Question

The force acting on a window of area $50cm$×$50cm$ of a submarine at a depth of $2000m$ in an ocean, the interior of which is maintained at sea level atmospheric pressure is (density of seawater = ${10^3}kg/{m^3}$ , g = $10m{s^{ - 2}}$ )
A) $5 \times {10^5}N$
 B) $25 \times {10^5}N$
 C) $5 \times {10^6}N$
 D) $25 \times {10^6}N$

Answer 1

Hint: Calculate the net pressure on the window by subtracting pressure on different sides of the window from each other. Take the absolute value of the answer afterwards. Then use the force formula to calculate net force acting on the window which will be the final answer.

Formula Used: In an open container filled with liquid, the net pressure on the walls = $P$ = ${P_0} + \rho g{h_{}}$
$Force = {\text{Pressure}} \times {\text{Area}}$

Complete step by step answer:
Consider the sea as an open container and the wall of submarine will be equivalent to the walls of the container. Therefore, net pressure exerted on the walls from the outside of the submarine will be equal to ${P_0} + \rho g{h_{}}$. Where ${P_0}$ is the sea level atmospheric pressure and $\rho gh$ is the pressure exerted by just the liquid on the walls of submarine, where, $\rho $ is the density of water, and $h$ is the depth of submarine in the ocean.
On the inside, it is given that sea level atmospheric pressure is maintained. Therefore, pressure on the inside = ${P_0}$ .
Now, on subtracting the equations as mentioned above we get,
Net Pressure $(P)= {P_0} + \rho g{h_{}}$−${P_0}$ which gives $P= \rho gh$.
Now, we are given that $\rho = {10^3}kg/{m^3}$ , $g= 10m{s^{ - 2}}$ , $h= 2000m$.
Therefore, $P$= ${10^3} \times 10 \times 2000=2 \times {10^7}Kg{m^{ - 1}}{s^{ - 2}}$
Now we multiply this with the area of the window to get the final answer.
Therefore, net force acting on the window = $2 \times {10^7}Kg{m^{ - 1}}{s^{ - 2}}$ × \[0.5 \times 0.5{m^2}\]
$ \Rightarrow F= 5 \times {10^6}N$
The correct answer is (C) $5 \times {10^6}N$

Note: Don’t forget to convert given values to SI units. In an open container, to calculate the net pressure on the walls, the sea level atmospheric pressure is also added to the pressure exerted by the liquid on the walls. Take the absolute value of pressure obtained by the difference whenever required.