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  • A small uniform tube is bent into a circular tube of radius R and kept in the vertical plane. Equal volumes of two liquids of densities

A small uniform tube is bent into a circular tube of radius R and kept in the vertical plane. Equal volumes of two liquids of densities \rho and \sigma (\, \rho > \sigma) fill half of the tube as shown in the figure. \theta is the angle which the radius passing through the interface makes with the vertical.

Option: 1

\theta =\tan ^{-1}\left ( \frac{\rho -\sigma }{\rho +\sigma } \right )

 

 

 


Option: 2

\theta =\tan ^{-1}\left ( \frac{\sigma -\rho }{\sigma +\rho } \right )


Option: 3

\theta =\tan ^{-1}\left ( \frac{\rho }{\rho +\sigma } \right )


Option: 4

\theta =\tan ^{-1}\left ( \frac{\rho }{\rho -\sigma } \right )


Answers (1)

best_answer

 

 

 

Pressure at 'A' from both sides must balance as shown in the Figure.

i.e \sigma h_{2}g= \rho h_{1}g

\sigma \left [ \cos \theta +\sin \theta \right ]= \rho \left [ \cos \theta -\sin \theta \right ]

\tan \theta =\frac{\rho -\sigma }{\rho +\sigma }

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Gunjita

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