A vessel with square cross-section and height of 6 m is vertically… | JEE Main 2025 (2 Apr, Shift 1)

Q6JEE Main 2025 · 2 APR · SHIFT 1Medium

Pressure in a Fluid

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of $100\text{ cm}^{2}$ with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density $1.5 \times 10^{3}\text{ kg/m}^{3}$ . What force one needs to apply on the hinged door so that it does not get opened? (Acceleration due to gravity $= 10\text{ m/s}^{2}$ )

Numerical answer type. Work it out, then open the answer.

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Answer: 150

Both sides are full (6 m), so the door at depth 3 m feels pressure from each liquid.
Net pressure: $\Delta P = (\rho_2 - \rho_1) g h = (1500 - 1000)\times10\times3 = 1.5\times10^4\text{ Pa}$ .
$F = \Delta P\, A = 1.5\times10^4\times100\times10^{-4} = 150\text{ N}$
So the force needed is 150 N.

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