Question

Height of mercury in a barometer is $760\text{mm}$ at any location. If mercury is replaced by water then height of water will be :

• A. $6.883\text{m}$
• B. $10.336\text{m}$
• C. $5.251\text{m}$
• D. $8.521\text{m}$

Answer 1

The correct option is B $10.336\text{m}$

We know that, atmospheric pressure in barometer is given by $P_o=\rho gh$ where $\rho$ is density of fluid.


For mercury, $P_o=13.6\times {10}^3\times 10\times 0.76$ ..........(1)
$[\rho =13.6\times {10}^3{\text{kg/m}}^3,h=0.76\text{m},$$]$
For water, $P_o=1\times {10}^3\times 10\times h$ ....(2)
$[\rho =1\times {10}^3{\text{kg/m}}^3]$

From equation (1) and (2),
$13.6\times {10}^3\times 10\times 0.76=1\times {10}^3\times 10\times h$
$\Rightarrow h=10.336m$
Height of water will be, $h=10.336\text{m}$