If $n$ drops of a liquid, each with surface energy $E$, join to form a single drop, then

A cube of side $a$ and mass $m$ just floats on the surface of water as shown in the figure. The surface tension and density of water are $T$ and ${\rho }_w$, respectively. If angle of contact between cube and water surface is zero, find the distance $h$ (in metres) between the lower face of cube and surface of the water.
(Take $m=1 \mathrm{kg}, g=10 \mathrm{m}{ \mathrm{s}}^{-2}, aT=\frac{10}{4}$ unit and ${\rho }_w{a}^{2}g=10$ unit )

A thin plate $AB$ of large area $A$ is placed symmetrically in a small gap of height $h$ filled with water of viscosity ${\eta }_0$ and the plate has a constant velocity $v$ by applying a force $F$ as shown in the figure. If the gap is filled with some other liquid of viscosity $0.75 {\eta }_0$, at what minimum distance (in $cm$ ) from minimum distance (in $\mathrm{cm}$ ) from top wall should the plate be placed in the gap, so that the plate can again be pulled at the same constant velocity $V$, by applying the same force $F ?$ (Take $h=20 \mathrm{cm}$ )