The relative humidity on a day,when the partial pressure of water vapour is $0.012 \times 10^5 \, Pa$ at $12^{\circ}C$,is ......... $\%$. (Take the vapour pressure of water at this temperature as $0.016 \times 10^5 \, Pa$.)

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 $g = 10 \ m/s^2$):

$A$ drop of water detaches itself from the exit of a tap when $(\sigma=$ surface tension of water, $\rho=$ density of water, $R=$ radius of the tap exit, $r=$ radius of the drop $)$

Why is skating possible on ice?

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)

Fill in the blanks:
$(i)$ The lines of flow and streamlines coincide with each other in ...... flow.
$(ii)$ The formula for the horizontal velocity of water coming from a hole at the bottom at a height $h$ from the surface of the water is ......
$(iii)$ $1 \ Pa = ...... \ dyne/cm^{2}$
$(iv)$ The relative velocity of two parallel layers of water is $6 \ cm/s$. If the perpendicular distance between the two layers is $0.1 \ mm$,then the velocity gradient will be ......