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An inverted test tube filled with a liquid of density rho accelerates vertically downward with acceleration a = 2g. Taking point Q at a depth h below the reference point P (P₀ being the pressure at P), find P_Q - P₀.
- (A) -rho g h / 3
- (B) 2 rho g h / 3
- (C) rho g h / 3
- (D) -rho g h
Correct answer: (D) -rho g h
Solution
For a fluid accelerating downward with acceleration a, the effective gravitational field is g_eff = g - a (downward positive). With a = 2g, g_eff = -g. So P_Q - P₀ = rho * g_eff * h = -rho g h; pressure decreases with depth in this frame.
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