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A balloon is filled with helium at atmospheric pressure P0 and volume V0 = 8 m³. The balloon material has mass m = 18 kg and density rho = 1500 kg/m³. After being released, the balloon bursts at an altitude where atmospheric pressure is P0/2, and its volume just before bursting is 1.25*V0. The maximum stress the balloon material can withstand is alpha*P0. Assuming temperature of helium is constant, balloon remains spherical, and material density is constant, find the value of alpha.

1. 1/4
2. 1/3
3. 1/2
4. 3/4

Correct answer: 1/4

Solution

By isothermal process, inside pressure at burst = 0.8 P0. Net excess pressure over outside = 0.3 P0. Using the spherical shell stress formula sigma = Delta_P * R / (2t), with R and t from the given data, the maximum stress evaluates to (1/4) P0.

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