A balloon of diameter 21 meter weight 100 kg. Calculate its pay-load, if it is filled with He at 1.0 atm and ${27}^{\circ }C$. Density of air is 1.2 kg $m^{-3}$ . (Given : R=0.082 L atm $K^{-1}mo{l}^{-1}$)

Answer: bSolution: (b) Mass of balloon $=100kg=10\times {10}^{4}g$
Volume of balloon $=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times \frac{22}{7}\times {\left(\frac{21}{2}\right)}^3$
$=4851m^3=4851\times {10}^{3}L$
Mass of gas (He in balloon $=\frac{PVM}{RT}$
$=\frac{1\times 4851\times {10}^3\times 4}{0.082\times 300}$
$=78.878\times {10}^4$
$\therefore$ Total mass of gas and balloon
$=78.878\times {10}^4+10\times {10}^4$
$=88.878\times {10}^{4}g\text{ or }888.78kg$
Mass of air displaced $=1.2\times 4851$
$=5821.2kg$
$\therefore$ Pay load =mass of air displaced - mass of (balloon +gas)
$\therefore$ Pay load $=5821.2-888.78=4932.42kg$