Question

The approximate height of mercury which exerts the same pressure at its base as 20 cm of water column is:

[Take : ${\rho }_w=1g/cc\text{and}{\rho }_{Hg}=13.6g/cc].$

• A. 3 cm
• B. 1.47 cm
• C. 148 cm
• D. 13.6 cm

Answer 1

Answer: (B)

1.47 cm

Pressure exerted by mercury column,

$P_m=h_m{d}_{m}g$

Pressure exerted by water column,

$P_w=h_w{d}_{w}g$

But,

$P_m=P_w$

$h_m{d}_m=h_w{d}_w$

$h_m=\frac{h_w{d}_w}{d_m}$

$=\frac{(20\times {10}^{-2})m\left(1\frac{g}{cc}\right)}{13.6\frac{g}{cc}}$

$=0.01471m$

Height of $Hg$ column $=1.47cm$