Question 15 - 9702/12/M/J/22

Hydrostatic pressure balance in U-tube

Steps:

Identify pressures at the liquid's lowest point, where the columns connect.
On the p₁ side, pressure at bottom equals p₁ plus hydrostatic pressure from liquid height y: p₁ + ρ g y.
On the p₂ side, pressure at bottom equals p₂ plus hydrostatic pressure from liquid height x: p₂ + ρ g x.
For stationary liquid, pressures at the bottom must balance: p₁ + ρ g y = p₂ + ρ g x.

Why C is correct:

Pascal's law states that pressure in a connected fluid at the same depth is equal, so the equation equates bottom pressures.

Why the others are wrong:

Final answer: C