A balloon of diameter 21 meter weight 100 kg. Calculate its pay-load, if it is filled with He at 1.0 atm and `27^(@)C`. Density of air is 1.2 kg `m^(-3)` . (Given : R=0.082 L atm `K^(-1)mol^(-1)`)

Options

A. 4952.42kg
B. 4932.42kg
C. 493.242kg
D. None of these

Answer

B

Explanation

Weight of balloon =100kg =`10 xx10^(4)`g volume of balloon =`(4)/( 3) pir^(3)`
`= (4)/( 3) xx ( 22)/( 7) xx ((21)/( 2))^(3) = 4851m^(3) =4851 xx 10^(3) L`
Weight of gas ( He ) in balloon =`( PVM)/( RT)`
`= ( 1xx4851 xx 4)/( 0.082 xx 300)`
`= 78.878 xx 0^(4)`
`:.` Total weight of gas and balloon
`= 78.878 xx10^(4) + 10 xx 10^(4)`
`= 88.878 xx 10^(4) g ` or `888.78 `kg
Weight of air displaced `= 1.2 xx 4851 = 5821 .2 kg `
`:.` Pay load = wt.of air displaced - wt. of ( ballon `+` gas )
`:.` Pay load `= 5821.2 - 888.78 =4932.42kg `