The force acting on a window of are 50`xx`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)` )

Options

A. `10 ^(6) N `
B. `5 xx 10 ^(5) N `
C. `25 xx N 10 ^(6) N`
D. `5 xx 10 ^(6) N `

Answer

D

Explanation

The pressure outside the submarine is
`P = P _(a)+ rho gh`
Pressure inside the submarine is `P _(a).`
Net pressure acting on the windown is
` P _(g) =P - P _(a) = rho g h = 10 ^(-3) kgm ^(-3)xx 10 ms ^(-2) xx 2000m`
`= 2 xx 10 ^(7) Pa`
Are of window is
`A = 50 cm xx 50 cm = 2500 xx 10 ^(-4) m ^(2)`
Force on the window is
`F = P _(g) A = 2 xx 10 ^(7) Pa xx 2500 xx 10^(-4) m ^(2) = 5 xx 10 ^(6)N`