$A$ ball is made of a material of density $\rho$ where $\rho_{\text{oil}} < \rho < \rho_{\text{water}}$,with $\rho_{\text{oil}}$ and $\rho_{\text{water}}$ representing the densities of oil and water,respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water,which of the following pictures represents its equilibrium position?

The vessel shown in the figure has two sections. The lower part is a rectangular vessel with area of cross-section $A$ and height $h$. The upper part is a conical vessel of height $h$ with base area $A$ and top area $a$,and the walls of the vessel are inclined at an angle $30^o$ with the vertical. $A$ liquid of density $\rho$ fills both the sections up to a height $2h$. Neglecting atmospheric pressure:

$A$ small air bubble is at the inner surface of the bottom of a beaker filled with cold water. Now,the water in the beaker is heated. The size of the bubble increases. The reason for this may be:

$A$ razor-blade floats on the surface of water contained in a glass. When the glass is gently shaken,the razor-blade sinks. Mark the incorrect statement.

$A$ drum of radius $R$ full of liquid of density $d$ is rotated at angular velocity $\omega \ rad/s$. The increase in pressure at the centre of the drum will be

The cross-sectional area of a horizontal tube increases along its length linearly as we move in the direction of flow. The variation of pressure, as we move along its length in the direction of flow ($x$-direction), is best depicted by which of the following graphs?