A balloon filled with a lighter gas occupies a volume of 1500 cu metre. Its mass (mass of material of balloon + mass of gas in it) is 1650 kg. Its tied with a rope and floating in air of density 1.3 kg/cubic metre. The pull on the rope is ?

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Answer 1 · 2018-08-13T09:31:48

The pull on the rope is $= 2940 N$ $=2940N$

The Buoyancy force is

$F_{b} = V \cdot ρ \cdot g$ $F_b=V*rho*g$

The volume of the balloon is $= 1500 m^{3}$ $=1500m^3$

The density of air is

$ρ = 1.3 k g m^{- 3}$ $rho=1.3kgm^-3$

The acceleration due to gravity is $g = 9.8 m s^{- 2}$ $g=9.8ms^-2$

The mass of the ballloon is $m = 1650 k g$ $m=1650kg$

The weight of the balloon is $w = 1650 \cdot 9.8 = 16170 N$ $w=1650*9.8=16170N$

The buoyancy force is

$F_{b} = 1500 \cdot 1.3 \cdot 9.8 = 19110 N$ $F_b=1500*1.3*9.8=19110N$

The pull on the rope is

$F_{b} - w = 19110 - 16170 = 2940 N$ $F_b-w=19110-16170=2940N$