A submarine is designed to withstand an absolute pressure of $100$ atm. How deep can it go below the water surface ?
(Consider the density of water $= 1000$ kg m $^{-3}$ , $1$ atm $= 1 \times 10^{5}$ Pa and gravitational acceleration $g = 10$ m/s $^2$ )

Question

A submarine is designed to withstand an absolute pressure of

100

atm. How deep can it go below the water surface ?
(Consider the density of water

= 1000

kg m

^{-3}

,

1

atm

= 1 \times 10^{5}

Pa and gravitational acceleration

g = 10

m/s

^2

)

Quantrex Academy · Accepted Answer

Correct answer: A. 990 m

The absolute pressure at a depth h below the water surface is given by P = P_0 + g h , where P_0 is the atmospheric pressure. Given: P = 100 atm = 100 × 10^5 Pa P_0 = 1 atm = 1 × 10^5 Pa = 1000 kg m ^ -3 g = 10 m/s ^2 Substituting the values into the equation: 100 × 10^5 = 1 × 10^5 + 1000 × 10 × h 99 × 10^5 = 10^4 × h h = (99 × 10^5)/(10^4) h = 990 m Answer: 990 m

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