Physics - Heat & Thermo Question with Solution | TestHub

A balloon is filled with helium at the atmospheric pressure ${\mathrm{P}}_0$. The volume of the balloon is ${\mathrm{V}}_0$. The balloon is made of the material of mass m and density $\rho$. After being released, the balloon bursts at an altitude where the atmospheric pressure is ( ${\mathrm{P}}_0/2$ ). Immediately before bursting, the balloon has a volume of $1.25{\mathrm{V}}_0$. The maximum stress that the balloon material can withstand is given by $\alpha {\mathrm{P}}_0$, find the value of $\alpha$. Assume that the temperature of helium remains constant, the balloon remains spherical, and the density of the material remains virtually constant. [Take: ${\mathrm{V}}_0=8{\mathrm{m}}^3,\mathrm{r}=1500\mathrm{kg}/{\mathrm{m}}^3,\mathrm{m}=18\mathrm{kg}$ ]