An open container full of water is moved vertically downward with a uniform linear acceleration a. Compared with the static (at rest) condition, the pressure at the container's bottom will be:

Introduction / Context:
Accelerating containers create an “apparent gravity” that modifies hydrostatic pressure distributions. This is important for sloshing analysis, accelerometer calibration with liquids, and spacecraft fluid handling (where effective gravity can be reduced or reversed).

Given Data / Assumptions:

• Vertical, uniform downward acceleration a.
• Open container of water (free surface exposed to atmosphere).
• No wave motion; quasi-static distribution during uniform acceleration.

Concept / Approach:

In an accelerating frame moving downward at acceleration a, the apparent gravity is g_eff = g − a (downward). Hydrostatic pressure varies as p = p_atm + ρ g_eff h. When 0 < a < g, g_eff is reduced, decreasing pressure at depth relative to the static case. If a → g, g_eff → 0 and the fluid becomes effectively weightless; pressure becomes nearly uniform at p_atm.

Step-by-Step Solution:

Verification / Alternative check:

Limit checks: a = 0 gives static pressure. a = g makes g_eff = 0 so p is nearly atmospheric throughout. These checks confirm the trend of decreasing pressure with increasing downward acceleration.

Why Other Options Are Wrong:

(a) contradicts the reduction in g_eff. (b) would only be true for a = 0. (d) is impossible unless in a perfect vacuum and even then p = p_atm at the free surface. (e) is incorrect; pressure depends explicitly on acceleration through g_eff.

Common Pitfalls:

Confusing downward acceleration with deceleration; also forgetting that hydrostatic pressure depends on effective body force, not merely depth.

Final Answer:

Less than static pressure