A big size balloon of mass M is held stationary in air with the help of a small block of mass `M//2` tied to it by a light string such that both float in mid air. Describe the motion of the balloon and the block when the string is cut. Support your answer with calcutations

Explanation

Free block diagram of balloon and block shown below :

When the balloon is held stationary in air, the forces acting on it get balance
Up thrust = Wt. of Balloon + Tension in string
U = Mg + T
M for the small block of mass `(M)/(2)` floating stationary in air
`T=(M)/(2)` g
`:. " " U=Mg+(M)/(2)g=(3)/(2)Mg`
When the string is cut T = 0, the small block begins to fall freely, the balloon rises up with an acceleration ‘a’ such that
U-Mg=Ma
`(3)/(2)Mg-Mg=Ma`
` a=(g)/(2)` in the upward direction.