question_answer 9)

A U tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10*0 cm of water in one arm and 12.5 cm of spirit in the other. What is the relative density of spirit?

Answer:

For water column in one arm of U tube, \[{{\rho }_{0}}=1\cdot 25kg{{m}^{-3}}\] For spirit column in other arm of U tube, \[{{y}_{0}}\] As the mercury columns in the two arms of U tube are in level, therefore pressure exerted by each is equal. Hence,\[{{m}^{3}}\] \[\left[ \text{Take }{{\text{y}}_{\text{0}}}\text{= 8000 m and }{{\text{ }\!\!\rho\!\!\text{ }}_{\text{He}}}=0\cdot 18kg/{{m}^{3}} \right]\] Therefore, relative density of spirit \[\text{-}\frac{\text{d }\!\!\rho\!\!\text{ }}{\text{dy}}\text{ }\!\!\alpha\!\!\text{ }\!\!\rho\!\!\text{ or }\frac{\text{d }\!\!\rho\!\!\text{ }}{\text{dy}}\text{ = - K }\!\!\rho\!\!\text{ }\]