Question

An open glass tube is immersed in mercury in such a way that a length 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? (Atmospheric pressure $=76cm$ of $Hg$)

• A. $38cm$
• B. $6cm$
• C. $16cm$
• D. $22cm$

Answer 1

The correct option is C $16cm$

let the length of air column be $x$ and pressure be $p$

$8_{p_0}=xp\Rightarrow P=\frac{8_{p_0}}{x}$

$\frac{8_{p_0}}{x}+\rho mg(54-x)=\rho mg\left(76\right)$

$\frac{8}{x}+\frac{54-x}{76}=1$

$x=16cm$