Figure shows an open tube which contains some water and a less dense liquid poured into the right hand side. If the density of the unknown liquid is `rho_(x)`, show that `rho_(x)=(rho_(w)h_(w))/(h_(x))`
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Consider levels `D` and `A` in the tube. If the pressures at `D` and `A` are not equal, then water would flow. Since water does no flow, the pressures at `D` and `A` are equal. `P_(A)=P_(atm)=rho_(w)gh_(w)` and `P_(D)=P_(atm)+rho_(x)gh_(x)` Equating `P_(A)` and `P_(D)` we obtain `rho_(x)=(rho_(w)h_(w))/(h_(x))`
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