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 = 103 kg m-3, g = l0 ms-2)
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a
5 × 105 N
b
25 × 105 N
c
5 × 106N
d
25 × 106N
answer is C.
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Detailed Solution
Here, h = 2000 m, ρ = 103 kg m-3, g = 10 ms-2The pressure outside the submarine is P = Pa+ρghwhere Pa is the atmospheric pressurePressure inside the submarine is Pa.Hence, net pressure acting on the window is guage pressure.Gauge pressure, Pg = P-Pa = ρgh = 103 kg m-3 × 10 ms-2× 2000 m = 2 ×107 PaArea of a window isA = 50 cm × 50 cm = 2500 × 10-4 m2Force acting on the window isF = PgA = 2×107 Pa × 2500 × 10-4 m2 = 5 × 106 N