A cylinder vessel of cross-sectional area $A = 40 c m^{2}$ is containing two immiscible liquids of density $ρ_{1} = 600 k g / m^{3}$ and $ρ_{2} = 1200 k g / m^{3}$ as shown in the figure. A small hole having cross-sectional area $a = 5 c m^{2}$ is made in right side vertical wall as shown. Take atmospheric pressure as $p_{0} = 10^{5} N / m^{2}, g = 10 m / s^{2}$ . For this situation, mark out the correct statement(s). (Mass of vessel is negligible. Consider a<<A).

(In the Diagram, hole has to be shown as horizontal).

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If the surface on which the vessel is placed is rough $(μ = 0.04)$ , then the maximum force (horizontal) needed to be applied on the vessel to maintain its static equilibrium is 19.67N.

If the surface on which the vessel is placed is rough $(μ = 0.04)$ , then the minimum force (horizontal) needed to be applied on the vessel to maintain its static equilibrium is zero.

If the surface on which the vessel is placed is smooth, then a rightward force of magnitude 3N is to be applied on the vessel to maintain its static equilibrium.

If the surface on which the vessel is placed is smooth, then no force is needed to maintain its static equilibrium.

answer is A, C, D.

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