A cylinder of mass $m$ and material density $\rho$ hanging from a string is lowered into a vessel of cross-sectional area $A$ containing a liquid of density $\sigma(<\rho)$ until it is fully immersed. The increase in pressure at the bottom of the vessel is

The angle of contact is $120^{\circ}$ when a cylindrical rod is vertically placed in a liquid. If the same rod is placed horizontally in the liquid, then the angle of contact is

In a well the pressure at a point 10 m below the surface of water is $\left(g=10 \mathrm{~ms}^{-2}\right)$

A liquid is taken in a long vertical cylindrical vessel and the cylinder is rotated about its vertical axis as shown in figure. During rotation, the liquid rises along its sides. If the radius of vessel is 0.05 m and speed of rotation is $10 \mathrm{rads}^{-1}$, then the height difference between the liquid at the centre of the vessel and its sides is $\left(g=10 \mathrm{~ms}^{-2}\right)$