A ballon of mass m is rising up with an acceleration a show that the fraction og weight of balloon that must be detached in order to double its acceleration , assuming the upthrust of air to remain the same

Explanation

Let F be the upthrust of air As the ballon rise with acceleration
`F - mg = ma` or `F = m (g + a)`
When mass `m _(1)` is removed from the ballon acceleration becomes (2 a ) Therefore
`F - (m - m_(1)) g = (m - m_(1)) 2 a`
or `F = (m - m_(1)) (g + 2a)`
From (i) and (ii) , `(m - m_(1)) (g +2a) = m (g + a)`
`m - m_(1) = m (g + a) //(g + 2a)`
`m_(1) = m -(m (g + a))/(g + 2a) = (ma)/(g + 2a)`
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