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 rises with acceleration (a)
`F = mg + ma`
Let mass `m_(1)` of ballon be detached so that accelertion becomes (2 a)
`F =(-m-m_(1)) g + (m-m_(1)) 2 a`
`=(m-m_(1)) (g+2 a )`
From (i) and (ii) , we get
`(m-m_(1) (g+2 a) = mg +a`
`m - m_(1) = (m (g+a))/(g+2 a)`
or `m_(1) = m - (m (g + a))/(g + 2 a )=(ma)/(g+2a)` .