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

Let T be the tension in the string with which a small block of mass `M//2` is tied to balloon of mass M. Refer to fig. , when small block of mass `M//2` is floating stationary, then
`T=(Mg)/(2)`

When balloon is held stationary in air , then
upthrust = weight of balloon + tension in string
`U= Mg + T = Mg + Mg//2 = 3 Mg//2`
When the string is cut, `T=0` , the small block will begin to fall freely with ac celeration g
Now the balloon will rise up with ac celeration a (say). then ` U- Mg =Ma`
or `3/2 Mg -Mg = Ma or a=g/2`