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  • Help me answer: An open glass tube is immersed in mercury in such a way that a length of 8 cm 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 46 cm. What will be l

 An open glass tube is immersed in mercury in such a way that a length of 8 cm 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 46 cm. What will be length of the air column above mercury in the tube now ?

(Atmospheric pressure =76 cm of Hg)

  • Option 1)

    16 cm

  • Option 2)

    22 cm

  • Option 3)

    38 cm

  • Option 4)

    6 cm

 

Answers (1)

best_answer

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

 

 

 

 

 


Option 1)

16 cm

Option 2)

22 cm

Option 3)

38 cm

Option 4)

6 cm

Posted by

SudhirSol

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