A balloon of mass m is descending with downward acceleration a (a

Question

A balloon of mass m is descending with downward acceleration a (a<g). How much mass must be removed so that it ascends with acceleration a? Assume buoyant force stays constant.

G1 Physics · Accepted Answer

Initially mg−Fᵦ=ma, hence buoyancy Fᵦ=m(g−a). Remove mass Δm; new mass is m−Δm. For upward acceleration a: Fᵦ−(m−Δm)g=(m−Δm)a. Substitute Fᵦ=m(g−a); rearrange Δm(g+a)=2ma. Therefore Δm=2ma/(g+a). Answer: A.