A test tube of length l is immersed inverted into a vessel having mercury ( ρ m ) of height l such that it is just immersed. Mercury was found to rise to a height x as shown. The pressure at A is (A

Question

A test tube of length l is immersed inverted into a vessel having mercury ( ρ m ​ ) of height l such that it is just immersed. Mercury was found to rise to a height x as shown. The pressure at A is (Atmospheric pressure is l length of mercury): (Neglecting surface tension)

TestHub · Accepted Answer

The mercury level inside the tube is at depth $(l - x)$ below the free surface. The trapped air has the pressure of mercury at this level:
$P_{A} = P_{0} + ρ_{m} g (l - x)$
Atmospheric pressure:
$P_{0} = ρ_{m} g l$
$P_{A} = ρ_{m} g l + ρ_{m} g (l - x)$
$P_{A} = (2 l - x) ρ_{m} g$

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