Discussion Forum



1)

 There is a circular tube in a vertical plane. Two liquids that do not mix and of densities  d1 and d2  are filled in the tube. Each liquid subtends  900 C  angle at centre. Radius joining  their interface  makes an angle   $\alpha$  with vertical, Ration d1/d2  is 

1732021153_C1.PNG


A) $\frac{1+\sin \alpha}{1-\sin \alpha}$

B) $\frac{1+\cos \alpha}{1-\cos \alpha}$

C) $\frac{1+\tan \alpha}{1-\tan \alpha}$

D) $\frac{1+\sin \alpha}{1-\cos \alpha}$

Answer:

Option C

Explanation:

 Equating  pressure at A, we get

   $R\sin\alpha d_{2}+R\cos\alpha d_{2}+R(1-\cos \alpha)d_{1}$

   =   $R(1-\sin\alpha)d_{1}$

1532021375_m11.JPG

$(\sin \alpha+\cos\alpha)d_{2}=d_{1}(\cos\alpha-\sin \alpha)$

  $\frac{d_{2}}{d_{1}}=\frac{1+\tan \alpha}{1-\tan \alpha}$