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There is a circular tube in a vertical plane.Two liquids which do not mix and of densities d1 and d2 are filled in the tube.Each liquid subtends 900 angle at centre.Radius joining their interface makes an angle \alpha with vertical. Ratio \frac{d_{1}}{d_{2}}  is :

  • Option 1)

    \frac{1+\sin \alpha }{1-\sin \alpha }

  • Option 2)

    \frac{1+\cos \alpha }{1-\cos \alpha }

  • Option 3)

    \frac{1+\tan \alpha }{1-\tan \alpha }

  • Option 4)

    \frac{1+\sin \alpha }{1-\cos \alpha }

 

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S SudhirSol
Answered Jun 06, 2018

as we have learn 

 

 

 

pressure at interface  a must be the same from both side in equilibrium.

 

(Rcos\alpha +Rsin\alpha)d_2g= (Rcos\alpha -Rsin\alpha)d_1g\\\frac{d_1}{d_2}=\frac{cos\alpha +sin\alpha}{cos\alpha -sin\alpha}=\frac{1+tan\alpha}{1-tan\alpha}


Option 1)

\frac{1+\sin \alpha }{1-\sin \alpha }

Option 2)

\frac{1+\cos \alpha }{1-\cos \alpha }

Option 3)

\frac{1+\tan \alpha }{1-\tan \alpha }

Option 4)

\frac{1+\sin \alpha }{1-\cos \alpha }

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