An empty glass jar is submerged in tank of water with open mouth of the jar downwards, so that air inside the jar is trapped and cannot get out. As the jar is pushed down slowly, the magnitude of net buoyant force on the system of volume of gas trapped in the jar and the jar

Diagram shows a jar filled with two non mixing liquids $1$ and $2$ having densities ${\rho _1}$ and  ${\rho _2}$  respectively. A solid ball, made of a material of density  ${\rho _3}$ , is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for ${\rho _1}$ ,  ${\rho _2}$ and ${\rho _3}$  ?

Acork of density $0.5\ gcm^{-3}$ floats on a calm swimming pool. The fraction of the cork’s volume which is under water is …….. $\%$

A cylindrical vessel filled with water upto height of $H$ stands on a horizontal plane. The side wall of the vessel has a plugged circular hole touching the bottom. The coefficient of friction between the bottom of vessel and plane is $\mu$ and total mass of water plus vessel is $M$. What should be minimum diameter of hole so that the vessel begins to move on the floor if plug is removed (here density of water is $\rho$ )

A body of density $\rho'$  is dropped from rest at a height $h$ into a lake of density $\rho$ , where $\rho > \rho '$ . Neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface.