A balloon of diameter 20m Weighs 100 kg- Calculate its payload if it is filled with helium at 1-0 atm and 27- Density of air is 1-2 Kgm -3 R -0-082 dm 3 atm K -1 mole -1A- 4260B- 4395C- 4247D- 4463

The correct option is C 4247Volume of balloon =4/3π r^3=4/3×22/7× 10^3=4190.47m^3 Mass of the air displaced = 4190.47 × 1.2=5028.56Kg No of moles of helium in ...

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Standard XII

Physics

Archimedes' Principle

A balloon of ...

Question

A balloon of diameter 20m Weighs 100kg. Calculate its payload if it is filled with helium at 1.0 atm and $27^{\circ}$ .
Density of air is $1.2 K g m^{- 3}$ (R = 0.082 $d m^{3} a t m K^{- 1} m o l e^{- 1}$ )

4260

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4395

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4247

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4463

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Solution

The correct option is C 4247
Volume of balloon $= \frac{4}{3} π r^{3} = \frac{4}{3} \times \frac{22}{7} \times 10^{3} = 4190.47 m^{3}$
Mass of the air displaced = 4190.47 $\times$ 1.2=5028.56Kg
No of moles of helium in the balloon= $\frac{P V}{R T}$
$= \frac{1 \times 4190.47 \times 10^{3}}{0.082 \times 300}$
= 170344
Mass of helium $= 4 \times 170.344 \times 10^{3} = 681.376 K g$
Mass of filled balloon = 681.376+100 =781.376Kg
Pay load = Mass of air displaced – Mass of filled balloon
=5028.56-781.376
=4247.184Kg

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