Question: A barometer is constructed using a liquid (density $=760 \mathrm{~kg} / \mathrm{m}^3$ ). What would be the height of the liquid column, when a mercury barometer reads $76 \mathrm{~cm}$ ?
(Density of mercury $=13600 \mathrm{~kg} / \mathrm{m}^3$ )
A) $1.36 \mathrm{~m}$
B) $13.6 \mathrm{~m}$
C) $136 \mathrm{~m}$
D) $0.76 \mathrm{~m}$
Answer: $13.6 \mathrm{~m}$
Sol:
Density of liquid, $\rho_l=760 \mathrm{~kg} / \mathrm{m}^3$ Density of mercury, $\rho_m=13600 \mathrm{~kg} / \mathrm{m}^3$ Height of liquid column in mercury barometer $$ h_m=76 \mathrm{~cm}=0.76 \mathrm{~m} $$
If height of liquid in liquid column be, then $$ \begin{aligned} p_{\text {liquid }} & =p_{\text {mercury }} \ \Rightarrow \quad h_l \rho_l g & =h_m \rho_m g \ \Rightarrow \quad h_l & =\frac{h_m \rho_m}{\rho_l}=\frac{0.76 \times 13600}{760} \ & =13.6 \mathrm{~m} \end{aligned} $$
