Hydrostatic pressure at base equals ρgh regardless of vessel shape

Steps:

• Pressure on base is ρgh, where h is liquid depth (same for both vessels).
• For vessel P, ρ_P = 2ρ_Q, so P_P = 2ρ_Q g h.
• For vessel Q, P_Q = ρ_Q g h.
• Ratio P_Q / P_P = (ρ_Q g h) / (2ρ_Q g h) = 1/2.

Why A is correct:

• Hydrostatic pressure formula ρgh depends only on density and vertical depth, not vessel shape or inclination.

Why the others are wrong:

• B and C: 1/√2 ignores density difference; 45° angle irrelevant to base pressure.
• D: 1 assumes equal densities, but ρ_P is twice ρ_Q.

Final answer: A