Hydrostatic pressure determines the force on the submerged plate

Steps:

• Pressure at depth h is P = ρ g h, with ρ = 930 kg/m³ and g = 9.8 m/s².
• Force on one side F = P A = ρ g h A, where A = 0.03 m² and F = 290 N.
• Rearrange for depth: h = F / (ρ g A).
• Calculate: ρ g = 930 × 9.8 = 9114; ρ g A = 9114 × 0.03 = 273.42; h = 290 / 273.42 ≈ 1.06 m (closest to 1.1 m).

Why B is correct:

• The formula F = ρ g h A directly yields h ≈ 1.06 m, matching option B per hydrostatic pressure law.

Why the others are wrong:

• A: 0.8 m gives F ≈ 219 N, underestimating the given 290 N.
• C: 1.8 m gives F ≈ 492 N, overestimating the given force.
• D: 0.7 m gives F ≈ 191 N, too low for the observed force.

Final answer: B