Aresearch submarine has a 10-cm-diameter window that is 8.4 cm thick. the manufacturer says the window can withstand forces up to 1.2×106 n . what is the submarine's maximum safe depth in salt water?
the pressure inside the submarine is maintained at 1.0 atm .
express your answer using two significant figures.

15 km

Explanation:

The maximum pressure that the submarine can withheld would be equal to the maximum pressure that the window can withstand.

The maximum pressure that window can sustain is given by:

Force = 1.2×10⁶ N

Area of the window =

∵radius = (0.1 m)/2 = 0.05 m

⇒P = 1.2×10⁶ N ÷ 7.85 ×10⁻³ m² = 1.52 ×10⁸ N/m²

The pressure of the salt water at depth h is given by

P = ρ g h

where, ρ = 1027 kg/m³ is the density of the salt water, g is the acceleration due to gravity and h is the depth.

⇒1.52×10⁸ Pa =  (1027 kg/m³)(9.8 m/s²)(h)

⇒ h ≈ 15 km

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