Question

The height of mercury which exerts the same pressure as 20 cm of water column is :( Given relative density of mercury=13.56)

• A. 1.47 cm
• B. 14.8 cm
• C. 148 cm
• D. None of these

Answer 1

The correct option is A 1.47 cm

Let pressure $=P,$ density $=\rho ,$ mass $=m$

$P_{\text{mercury}}=h_m{\rho }_{m}g\to$ Pressure exerted by mercury

$P_{\text{water}}=h_w{\rho }_{w}g\to$ Pressure exerted by water

Since given $P_{\text{mercury}}$ $=P_{\text{water}}$ at $h_w=20cm$

$\Rightarrow h_m{\rho }_m=h_w{\rho }_w$ where ${\rho }_m=13.56{\rho }_w$ relative density

$\Rightarrow \frac{{\rho }_w}{{\rho }_m}=\frac{h_m}{h_w}$

$\Rightarrow \frac{1}{10.8}=\frac{h_m}{20}$

$\Rightarrow h_m=\frac{20}{10.8}=1.47cm$