A spherical balloon with a diameter of 10 m, shown in the

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A spherical balloon with a diameter of 10 m, shown in the figure below is used for advertisements. The balloon is filled with helium (R_He = 2.08 kJ/kgK) at ambient conditions of 15°C and 100 kPa. Assuming no disturbances due to wind, the maximum allowable weight (in Newton) of balloon material and rope required to avoid the fall of the balloon (R_air = 0.289 kJ/kgK) is_______.

1. 5303.67 N
2. 5203.67 N
3. 5403.67 N
4. 5213.67 N

Correct Option: A

V_baloon =		4	πr³ =	4 × 3.14 × 5³	= 523.33m³
		3		3

ρHe =		P	=	100 × 10₃	= .1669 kg/m³
		RT		2080 × 288

Total mass = .1669 × 523.33 = 87.36 kg mass of air:

ρ =		P	=	100 × 10³	= 1.2 kg/m³
		RT		2080 × 288

Mass of displaced volume of air = 1.2 × 523.33 = 628 kg
Net Buoyant mass = 628 – 87. 36 = 540.64 kgl Allowable Mass, M_allowable = 540.64 × 9.81
= 5303.67 N