A hot air balloon along with its cargo has a mass of 4.0 × 10⁵ kg,and it holds 7.0 × 10⁵ m³ of hot air.It is floating at a constant height in air with a density of 1.29 kg/m³.What is the density of the hot air in the balloon?

Question

Quizplus · Accepted Answer

The hot air balloon floats at a constant height, which means the buoyant force is equal to the weight of the balloon and its cargo (m*g). 
Buoyant force = (density of air)*(volume of displaced air)*g 
Let the density of hot air inside the balloon be rho. 
Buoyant force = (density of air)*(volume of displaced air)*g = (m+rho*V)*g 
Solving for rho gives 
rho = (density of air)*(volume of displaced air - (m/g)) 
rho = (1.29 kg/m^3)*(7.0*10^13 m^3 - 4.0*10^15 kg/9.8 m/s^2) 
rho = 0.72 kg/m^3 
Therefore, the density of the hot air in the balloon is 0.72 kg/m^3. 
The correct answer is (B).

A Hot Air Balloon Along with Its Cargo Has a Mass