(a). It is known that density `rho` of air decreases with height y as
`rho=rho_(0)e^(-y//y(_o))` ltb rgt where `p_(o)=1.25kgm^(-3)` is the density at sea level, and `y_(o)` 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 `1425m^(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_(o)=8000m and rho_(He)=0.18kgm^(-3)`]

Explanation

8km, If we consider the variation of g with altitude the height is somewhat more. About 8.2km.