Question

The height of mercury which exerts the same pressure as 20 cm of a water column, is equal to

• A. $1.48$ cm
• B. $14.8$ cm
• C. $148$ cm
• D. none of these

Answer 1

The correct option is A $1.48$ cm

Let ${\rho }_w$ be density of water

${\rho }_m$ be density of mercury

$h_w$ be height of water

$h_m$ be height of mercury

$g$ be acceleration due to gravity

$P_w$ be pressure exerted by water column

$P_m$ be pressure exerted by mercury column

Now $P_w={\rho }_{w}g{h}_w$ (1)

${\rho }_w=1g/cc$

$h_w=20cm$

So from (1)

$P_w=1\times 10\times 20$ (2)

$P_m={\rho }_{m}g{h}_m$ (3)

${\rho }_m=13.6g/cc$

From (3)

$P_m=13.6\times 10\times h_m$ (4)

As $P_w=P_m$

So from (2) and (4)

$1\times 10\times 20=13.6\times 10\times h_m$

$h_m=\frac{20}{13.6}$

$h_m=1.48cm$