A scuba diver is exploring a freshwater lake at a depth of 10 m. What is the ratio of the absolute pressure to the gauge pressure experienced by the diver at this depth? (Take the density of water as 1000 kg m ⁻³ , atmospheric pressure as 1 10^5 Pa, and g = 10 m/s ^2 )

Step-by-step solution

The gauge pressure at a depth h is given by P_ gauge = g h . Given: h = 10 m = 1000 kg m ⁻³ g = 10 m/s ^2 Substituting the values: P_ gauge = 1000 10 10 = 1 10^5 Pa The absolute pressure is the sum of atmospheric pressure and gauge pressure: P_ abs = P_ atm + P_ gauge Given P_ atm = 1 10^5 Pa: P_ abs = 1 10^5 + 1 10^5 = 2 10^5 Pa The required ratio is: P_ abs P_ gauge = 2 10^5 1 10^5 = 2 1 The ratio is 2:1 . Answer: 2:1