Question

A cylindrical vessel of a very large cross-sectional area is containing two immiscible liquids of density ${\rho }_1=600kg/m^3$ and ${\rho }_2=1200kg/m^3$ as shown in the figure.A small hole having cross-section area $5c{m}^2$ is made In right side vertical wall as shown. Take atmospheric pressure as ${\rho }_0={10}^{5}N/M^2$ $g=10m/s^2$. From this situation, mark out the correct statement(s). (Take cross-section area of the cylindrical vessel as $1000c{m}^2$. Neglect the mass of the vessel.)

• A. 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
• B. If the surface on which the vessel smooth, then a rightward force of maintain its static equilibrium
• C. If the surface on which the vessel is placed is rough $(\mu =0.04)$, then the minimum force (horizontal) needed to be applied on the vessel to maintain its static equilibrium is zero
• D. If the surface on which the vessel is placed is rough $(=0.04)$, then the maximum force (horizontal) needed to be applied on the vessel to maintain its static equilibrium is $19.8N$

Answer 1

Answer: (A), (C), (D)

The correct options are
A 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
C If the surface on which the vessel is placed is rough $(\mu =0.04)$, then the minimum force (horizontal) needed to be applied on the vessel to maintain its static equilibrium is zero
D If the surface on which the vessel is placed is rough $(=0.04)$, then the maximum force (horizontal) needed to be applied on the vessel to maintain its static equilibrium is $19.8N$