A balloon of mass 1000 kg is floating at some height. If 100 kg mass is released from the balloon (without
changing volume of the ballon). Then the acceleration of the balloon is
Consider V is the volume of the balloon.
ρ is the density of the air.
Initial mass be m = 1000 kg
Final mass be m' = (1000 - 100) = 900 kg
Initially the balloon is at rest, i.e.
Weight of the balloon = Weight of the air displaced by the balloon
mg = Vρg = 1000g
Vρ = 1000 ...(i)
When 100 kg mass is dropped,
Weight of the balloon < Weight of the air displaced by the balloon
Net force in upward direction = Weight of the air displaced by the balloon - Weight of the balloon
m'a = Vρg - m'g = (Vρ - m')g = 100g
m'a = 100x9.8
a = 1.089 m/s2