Pay load is defined as the difference between the mass of displaced air and the mass of the ballon Calculate the pay-load when a balloon of radius `10m` mass `100 kg` is filled with helium at 1.66 bar at `27^(@)C` (Density of air ` = 1.2 kg m^(-3)` and `R = 0.083` nar `dm^(-3) K^(-1) mo1^(-1)`) .

Explanation

Weight of balloon `=100 kg = 100 xx 10^(3) g = 10^(5) g`
Volume of balloon ` = (4)/(3) pir^(3) = (4)/(3) xx (22)/(7) xx (10 xx 100)^(3) cm^(3)`
`=4190 xx 10^(6) cm^(3) = 4190 xx 10^(3) litre`
Weight of the gas filled in ballon
` = (PVm)/(RT) = (1.66 xx 4190 xx 10^(3) xx 4)/(0.083 xx 300) = 1.117 xx 10^(6) g`
Total weight of (gas+ballon)
`11.17 xx 10^(5) + 10^(5) = 12. 17 xx 10^(5) g`
Weight of air displaced (Volume x density)
by balloon `= 1.2 xx 10^(-3) xx 4190 xx 10^(6)`
`5.028 xx 10^(6)g`
`:.` Pay load `=50.28 xx 10^(5) -12.17 xx 10^(5)`
`=38.11 xx 10^(5) g =3811 kg` .