Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius $10 m,$ mass $100 k g$ is filled with helium at $1.66$ bar at $27^{o} C ($ Density of air $= 1.2 k g m^{- 3}$ and $R = 0.83$ bar $d m^{3} K^{- 1} m o l^{- 1}) .$

1138.12

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3811.12

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1381.12

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3112.38

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Solution

The correct option is D $3811.12$ Kg
Payload of the ballon = mass of the displaced air- mass of the ballon
Radius of the ballon, $r = 10 m$
Mass of the ballon, $m = 100 k g$
Therefore volume of the ballon $= 4.3 n r^{3} = 4 / 3 \times 22 / 7 \times (10)^{3} = 4190.5 m^{3}$
Now volume of the displaced air $= 4190.5 m^{3}$
Given :
Density of air $= 1.2 k g m^{- 3}$
Therefore, the mass of the displaced air $= 4190.5 \times 1.2 = 5028.6 k g$
Let $w$ be the mass of helium gas filled into the ballon, then
$P V = (w / m) R T$
OR $w = P V M / R T$
$= (1.66 \times 4190.5 \times 10^{3} \times 4) / (0.083 \times 300)$
$= 1117 k g$ (approx)
Total mass of the balloon filled with He $= 1117 + 100 = 1217 k g$
Therefore payload of the balloon $= 5028.6 - 1217 = 3811.6 k g$
Hence,m the pay load of the balloon is $3811.6 k g$
Therefore, the correct option is B.

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Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius 10m, mass 100kg is filled with helium at 1.66 bar at 27oC( Density of air =1.2kgm−3 and R=0.83 bar dm3K−1mol−1).