Hydrostatic Pressure Increases Linearly with Depth

Steps:

• Total pressure at depth h is P_atm + ρgh, where ρ is water density, g is gravity.
• At depth d: P + ρgd = 2P, so ρgd = P.
• For total pressure 4P: P + ρgh = 4P, so ρgh = 3P.
• Substitute ρgd = P to get h = 3d.

Why C is correct:

• Hydrostatic pressure ρgh is directly proportional to depth h; tripling hydrostatic pressure from P to 3P requires tripling depth to 3d.

Why the others are wrong:

• A: At 1.5d, hydrostatic pressure is 1.5P, total 2.5P (too low).
• B: At 2d, hydrostatic pressure is 2P, total 3P (too low).
• D: At 4d, hydrostatic pressure is 4P, total 5P (too high).

Final answer: C