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JEE Advanced2020PhysicsMechanical Properties of FluidsActual

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 V . The balloon is floating at an equilibrium height of 100 m . When N number of sandbags are thrown out, the balloon rises to a new equilibrium height close to 150 m with its volume V remain unchanged. If the variation of the density of air wit

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Step-by-step solution

Initially m g = F b 480 × g = V ρ 0 e - 100 6000 g ....(1) Finally ( 480 - m ) g = V ρ 0 e - 150 6000 g .....(2) dividing 480 - m 480 = e - 1 40 + 1 60 m = 480 1 - e - 1 / 120 Hence e - 1 / 120 ≈ 1 - 1 120 1 - e - 1 / 110 = 1 120 m = 4   kg Hence, four sandbags are thrown.

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