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# Question 42

(a) Calculate the height of a water column which will exert on its base the same pressure as the 70cm column of mercury. The density of mercury is 13.6 g cm^{-3} .

(b) Will the height of the water column in part (a) change if the cross-section of the water column is made wider?

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(a) We know that the pressure exerted by the water column, P = h ρ g

The density of water = 1

As the pressure of water and mercury is the same,

\begin{array}{l} h_{w} \rho_{w} g=h_{m} \rho_{m} g \\ h_{w} \times 1 \times g=h_{m} \rho_{m} g \\ h_{w}=h_{m} \rho_{m} \\ \quad=\frac{70}{100} \times 13.6 \end{array}

Height of the water column= 9.52m

(b) If the water column is made wider, the height of the water column will be unaffected.

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