Question

a balloon of mass M is rising up with acceleration is show that the fraction of weight balloon that mostly detach in order to double its acceleration is any up onto a pleasure as you mean the upthrust appear be to remain the same

Answer 1

Let u be the up thrust on the balloon

Case i):  

            $ma\quad =\quad u-mg\longrightarrow \left (1 \right)$

Case ii):

Let m' be the mass detached,

            $(m-m')2a = u - (m-m')g \longrightarrow (2)$

            $(m-m')2a = u - mg + m'g$

Substitute (1) in (2),

            $(m-m')2a = ma + m'g$

            $2ma - 2m'a = ma + m'g$

            $ma = m'g + 2m'a$

            $m' (g+2a) = ma$

            $m'\quad =\quad \frac { ma }{ g\quad +\quad 2a}$