An open glass tube is immersed in mercury in such a way that a lenth of 8cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46cm. What will be length of the air column above mercury in the tube now?
(Atmosphere pressure =76cm of Hg)

Options

A. `16 cm`
B. `22 cm`
C. `38cm`
D. `6cm`

Answer

A

Explanation

For air trapped in tube `P_(1)V_(1) = P_(2)V_(2)`
`P_(1) = P_(atm) = rho g 76`
`V_(1) = A.8 (A =` area of cross section)
`P_(2) = P_(atm) - rho g (54 -x) = rho g(22 +x)`
`V_(2) = A.x`
`rho g 76. A8 = rho g (22+x) Ax`
`x^(2) +22x - 78 xx 8 = 0`
`rArr x = 16 cm`.