A hot air balloon is carrying some passengers

PHYSICS · Subjective · CBSE · Physics · Gravitation · Gravitation

Problem

A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total mass is 480 kg. Its effective volume giving the balloon its buoyancy is VV . The balloon is floating at an equilibrium height of 100 m. When NN number of sandbags are thrown out, the balloon rises to a new equilibrium height close to 150 m with its volume VV remaining unchanged. If the variation of the density of air with height hh from the ground is ρ(h)=ρ0e−h/h0\rho(h) = \rho_0 e^{-h/h_0} , where ρ0=1.25 kg m−3\rho_0 = 1.25 \text{ kg m}^{-3} and h0=6000 mh_0 = 6000 \text{ m} , the value of NN is ____.

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