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A ballon of mass m is rising up with an ...

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

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Let F be the upthrust of air. As the balloon rises with acceleration a (see figure)
`:. F - mg = ma` or f = m (g + a) - (i)
When was `m_(1)` is removed from the ballon, acceleration becomes (2 a). Therefore
`F - (m - m_(1)) g = (m - m_(1)) 2a`
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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