Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

A balloon of diameter 20 metre weighs 100kg . Calculate its pay-load if it is filled with He at 1.0atm and $27^{\large\circ}C$ . Density of air is 1.2 $kgm^{-3}$ . [$R = 0.082dm^3\;atm\; K^{-1}\;mol^{-1}$]

$\begin{array}{1,1}(a)\;424.67\times10^4g\\(b)\;4.2467\times10^4g\\(c)\;42.467\times10^4g\\(d)\;0.424\times10^4g \end {array}$

Can you answer this question?

1 Answer

0 votes
Weight of balloon = 100 kg or $10\times10^4g$
Volume of balloon = $\large\frac{4}{3}\pi r^3$
$\;\;\;\;\;\;\;\;\;= \large\frac{4}{3}\times\large\frac{22}{7}\times(\large\frac{20}{2}\times100)^3$
Weight of gas (He) in balloon = $\large\frac{PV_m}{RT}$
(Since PV = $\large\frac{w}{m}RT$)
$\therefore$ Total weight of gas and balloon = $68.13\times10^4+10\times10^4 = 78.13\times10^4$
Weight of air displaced = $\large\frac{1.2\times4190\times10^6}{10^3}$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;= 502.8\times10^4g$
$\therefore$ Pay load = weight of air displaced - (weight of balloon + weight of gas)
$\therefore$ Pay load = $502.8\times10^4 - 78.13\times10^4$
Hence answer is (A)
answered Apr 1, 2014 by sharmaaparna1

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App