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Mayank Amichand Sharma Grade: 12
        

A balloon of diameter 20m weighs 100 kg. Calculate it's payload if it is filled with He at 1 atm and 300K. Density of air is 1.2 kg/(m^3).

7 years ago

Answers : (1)

AskiitianExpert Pramod-IIT-R
47 Points
										weight of ballon = 100 Kg

displayed air by this ballon = density of air*volume of ballon
= 1.2 kg/(m^3) * 4/3 * Pi * 10^3
= 5026.55 Kg
Byuoncy Force = 5026.55 * g (upward direction)
weight of gas inside ballon = molecular weight of He * (PV)/(RT)
= 4*10^(-3)*(1*4/3 * Pi * 10^3)/(.082*300)Kg
=681.10*10^(-3) Kg

total upward force = total downside force
Byuoncy Force= payload+force of weight of ballon's gas+force of weight of ballon
5026.55*g = payload(N) + 681.10*10^(-3) g + 100 g
681.10*10^(-3) g is very small quantity so we can neglect this

==> 5026.55 * g = payload(N) + 100 * g
==> payload(N) = 5026.55 * g - 100 *g
=4926 * g

payload(Kg)= 4926.55 Kg Ans
7 years ago
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