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Pa is the atmospheric pressure and P is the absolute pressure at a depth \(h\) in an ocean. The gauge pressure at the depth \(h\) is

  • A.\(P + P_{a}\)
  • B.\(\frac{P - P_{a}}{2}\)
  • C.\(2P - P_{a}\)
  • D.\(\frac{P + P_{a}}{2}\)
  • E.\(P - P_{a}\)

Answer: E

The gauge pressure is \(P - P_{a}\).

Absolute pressure at depth h is \(P = P_{a} + \rho gh\). Gauge pressure is the excess over atmospheric pressure, the part a pressure gauge open to the air reads.

\[ P_{gauge} = P - P_{a} = \rho gh \]

\(P + P_{a}\) double-counts the atmosphere, and the halved or doubled forms have no physical meaning here.

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