A submarine has a window of area $30 \times 30 \,cm ^2$ on its ceiling and is at a depth of $100 \,m$ below sea level in a sea. If the pressure inside the submarine is maintained at the sea-level atmosphere pressure, then the force acting on the window is ............. $N$ (consider density of sea water $=1.03 \times 10^3 \,kg / m ^3$, acceleration due to gravity $=10 \,m / s ^2$ )
KVPY 2020, Medium
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(a)
Given, area, $A=30 \times 30 \,cm ^2$
$=900 \times 10^{-4} \,m ^2$
Depth, $h=100 \,m$
Density of water, $\rho=1.03 \times 10^3 \,kg / m ^3$
Acceleration due to gravity, $g=10 \,m / s ^2$ As we know that,
pressure, $p=\frac{\text { Force }(F)}{\text { Area }(A)}$
or $F=p \times A=\rho g h A$
$=1.03 \times 10^3 \times 10 \times 100 \times 900 \times 10^{-4}$
$=9.27 \times 10^4 \simeq 9.3 \times 10^4$
$=0.93 \times 10^5 \,N$
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