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 ?

Step-by-step solution

Let F be the upward buoyant force acting on the balloon. When the balloon of mass m is descending with acceleration a , the equation of motion is mg - F = ma . From this, F = m(g - a) . Let m' be the mass to be removed, so the new mass is m - m' . When the balloon moves up with acceleration a , the equation of motion is F - (m - m')g = (m - m')a . Substituting F = m(g - a) into the equation, we get m(g - a) - (m - m')g = (m - m')a . mg - ma - mg + m'g = ma - m'a . m'g + m'a = 2ma . m'(g + a) = 2ma . m' = 2ma g + a