Question

The height of mercury which exerts the same pressure as $20\mathrm{cm}$ of water column, is equal to

• A. $1.48\mathrm{cm}$
• B. $14.8\mathrm{cm}$
• C. $148\mathrm{cm}$
• D. None of these

Answer 1

The correct option is A

$1.48\mathrm{cm}$

Step 1: Assuming Values

Let ${\rho }_{\mathrm{w}}$​ be the density of water

${\rho }_{\mathrm{m}}$ be the density of mercury

${\mathrm{h}}_{\mathrm{w}}$ be the height of water

${\mathrm{h}}_{\mathrm{m}}$ be the height of the mercury

$\mathrm{g}$ be the acceleration due to gravity

${\mathrm{P}}_{\mathrm{w}}$ be the pressure exerted by the water column

$P_m\mathrm{be}\mathrm{pressure}\mathrm{exerted}\mathrm{by}\mathrm{mercury}\mathrm{column}$

Step 2:Finding pressure exerted by the mercury column

$$\begin{gathered} P_w={\rho }_{w}g{h}_w----1 \\ {\rho }_w=1g/cc \\ {h}_w=20cm \\ \text{so From 1} \\ {P}_w=1\times 10\times 20----2 \end{gathered}$$

Step 3: Finding pressure exerted by the mercury column

$$\begin{gathered} P_m={\rho }_{m}g{h}_w----3 \\ {\rho }_m=13.6g/cc \\ {h}_m=20cm \\ \text{so From 3} \\ {P}_m=13.6\times 10\times h_m----4 \\ As{P}_m=P_w \end{gathered}$$

Step 4: Finding the height the of mercury

$$\begin{gathered} \mathrm{From}3a\mathrm{nd}4 \\ 1\times 10\times 20=13.6\times 10\times {\mathrm{h}}_{\mathrm{m}} \\ {\mathrm{h}}_{\mathrm{m}}=\frac{20}{13.6} \\ {\mathrm{h}}_{\mathrm{m}}=1.48c\mathrm{m} \end{gathered}$$

Hence, The height of mercury which exerts the same pressure as $20\mathrm{cm}$ of water column is equal to 1.48 cm.