Laws of Motion

When the balloon is descending, the net force acting on it is given by F‌net ‌=mg−B=ma, where B is the Buoyant force.
Thus, B=mg−ma
For the balloon to move upwards with the same acceleration a, a mass ∆m must be removed. The new net force equation becomes
B‌−(m−∆m)g=(m−∆m)a
mg−ma‌−(m−∆m)g=(m−∆m)a‌‌[‌ FromEq. ‌(i)]
⇒‌‌∆m=‌

2ma

g+a

‌