(a) It is known that density ρ of air decreases with height y as `ρ = ρ_0e^((-y)/y_0)` where `ρ_0`= 1.25 kg `m^(–3)` is the density at sea level, and `y_0` is a constant. This density variation is called the law of atmospheres. Obtain this law assuming that the temperature of atmosphere remains a constant (isothermal conditions). Also assume that the value of g remains constant. (b) A large He balloon of volume 1425 `m^3` is used to lift a payload of 400 kg. Assume that the balloon maintains constant radius as it rises. How high does it rise ? [Take `y_0` = 8000 m and `ρ_(He)` = 0.18 kg `m^(–3)`].