A vessel wih square cross-section and height of 6 m is vertically partitioned. A small window of 100 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 w

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Solution

Q.
A vessel wih square cross-section and height of 6 m is vertically partitioned. A small window of 100 ${cm}^{2}$ 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 $1.5 \times 10^{3} kg / m^{3}$ . What force one needs to apply on the hinged door so that it does not get opened (Acceleration due to gravity = 10 $m / s^{2}$ ) [2025]

Ans.
(150)

in equilibrium

$F_{ext} + F_{w} = F_{l}$

$\Rightarrow F_{ext} = F_{l} - F_{w}$

$= (P_{0} + ρ_{l} g h) A - (P_{0} + ρ_{w} g h) A$

$= (ρ_{l} - ρ_{w}) g h A$

$= (1500 - 1000) \times 10 \times 3 \times (100 \times 10^{- 4})$

= 150 N.

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