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# Question 44

A simple U tube contains mercury to the same level in both of its arms. If water is poured to a height of 13.6cm in one arm, how much will be the rise in mercury level in the other arm?

Given: density of mercury = 13.6\times10^3\mathrm{kg}\mathrm{m}^3 and density of water = 10^3\mathrm{kg}\mathrm{m}^{-3}

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Rise of water on the other side of the u-tube when water is added from one end depends on the density of water and mercury.

Given: Water poured to the height 13.6cm or 0.136m in one arm.

To find the rise at the other end of the u-tube:

Since it is a u-tube, pressure on both the arms is the same, hence:

The difference in pressure in the water column = difference in pressure in the mercury column

\begin{array}{l} h_{x} \rho_{w} g=h_{m} \rho_{m} g \\ \mathrm{h}_{\mathrm{m}} =\mathrm{h}_{\mathrm{w}} \rho_{\mathrm{w}} / \mathrm{p}_{\mathrm{m}} \\ =13.6 \mathrm{x} 10^{3} / 13.6 \times 10^{3} \\ =1 \mathrm{cm} \end{array}

∴ The other end of the u-tube will see a rise of 1cm in the mercury level.

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