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Grade 11IIT JEE Entrance Exam

Open glass tube is immersed in Mercury in such a way that a length of 8 cm extends about the Mercury level. The open end of the tube is then closed and raised further by 55 cm. What will be the length of a air column about Mercury in the tube? ( Atmospheric pressure = 76 cm of Hg)

Laltesh Singh

8 Years agoGrade 11

1 Answer

Arun

6 Years ago

As We have learned

Absolute Pressure -

$P= P_{0}+\rho\: gh$

- wherein

$P\rightarrow hydrostatics \: Pressure$

$P_{0}\rightarrow atmospheric \: Pressure$

For air trapped in tube T = constant

$\Rightarrow P_1 V_1 = P_2V_2 \Rightarrow P_1 = P_{atm}= \rho g(76) \\V_1 = A \pi 8 cm$

$P_2 = P_a - \rho g(54- x )= \rho g (76-54+x )\\P_2 = \rho g (22+x )\\V_2 = A \cdot x \\\Rightarrow \rho g(76 )\times (8A )= \rho g(22+x )(Ax )\\\Rightarrow x^2 +22x - 76 \times 8 = 0 \\\Rightarrow x = 16 cm$

Hope it helps

Thanks and regards

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