A balloon of volume 800 cm^{3} is filled with hydrogen gas of density 9 x 10^{-5} gem^{-3}. If the empty balloon weighs 0.3 gf and density of air is 1.3 x 10^{-3} gem^{-3}, calculate the lifting power of balloon.

#### Solution

Volume of balloon = V = 800 cm^{3}

Density of hydrogen gas = p_{H} = 9 x 10^{-5} g cm^{-3}

Weight of empty balloon = 0.3 gf

Density of air = ρ_{a} = 1.3 x 10^{-3} g cm^{-3}

Weight of hydrogen gas in balloon = Vρ_{H}g

= 800 x 9 x 10^{-5} x g

= 72 x 10^{-3}gf

= 0.072 gf

Volume of balloon = Volume of hydrogen gas in the balloon = volume of air displaced by balloon.

Downthrust = Wt. of empty balloon + wt. of hydrogen gas in balloon

= 0.3 + 0.072 = 0.372 gf

Upthrust = Wt. of air displaced by balloon

= Vρ_{a}g

= 800 x 1.3 x 1o^{-3} x g_{}

= 8 x 1.3 x 1o^{-1} x g

= 10.4 x 10^{-1} x g = 1.04 gf

Lifting power of balloon = Upthrust – Down thrust

=1.04 - 0.372 = 0.668 gf