Question -
Answer -
(a) Volume of theballoon, V = 1425 m3
Mass of the payload, m = 400 kg
Acceleration due to gravity, g = 9.8 m/s2
Density of the balloon = ρ
Height to which the balloon rises = y
Density (ρ) of air decreases with height (y) as:
This density variation is called the law of atmospherics.
It can be inferred from equation (i) that the rate ofdecrease of density with height is directly proportional to ρ,i.e.,
Where, k is the constant of proportionality
Height changes from 0 to y, while density changesfrom 
to ρ.
Integrating the sides between these limits, we get:
(b)
Hence, the balloon will rise to a height of 8 km.