As shown in the figure, a liquid is at the same level in both arms of a $U$-tube of uniform cross-section when at rest. If the $U$-tube moves with an acceleration '$f$' towards the right, the difference between the liquid heights in the two arms of the $U$-tube will be (acceleration due to gravity $= g$):

Two cylindrical vessels of equal cross-sectional area of $2 \ m^2$ contain water up to heights of $10 \ m$ and $6 \ m$,respectively. If the vessels are connected at their bottom,then the work done by the force of gravity is (Density of water is $10^3 \ kg/m^3$ and $g = 10 \ m/s^2$):

$STATEMENT-1$: The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up,but tends to narrow down when held vertically down.
$STATEMENT-2$: In any steady flow of an incompressible fluid,the volume flow rate of the fluid remains constant.

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.

Fill in the blanks using the word$(s)$ from the list appended with each statement:
$(a)$ Surface tension of liquids generally . . . with temperatures (increases / decreases)
$(b)$ Viscosity of gases . . . with temperature,whereas viscosity of liquids . . . with temperature (increases / decreases)
$(c)$ For solids with elastic modulus of rigidity,the shearing force is proportional to . . .,while for fluids it is proportional to . . . (shear strain / rate of shear strain)
$(d)$ For a fluid in a steady flow,the increase in flow speed at a constriction follows (conservation of mass / Bernoulli's principle)
$(e)$ For the model of a plane in a wind tunnel,turbulence occurs at a . . . speed for turbulence for an actual plane (greater / smaller)

$A$ 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?