Question

A balloon with it's contents weighing 160N moving down with an acceleration of g/2 ms^{​​​​-2} . The mass removed from it so that the balloon moves up with an acceleration of g/3ms^-2 is

Answer 1

F = Upward Force due to balloon
g=10m/s^2

Before removing mass
Mg - F = Ma
160 - F = Mg/2
160 - F = 160/2
F = 80 N

After removal of mass (m)
F - (M - m)g = (M - m)a
F - (M - m)g = (M - m)g/3
F - Mg + mg = Mg/3 - mg/3
4mg/3 = 4Mg/3 - F
m = 3/(4g) × [4Mg/3 - F]
m = 3/(4 × 10) × [(4 × 160 / 3) - 80]
m = 10 kg

Mass to be removed is 10 kg.