Tag: floating bodies

Questions Related to floating bodies

The force acting on a window of area 50 cm x 50 cm of a submarine at a depth of 2000 m in an ocean, the interior of which is maintained at sea level atmospheric pressure is (Density of sea water = 10$^3$ kg m$^{-3}$,g = 10 m s$^{-2}$)

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. 5 x 10$^5$ N

  2. 25 x 10$^5$ N

  3. 5 x 10$^6$ N

  4. 25 x 10$^6$ N

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Correct Option: C
Explanation:

Here, $h = 2000 m,$

          $ \rho= 10^3\, kg\, m^{-3},$ 
          $g = 10 \,m \,s^{-2}$
The pressure outside the submarine is
$P = P _a + \rho gh$
where $P _a$ is the atmospheric pressure. Pressure inside the submarine is $P _a$.
Hence, net pressure acting on the window is gauge pressure. Gauge pressure,
 $P _g = P - P _a = \rho gh $
$= 10^3\, kg\, m^{-3} \times 10 \,m\,s^{-2} \times 2000 \,m$
$ = 2 \times 10^7 Pa$
Area of a window is $A= 50 cm\times50 cm $
                                    $= 2500 \times 10^{-4}\, m^{2}$
Force acting on the window is
$F = P _gA $
$= 2 \times 10^7 \,Pa \times 2500 \times 10^{-4} m^2 $
$= 5 \times 10^6\,N$