A balloon is filled with helium at the atmospheric pressure P0 . The volume of spherical balloon is V0 . After being released, the balloon burst at an altitude where the atmospheric pressure is P02. Before bursting the balloon has volume 5V04, temperature remaining the same. If the mass of material of balloon is m and density at the time of bursting is ρ0 then:

P0V0=P54V0P=45P045P0−P02=2σtr3P010=2σtr,4πr2tρ0=m&43πr3=5V04∴tr=15V0ρ04mσ=9P0V0ρ016m

A balloon is filled with helium at the atmospheric pressure P0 . The volume of spherical balloon is V0 . After being released, the balloon burst at an altitude where the atmospheric pressure is P02. Before bursting the balloon has volume 5V04, temperature remaining the same. If the mass of material of balloon is m and density at the time of bursting is ρ0 then:

P0V0=P54V0P=45P045P0−P02=2σtr3P010=2σtr,4πr2tρ0=m&43πr3=5V04∴tr=15V0ρ04mσ=9P0V0ρ016m

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A balloon is filled with helium at the atmospheric pressure P₀ . The volume of spherical balloon is V₀. After being released, the balloon burst at an altitude where the atmospheric pressure is $\frac{P_{0}}{2} .$ Before bursting the balloon has volume $\frac{5 V_{0}}{4}$ , temperature remaining the same. If the mass of material of balloon is m and density at the time of bursting is $ρ_{0}$ then:

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Pressure inside the balloon before bursting is $\frac{5}{4} P_{0}$

Pressure inside the balloon before bursting is $\frac{4}{5} P_{0}$

Maximum stress which balloon can withstand is $\frac{9 P_{0} V_{0} ρ_{0}}{16 m}$

Maximum stress which balloon can withstand is $\frac{3 P_{0} ρ_{0} V_{0}}{8 m}$

answer is B, C.

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Detailed Solution

$\begin{array}{l} P_{0} V_{0} = P (\frac{5}{4} V_{0}) P = (\frac{4}{5} P_{0}) (\frac{4}{5} P_{0} - \frac{P_{0}}{2}) = \frac{2 σ t}{r} \\ \frac{3 P_{0}}{10} = \frac{2 σ t}{r}, 4 π r^{2} t ρ_{0} = m & \frac{4}{3} π r^{3} = \frac{5 V_{0}}{4} ∴ \frac{t}{r} = \frac{15 V_{0} ρ_{0}}{4 m} σ = \frac{9 P_{0} V_{0} ρ_{0}}{16 m} \end{array}$