Question

A balloon of volume 1000 m³ is filled with a mixture of hydrogen and helium of density 0.32 kgm^-3. If the fabric of balloon weighs 40 kgf and the density of cold air is 1.32 kgm^-3, find the tension in the tope, which is holding the balloon to ground.

Answer 1

Volume of balloon = V = 1000 m³

Density of mixture of hydrogen and helium =ρ = 0.32 kgm³

Density weight of empty balloon = 40 kgf

Density of cold air = p’ = 1.32 kgm³

Volume of balloon=Volume of mixture of hydrogen and helium gas

= Volume of cold air displaced by balloon

= V= 1000 m³

Weight of mixture of hydrogen and helium gas in balloon = Vρg

= 1000 x 0.32 x g = 320 kgf

Down thrust = Weight of empty balloon + Weight of mixture of hydrogen and helium gas

= 40+ 320 = 360 kgf

Upthrust = Weight of cold air displaced by balloon = Vρ’g

= 1000 x 1.32 x g= 1320kgf

Tension in the rope = Upthrust – downthrust

= 1320-360 = 960 kgf