A balloon with mass m is descending down with an acceleration a where a

Options

A. `(2ma)/(g+a)`
B. `(2ma)/(g-a)`
C. `(ma)/(g-a)`
D. `(ma)/(g-a)`

Answer

A

Explanation

Let F be the upthrust of the air .As the balloon is descending down with an acceleration a ,
` therefore mg -F =ma .......(i)` Let mass ` m_0` be removed from the balloon so that it starts moving up with an
acceleration a. then
` F- (m-m_0) g= ( m-m_0)a`
` f-mg + m_0 g = ma - m_0 a `....(ii)
adding eqn . (i ) and eqn (ii) we get
` m_0 g - 2ma - m_0 ,m_0 g + m_0 a = 2ma,m_0 ( g+a ) = 2ma `
` m_0 = (2ma )/( g+a)`