$A$ liquid is kept in a cylindrical vessel. When the vessel is rotated about its axis,the liquid rises at its sides. If the radius of the vessel is $0.05\, m$ and the speed of rotation is $2$ revolutions per second,the difference in the heights of the liquid at the centre and at the sides of the vessel will be ...... $cm$. (Take $g = 10\, ms^{-2}$ and $\pi^2 = 10$)

Liquid and gas both are fluids; distinguish between them and state which property is common between them.

Two solid spheres $A$ and $B$ of equal volumes but of different densities $d_A$ and $d_B$ are connected by a string. They are fully immersed in a fluid of density $d_F$. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if:
$(A)$ $d_A < d_F$
$(B)$ $d_B > d_F$
$(C)$ $d_A + d_B = 2d_F$
$(D)$ $d_A > d_F$

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

$A$ liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is $r$ and the angular velocity of rotation is $\omega$,then the difference in the heights of the liquid at the centre of the vessel and the edge is

State whether the following statements are True or False:
$(i)$ In incompressible flow,the density of a fluid changes with time and position.
$(ii)$ Non-viscous flow can be a streamline flow.
$(iii)$ In a steady flow,the velocity of the fluid at each point remains identical with time.