Question

At a depth of $1000\text{m}$ in an ocean, what is the gauge pressure, when density of sea water is given as $1.03\times {10}^3{\text{kg/m}}^3$? (Take $g=10{\text{m/s}}^2$)

• A. $1.04\times {10}^7\text{Pa}$
• B. $1.03\times {10}^7\text{Pa}$
• C. $1.02\times {10}^7\text{Pa}$
• D. $1\times {10}^7\text{Pa}$

Answer 1

The correct option is B $1.03\times {10}^7\text{Pa}$

Given height $\left(h\right)=1000\text{m}$
Density of sea water, $\rho =1030{\text{kg/m}}^3$
Gauge pressure at a depth of $h,$ $\left(P_g\right)=\rho gh$
$\Rightarrow P_g=\rho gh=1030\times 10\times 1000\text{Pa}$
$\Rightarrow P_g=103\times {10}^5\text{Pa}$
$\Rightarrow P_g=1.03\times {10}^7\text{Pa}$