Question

A uniform tube closed at one end contains a pallet of mercury $10cm$ long. When the tube is kept vertically with the closed end upward, the length of the air column trapped is $20cm$. Find the length (in $cm$ ) of the air column trapped when the tube is inverted so that the closed end goes down. Atmospheric pressure $=75cm$ of mercury.

Answer 1

Answer: 15.00

For air column,
$P_1=P-\frac{mg}{A}$
$\Rightarrow P_1=\rho g(75-10)=65cm$ of $Hg$
$V_1=20A,T_1=T$
$P_2=P+\frac{mg}{A}$
$\Rightarrow P_2=\rho g(75+10)$
$P_2=85cm$ of $Hg$
$V_2=hA,T_2=T$
$P_1{V}_1=P_2{V}_2$
$\Rightarrow 65\times 20A=85\times Ha$
$h=15.294cm$