One end of a long iron chain of linear mass density $\lambda$ is fixed to a sphere of mass m and specific density $1/3$ while the other end is free. The sphere along with the chain is immersed in a deep lake. If specific density of iron is $7$, the height $h$ above the bed of the lake at which the sphere will float in equilibrium is (Assume that the part of the chain lying on the bottom of the lake exerts negligible force on the upper part of the chain.)

Equal volumes of a liquid are poured in the three vessels $A, B$ and $C\left(h_1<h_2<h_3\right).$ All the vessels have the same base area. Select the correct alternatives.

In this figure, an ideal liquid flows through the tube, which is of uniform cross-section. The liquid has velocities $V_A$ and $V_B$, and pressure $P_A$ and $P_B$ at points $A$ and $B$ respectively.Choose correct option.

Figure shows a container filled with a liquid of density $\rho$. Four points $A,B,C$ and $D$ lie on the vertices of a vertical square. Points $A$ and $C$ lie on a vertical line and points $B$ and $D$ lies on a horizontal line. Choose the correct statement(s) about the pressure at the four points.