29$ kg$/$m$3$ and the density of helium is $0\mathrm{.}179$ kg$/$m$3.)$