${}_{\text{a}\text{i}\text{r}}=1\mathrm{.}20k\frac{g}{m^3},$ it lifts a length $h$ of string and then remains stationary as shown in the figure below. 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$?$

a particle under constant velocity model

$$ the ideal fluid model

a particle under constant acceleration model

a particle in equilibrium model along with the following as necessary: $.$ Follow the sign convention that upward is the positive direction.$)$

$F_y=B-F_b-F_{He}-F_s=0$

above along with the following as necessary: $.)$

$m_s=\frac{4}{3}{r}^3({}_{\text{a}\text{i}\text{r}}-{}_{He})-m_b$

$($d$)$ Find the numerical value of the mass $m_s.$

kg

$($e$)$ Find the length $h$ numerically.