Question

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

• A. 4952.42 kg
• B. 4932.42 kg
• C. 493.242 kg
• D. None of these

Answer 1

The correct option is B 4932.42 kg

Weight of balloon$=100kg=10\times {10}^{4}g$.

Volume of balloon$=\frac{4}{3}\pi r^3$.

$=\frac{4}{3}\times \frac{22}{7}\times (\frac{21}{2}{)}^3$

$=4851m^3=4851\times {10}^{3}L$

Weight of gas $\left(He\right)$ 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 weight of gas and balloon
$=78.878\times {10}^4+10\times {10}^4$

$=88.878\times {10}^{4}g$ or $888.78kg$

Weight of air displaced$=1.2\times 4851$
$=5821.2kg$

$\therefore$ Pay load=wt. of air displaced-wt. of (balloon+gas)
$\therefore$ Pay load$=5821.2-888.78=4932.42kg$.