Question 188: Properties of Matter

Question

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $${d_1}$$ and $${d_2}$$ are filled in the tube. Each liquid subtends $${90^ \circ }$$ angle at center. Radius joining their interface makes an angle $$\alpha $$ with vertical. Radio $${{{d_1}} \over {{d_2}}}$$ is :

Accepted Answer

Pressure at interface A must be same from both the sides to be in equilibrium.
$$	herefore$$ $$\left( {R\cos \alpha  + R\sin \alpha } ight){d_2}g = \left( {R\cos \alpha  - R\sin \alpha } ight){d_1}g$$
$$ \Rightarrow {{{d_1}} \over {{d_2}}} = {{\cos \alpha  + \sin \alpha } \over {\cos \alpha  - \sin \alpha }} = {{1 + 	an \alpha } \over {1 - 	an \alpha }}$$

Answer

$${{1 + \sin \,\alpha } \over {1 - \sin \,\alpha }}$$

Answer

$${{1 + \cos \,\alpha } \over {1 - \cos \,\alpha }}$$

Answer

$${{1 + 	an \,\alpha } \over {1 - 	an \,\alpha }}$$

Answer

$${{1 + \sin \,\alpha } \over {1 - \cos \,\alpha }}$$

Properties of Matter

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities ${d_1} and {d_2} are filled in the tube. Each liquid subtends {90^ \circ } angle at center. Radius joining their interface makes an angle \alpha with vertical. Radio {{{d_1}} \over {{d_2}}}$ is :

Choose the correct answer: