Question bank/JEE Advanced/Physics

A hot air balloon is carrying some passengers, and a few sandbags of mass $1 \mathrm{~kg}$ each so that its total mass is $480 \mathrm{~kg}$. Its effective volume giving the balloon its buoyancy is $V$. The balloon is floating at an equilibrium height of $100 \mathrm{~m}$. When $N$ number of sandbags are thrown out, the balloon rises to a new equilibrium height close to $150 \mathrm{~m}$ with its volume $V$ remaining unchanged. If the variation of the density of air with height $h$ from the ground is $\rho(h)=\rho_{0} e^{-\frac{h}{h_{0}}}$, where $\rho_{0}=1.25 \mathrm{~kg} \mathrm{~m}^{-3}$ and $h_{0}=6000 \mathrm{~m}$, what is the value of $N$?

Source: JEEBench (IIT Delhi) / JEE Adv 2020 Paper 2