Question
A balloon with mass m is descending down with an acceleration a (where a <g). How much mass should be removed from it so that it starts moving up with an acceleration a?
Solution
A.
When the balloon is descending down with acceleration a,
So, mg - B = mx A ... (i)
where B is the buoyant force.
We assume here that while removing same mass, the volume of balloon and hence buoyant force will not change.
Let, us assume the new mass of the balloon is m'.
So, mass removed is (m-m')
Therefore,
B-m'g = m'x a ... (ii)
On solving equations (i) and (ii), we have
mg - B = m x a
B - m'g = m' x a
mg - m'g = ma + m'a
(mg - ma) = m' (g+a) = m (g-a) = m' (g+a)
That is,
That is, mass removed is m-m'
