A balloon carring some sand is moving down with a constant acceleration `a_(0)`. How much mass of sand should be removed, so that the balloon move up with same acceleration?

Options

A. `((2Ma)/(g+a))`
B. `((2Mg)/(g+a))`
C. `((Mg)/(g+a))`
D. `((Mg)/(g+a))`

Answer

A

Explanation

`Mg-F_(0)=M_(0)rArrF_(0)=M(g-a)`
Let `m_(0)` be the mass removed.

`F_(0)=(M-m_(0))g=(M-m_(0))a`
`F_(0)(M-m_(0))(g+a)`
`M(g-a)=(M-m_(0))(g+a)`
`Mg-Ma=Mg+Ma-m_(0)g-m_(0)a`
`m_(0)(g+a)=2Ma`
`m_(0)=(2Ma)/((g+a))`