Question

At a depth of $2\text{km}$ in an ocean, what is force acting on a window of area $25\text{cm}\times 20\text{cm}$ of a submarine at this depth, the interior of which is kept at sea level atmospheric pressure? (The density of sea water is $1030{\text{kg m}}^{–3},g=10{\text{m/s}}^2)$

• A. $6.02\times {10}^5\text{N}$
• B. $1.02\times {10}^8\text{N}$
• C. $1.03\times {10}^6\text{N}$
• D. $2.06\times {10}^5\text{N}$

Answer 1

The correct option is C $1.03\times {10}^6\text{N}$

Pressure at depth of $2\text{km}$ is
$P=P_0+h\rho g$
Excess pressure on window $=P-P_0=h\rho g$
Force on window $=h\rho g\times A$
$=2000\times 1030\times 10\times 0.25\times 0.20$
$=1.03\times {10}^6\text{N}$