On the bottom of lake at a depth `h=100m`, a horizontal pipe of length `80m` with piston is kept is shown in the figure. The piston is light and movable. Between the piston and pipe some air is captured `(x_(0)=9m)`. The pipe is slowly raised to vertical position and open end upward. The length of air column `(x)` in SI units is `5K`. Find value of `K`. (Disregard the atmospheric pressure & Piston and pipe are air tight. Temperature of gas remains constant).

Answer

5

Explanation

`P_(2)=rhog(h-x), P_(1)=rhogh`
`V_(2)=Ax V_(1)=Ax_(0)`
Using Boyle's low we can write
`rhog(h-x)Ax=rhogh(Ax_(0))`
`impliesx^(2)-hx+hx_(0)impliesx= h/2+-sqrt((h^(2))/4- hx_(0))`
`implies x=10m, 90m`
`x lt l` (length of pipe)
So answer will be `x=10m`